tag:blogger.com,1999:blog-8303359655412909672024-03-28T19:23:34.924+05:30Knowledge SharingSaurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.comBlogger348125tag:blogger.com,1999:blog-830335965541290967.post-9327393405195754052024-03-17T10:19:00.007+05:302024-03-17T10:19:40.158+05:30Replication Errors (Publisher and Subscriber are at different version)<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: Courier New, Courier, monospace;"><span style="font-size: large;">Today I was setting up replication (Transactional and merge) From SQL server 20008R2 publisher to SQL server 2012 Subscriber and I faced a lot of issues. Some of them are<o:p></o:p></span></span></div>
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<li><i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace;">Microsoft SQL Server Management Studio is unable to access replication components because replication is not installed on this instance of SQL Server</span></i></li>
<li><span style="font-family: Courier New, Courier, monospace;">The selected Subscriber does not satisfy the minimum version compatibility level of the selected publication.</span></li>
<li><span style="font-family: Courier New, Courier, monospace;">A network-related or instance-specific error occurred while establishing connection to sqlserver. The server was not accessible, verify that the instance name is correct and that sql server is configured to allow remote connections.</span></li>
<li><i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace;">SQL Server replication requires the actual server name to make a connection to the server. Connections through a server alias, IP address, or any other alternate name are not supported. Specify the actual server</span></i></li>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><o:p></o:p></span><br />
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">Here scenarios 1 , and 2,3 have the same fix<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><b>Scenerio1</b>: <o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><i>Error:”<span style="color: #333333;"> </span>The selected Subscriber does not satisfy the minimum version compatibility level of the selected publication”</i><o:p></o:p></span><br />
<span style="font-family: Courier New, Courier, monospace; font-size: large;"><i><br /></i></span></div>
<div class="MsoNormal"><span style="font-family: Courier New, Courier, monospace; font-size: large;">The publication created successfully on SQL server 2008 R2 Server using 2008R2 SSMS<o:p></o:p></span><br />
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">RDP to SQL 2008R2 Server, While creating Subscriber on SQL Server 2012 from 2008R2 Server add subscriber using SSMS of SQL 2008R2 I got this error<o:p></o:p></span><br />
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">RDP to SQL 2008R2 Server, While creating Subscriber on SQL Server 2012 from SQL 2012 Server add subscriber using SSMS of SQL 2008R2 I got this error<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><b>Scenerio2</b>:<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><i>Error: “SSMS is unable to access replication components because replication is not installed on the instance of SQL server”</i><o:p></o:p></span><br />
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<div class="MsoNormal"><span style="font-family: Courier New, Courier, monospace; font-size: large;">The publication created successfully on SQL server 2008 R2 Server using 2008R2 SSMS<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">RDP to SQL 2012 Server, While creating a Subscriber on SQL Server 2008R2 from SQL 2012 Server add subscriber using SSMS of SQL 2012 I got this error<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><b>Scenerio</b>3: <o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">Error: <i>“A network-related or instance-specific error occurred while establishing a connection to SQL server. The server was not accessible, verify that the instance name is correct and that the SQL server is configured to allow remote connections.”</i><o:p></o:p></span><br />
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<div class="MsoNormal"><span style="font-family: Courier New, Courier, monospace; font-size: large;">The publication was created successfully on SQL server 2008 R2 Server using 2008R2 SSMS<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">RDP to SQL 2012 Server, While creating a Subscriber on SQL Server 2012 from SQL 2012 Server add subscriber using SSMS of SQL 2012 I got this error<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">All three errors are just a waste of time and don’t actually mean anything what they say. These errors are only coming due to compatibility issues with SSMS<o:p></o:p></span><br />
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><u>Solution</u></b>:<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">Install SQL Server 2012 client component i.e. SSMS (SSMS of subscriber server version on publisher server) and then from the publisher server try to set replication subscriber and this will be as smooth as butter<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">Assumption: Both the server (publisher and subscriber already have replication installed)<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">This means if the subscriber is on the higher version we have to use ssms of the subscriber version on the publisher. <o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><b>Scenerio</b>4:<o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;">Error<i>”<span style="color: #333333;"> <span lang="EN">SQL Server replication requires the actual server name to make a connection to the server. Connections through a server alias, IP address, or any other alternate name are not supported. Specify the actual server"<o:p></o:p></span></span></i></span></div>
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<i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace; font-size: large;"><b><u>Solution</u></b>:<o:p></o:p></span></i></div>
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<li><i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace; font-size: large;">If you are giving IP, alias name, Fully qualified domain name of server, and server name with port, you will get this error.</span></i></li>
<li><i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace; font-size: large;">So run @@servername in query analyzer and use this name to connect</span></i></li>
<li><i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace; font-size: large;">If @@servername is null then run</span></i></li>
<li><i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace; font-size: large;">EXEC sp_addserver 'servername\instance', 'LOCAL'</span></i></li>
<li><i><span lang="EN" style="color: #333333; font-family: Courier New, Courier, monospace; font-size: large;">And now try you will be successful</span></i></li>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><b>Note</b>: error: “<span lang="EN">For merge replication, a Subscriber to a merge publication can be any version no later than the Publisher version”<o:p></o:p></span></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><span lang="EN">Issue: Merger replication doesn’t support subscribers at higher versions than publisher</span><o:p></o:p></span></div>
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<span style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiK-JNcaDAq7T7wGqIDS9tHvqIqgj18lcNsXJp8UDH3eWArpaEnR2zf6L5PI14zpNaZJ3rI8jCQ7N3nhnMhV5SnNnsoeBCYgR8H8-AaNbRnsEg38MQ1XYpWSldxsps1Oeqq-90pJIYY8Q/s1600/image002-743972.png"><img alt="" border="0" height="42" id="BLOGGER_PHOTO_ID_6104852101509098370" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiK-JNcaDAq7T7wGqIDS9tHvqIqgj18lcNsXJp8UDH3eWArpaEnR2zf6L5PI14zpNaZJ3rI8jCQ7N3nhnMhV5SnNnsoeBCYgR8H8-AaNbRnsEg38MQ1XYpWSldxsps1Oeqq-90pJIYY8Q/s320/image002-743972.png" width="640" /></a><o:p></o:p></span></div>
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Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com07JPC5R5X+XV24.159981 68.849728224.034625072096816 68.7123990984375 24.285336927903181 68.9870573015625tag:blogger.com,1999:blog-830335965541290967.post-49209938240567522302024-02-11T10:23:00.003+05:302024-03-05T23:59:55.499+05:30Microsoft Fabric - Resource Cleanup in Lab - 6 <p><span></span></p><a name='more'></a><br /><p></p><h1 style="text-align: center;">Resource Cleanup in Microsoft Fabric </h1><p><br /></p><p><br /></p><h3 style="text-align: left;">Exercise: Clean up resources</h3><p><span style="font-size: medium;">You can delete individual reports, pipelines, warehouses, and other items or remove the entire workspace. Use the following steps to delete the workspace you created for this tutorial.</span></p><p></p><ol style="text-align: left;"><li><span style="font-size: medium;">Select your workspace, the Fabric Lakehouse Tutorial-XX from the left-hand navigation menu. It opens the workspace item view.</span></li><li><span style="font-size: medium;">Select the … option under the workspace name and select Workspace settings.</span></li><li><span style="font-size: medium;">Select Other and Remove this workspace.</span></li><li><span style="font-size: medium;">Click on Delete in the warning that pops up.</span></li><li><span style="font-size: medium;">Wait for a notification that the Workspace has been deleted, before proceeding to the next lab.</span></li></ol><div><br /></div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgFx60Y8xG12j_VYsc56h68mCZWpB0IEUO-p3UJBe1I5yTTT9TAkD_LaRwzIsz-FmHm4yZmzrypFRz4H9AuJcJqnpiP9_1OSkciueOMXFe4QmH3vrNxUP-YeC9k51FYoRKsInxEeOVzazZBTjcDfF1XOyvFiIv1_H9bgEUdT8EyNkcBaOrxXTvq46wPGx4" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="747" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgFx60Y8xG12j_VYsc56h68mCZWpB0IEUO-p3UJBe1I5yTTT9TAkD_LaRwzIsz-FmHm4yZmzrypFRz4H9AuJcJqnpiP9_1OSkciueOMXFe4QmH3vrNxUP-YeC9k51FYoRKsInxEeOVzazZBTjcDfF1XOyvFiIv1_H9bgEUdT8EyNkcBaOrxXTvq46wPGx4" width="313" /></a></div><div class="separator" style="clear: both; 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text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh5DlRymY21jaATNNnFJQ3YyQp_LUVfwBbN-S5SnECn8SD6T0oUodBjkIrsJ4R22VtazChtoRH3SNScsmA5W_WmrnbFdY0y98ctF9NGZI3Au3CkrffB0yjTKx4AHAZckvO7w-fV3P5WyMlCTrakE5G3dHhlMlUyuxupviXOMhKfyBu_89d5-nK_WIuKTnU" style="margin-left: 1em; margin-right: 1em;"><img alt="fabric Clear Resource, Microsoft Azure" data-original-height="323" data-original-width="975" height="212" src="https://blogger.googleusercontent.com/img/a/AVvXsEh5DlRymY21jaATNNnFJQ3YyQp_LUVfwBbN-S5SnECn8SD6T0oUodBjkIrsJ4R22VtazChtoRH3SNScsmA5W_WmrnbFdY0y98ctF9NGZI3Au3CkrffB0yjTKx4AHAZckvO7w-fV3P5WyMlCTrakE5G3dHhlMlUyuxupviXOMhKfyBu_89d5-nK_WIuKTnU=w640-h212" title="Saurabh Sinha" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><h4 style="clear: both; text-align: center;"><span style="font-size: large;">Microsoft Fabric Labs</span></h4></div></div></div></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Azure Microsoft Fabric - Lab -1 for Beginners:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a></li></ul><li>Azure Microsoft Fabric - Auto Power BI Reports Lab -2:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html</a></li></ul><li>Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></li></ul><li>Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></li></ul><li>Microsoft Fabric and Power BI Reports Lab - 5:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></li></ul><li>Microsoft Fabric - Resource Cleanup in Lab -6 </li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</a></li></ul></ul></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><p></p>
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</script>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0MWVJ+CC Jammu32.6935763 74.931005832.664680933706705 74.896673524609369 32.722471666293288 74.965338075390619tag:blogger.com,1999:blog-830335965541290967.post-85833536992785897252024-02-11T10:04:00.002+05:302024-02-11T10:43:38.243+05:30Microsoft Fabric and Power BI Reports Lab - 5<p><span></span></p><a name='more'></a><br /><p></p><h1 style="text-align: center;">Building reports in Microsoft Fabric</h1><p><br /></p><p><br /></p><h3 style="text-align: left;">In this section of the tutorial, you create a Power BI data model and create a report from scratch.</h3><p>Power BI is natively integrated into the whole Fabric experience. This native integration brings a unique mode, called DirectLake, of accessing the data from the lakehouse to provide the most performant query and reporting experience. DirectLake mode is a groundbreaking new engine capability to analyze very large datasets in Power BI. The technology is based on the idea of loading parquet-formatted files directly from a data lake without having to query a data warehouse or lakehouse endpoint, and without having to import or duplicate data into a Power BI dataset. DirectLake is a fast path to load the data from the data lake straight into the Power BI engine, ready for analysis.</p><p>In traditional DirectQuery mode, the Power BI engine directly queries the data from the source to execute each query, and the query performance depends on data retrieval speed. DirectQuery eliminates the need to copy data, ensuring that any changes in the source are immediately reflected in the query results during the import. On the other hand, in Import mode, performance is better because the data is readily available in the memory without querying data from the source for each query execution. However, the Power BI engine must first copy the data into memory during data refresh. Only changes to the underlying data source are picked up during the next data refresh(in scheduled as well as on-demand refresh).</p><p>DirectLake mode now eliminates this import requirement by loading the data files directly into memory. Because there's no explicit import process, it's possible to pick up any changes at the source as they occur, thus combining the advantages of DirectQuery and import mode while avoiding their disadvantages. DirectLake mode is therefore the ideal choice for analyzing very large datasets and datasets with frequent updates at the source.</p><p><br /></p><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><h4 style="clear: both;"><span style="font-size: xx-small;">Microsoft Fabric Labs</span></h4></div></div></div></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Lab -1 for Beginners:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a></span></li></ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Auto Power BI Reports Lab -2:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric and Power BI Reports Lab - 5:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Resource Cleanup in Lab -6 </span></li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html"><span style="font-size: xx-small;">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</span></a></li></ul></ul></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h2 style="text-align: left;">Task 1: Explore data in the silver layer using the SQL endpoint</h2><p></p><ul style="text-align: left;"><li><span style="font-size: medium;">From your left navigation pane, select Fabric_LakehouseXX and then select wwilakehouse of Type SQL endpoint.</span></li><li><span style="font-size: medium;">From the SQL endpoint pane, you should be able to see all the tables you created. If you don't see them yet, select the Refresh icon at the top. Next, select the Model tab at the bottom to open the default Power BI dataset.</span></li></ul><p></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEilrLnuuqT-B7iBAyuTqeofVTvXcEMupeqEivh61oL6zTh5Go5t10CfLKIQGOqsxsDol0Kn0gEtKKPkdn9k_OTiHyc2kj9KXQaHXk8aE9eCciI2d3X4FqHD2lVd3RTunplthUZAeQTUeDwGTvKO2g_PvVMIoUIi5VjAwyhCWmPbsJ7UGVmEVSEp79L1Tvc" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="573" data-original-width="975" height="188" src="https://blogger.googleusercontent.com/img/a/AVvXsEilrLnuuqT-B7iBAyuTqeofVTvXcEMupeqEivh61oL6zTh5Go5t10CfLKIQGOqsxsDol0Kn0gEtKKPkdn9k_OTiHyc2kj9KXQaHXk8aE9eCciI2d3X4FqHD2lVd3RTunplthUZAeQTUeDwGTvKO2g_PvVMIoUIi5VjAwyhCWmPbsJ7UGVmEVSEp79L1Tvc" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjipZRHjETCOj45uedlI6aDjzM5G2mz9jeWpkVXj_lOp7EhZGSF455RUlCCGn0Bp4uuXT6Gija6SisHlI0zzD5DbGieTGFzVllkPJ6M1ac0ofud3CNumZJVhk7vhfnfHWrt1x5mklRJ-gy3g96-9w2JvT0XSuz8gJ50AjBS-bGcUP71JaMBFSWZwAWdTDc" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="769" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjipZRHjETCOj45uedlI6aDjzM5G2mz9jeWpkVXj_lOp7EhZGSF455RUlCCGn0Bp4uuXT6Gija6SisHlI0zzD5DbGieTGFzVllkPJ6M1ac0ofud3CNumZJVhk7vhfnfHWrt1x5mklRJ-gy3g96-9w2JvT0XSuz8gJ50AjBS-bGcUP71JaMBFSWZwAWdTDc" width="304" /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjipZRHjETCOj45uedlI6aDjzM5G2mz9jeWpkVXj_lOp7EhZGSF455RUlCCGn0Bp4uuXT6Gija6SisHlI0zzD5DbGieTGFzVllkPJ6M1ac0ofud3CNumZJVhk7vhfnfHWrt1x5mklRJ-gy3g96-9w2JvT0XSuz8gJ50AjBS-bGcUP71JaMBFSWZwAWdTDc" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br /></a></div><br /><br /></div><p></p><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">For this data model, you need to define the relationship between different tables so that you can create reports and visualizations based on data coming across different tables.</span></li><li><span style="font-size: medium;">From the fact_sale table, drag the CityKey field and drop it on the CityKey field in the dimension_city table to create a relationship. The Create Relationship dialog box appears.</span></li></ul></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both;"><span style="font-size: medium;"><b>Note:</b> Rearrange the tables by clicking on the table, dragging and dropping to have the dimension_city and the fact_sale tables next to each other. The same holds good for any two tables that you are trying to create a relationship. This is just to make the drag and drop of the columns between the tables is easier.</span></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjc_xUL8bYb_98p7ACFok28gj-ANkXpJbnYX8nRzwn5vzDOi1GErzEjhcmUM_l2onGRhkn69sZU2NCbwjfAI43CzfJfPEW1WtdNUMhSy2Zd_2tuC7hy5Dt1xvaI4MBBPVh86MIACGk1XDi1OKSmtYdM5VcqpO1sSXcRx-Q6y8m1TTjbxmpjlOwXg0sKGvs" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="559" data-original-width="975" height="366" src="https://blogger.googleusercontent.com/img/a/AVvXsEjc_xUL8bYb_98p7ACFok28gj-ANkXpJbnYX8nRzwn5vzDOi1GErzEjhcmUM_l2onGRhkn69sZU2NCbwjfAI43CzfJfPEW1WtdNUMhSy2Zd_2tuC7hy5Dt1xvaI4MBBPVh86MIACGk1XDi1OKSmtYdM5VcqpO1sSXcRx-Q6y8m1TTjbxmpjlOwXg0sKGvs=w640-h366" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h4 style="clear: both; text-align: left;"><b>In the Create Relationship dialog box:</b></h4><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">Table 1 is populated with fact_sale and the column of CityKey.</span></li><li><span style="font-size: medium;">Table 2 is populated with dimension_city and the column of CityKey.</span></li><li><span style="font-size: medium;">Cardinality: Many to one (*:1)</span></li><li><span style="font-size: medium;">Cross filter direction: Single</span></li><li><span style="font-size: medium;">Leave the box next to Make this relationship active selected.</span></li><li><span style="font-size: medium;">Select the box next to Assume referential integrity.</span></li><li><span style="font-size: medium;">Select Confirm.</span></li></ul></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiFGhLYdFo27yK_nd-3_Eqq7XsU3jefXjiJ4lkn2IsnScO1uUd_2V2w3g1iqNfjcP0vW5Q8HryOBG1QL1xpfz1mUXCue6A2O8j6NFvfOWV4dxn8d4ZqB9BQT89AYO-MeB6fASue5nZsV08gTrRGag1A8DAYKlh4tZV2xum1dSKIQAotU4HjeTwActhXHC4" style="margin-left: 1em; margin-right: 1em;"><img alt="Azure AI Saurabh Sinha" data-original-height="787" data-original-width="975" height="517" src="https://blogger.googleusercontent.com/img/a/AVvXsEiFGhLYdFo27yK_nd-3_Eqq7XsU3jefXjiJ4lkn2IsnScO1uUd_2V2w3g1iqNfjcP0vW5Q8HryOBG1QL1xpfz1mUXCue6A2O8j6NFvfOWV4dxn8d4ZqB9BQT89AYO-MeB6fASue5nZsV08gTrRGag1A8DAYKlh4tZV2xum1dSKIQAotU4HjeTwActhXHC4=w640-h517" title="Microsoft Fabric" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">Now, add these relationships with the same Create Relationship settings as shown above but with the following tables and columns:</span></li><ul><li><span style="font-size: medium;">StockItemKey(fact_sale) - StockItemKey(dimension_stock_item)</span></li><li><span style="font-size: medium;">Salespersonkey(fact_sale) - EmployeeKey(dimension_employee)</span></li><li><span style="font-size: medium;">CustomerKey(fact_sale) - CustomerKey(dimension_customer)</span></li><li><span style="font-size: medium;">InvoiceDateKey(fact_sale) - Date(dimension_date)</span></li></ul><li><span style="font-size: medium;">After you add these relationships, your data model should be as shown in the below image and it will be ready for reporting.</span></li></ul></div><div><br /></div></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjbNzpLSfoXbPTna9NWrCcj_Wh1DYT0e0zycBzQ73HJ1e3fpL7Qv5Mat4pBDNv_GCFB6hPEGMvYKp3qVRQanihypwz5278_VFR6IwKX9mSA6ydoVfteY81fNdfr8X00feFOKqWUZDFyzT0Mb0OmIAy1aHwjzfJy8LGh8QS5ynoKsTrJhZ0yrqjBzFumi-A" style="margin-left: 1em; margin-right: 1em;"><img alt="Power BI, Fabric Microsoft , Saurabh Sinha Algae Services" data-original-height="489" data-original-width="975" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEjbNzpLSfoXbPTna9NWrCcj_Wh1DYT0e0zycBzQ73HJ1e3fpL7Qv5Mat4pBDNv_GCFB6hPEGMvYKp3qVRQanihypwz5278_VFR6IwKX9mSA6ydoVfteY81fNdfr8X00feFOKqWUZDFyzT0Mb0OmIAy1aHwjzfJy8LGh8QS5ynoKsTrJhZ0yrqjBzFumi-A=w640-h320" title="Power BI, Fabric Microsoft , Saurabh Sinha" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;">Task 2: Build Report</h3><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">From the top ribbon, select New Report to start creating reports/dashboards in Power BI.</span></li></ul></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhyh6DDMgY248PyXelz-Rg4BaPbZ3kKW90mtAv8ZlyDWUoHCo-jyXaVUwhlBBUgOJve-e7PBPf8EINzkQsSIrYG4e5_4qz2jW0pWG18dg_Pg8GiBqSY_14v801jfToCewREh4DEpbtBGtQuXXRJK41MpMwMSQflbw1jlr0okQ0M0-7SGnQDtpoBodlqoZo" style="margin-left: 1em; margin-right: 1em;"><img alt="Saurabh Sinha" data-original-height="325" data-original-width="975" height="214" src="https://blogger.googleusercontent.com/img/a/AVvXsEhyh6DDMgY248PyXelz-Rg4BaPbZ3kKW90mtAv8ZlyDWUoHCo-jyXaVUwhlBBUgOJve-e7PBPf8EINzkQsSIrYG4e5_4qz2jW0pWG18dg_Pg8GiBqSY_14v801jfToCewREh4DEpbtBGtQuXXRJK41MpMwMSQflbw1jlr0okQ0M0-7SGnQDtpoBodlqoZo=w640-h214" title="Fabric , Azure, Spark , Power BI" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">On the Power BI report canvas, you can create reports to meet your business requirements by dragging the required columns from the Data pane to the canvas and using one or more of the available visualizations.</span></li><ul><li><span style="font-size: medium;">Add a title:</span></li><ul><li><span style="font-size: medium;">In the Ribbon, select Text box. Type in WW Importers Profit Reporting. Highlight the text and increase the size to 20.</span></li><li><span style="font-size: medium;">Resize the text box place it in the upper left of the report page and click outside the textbox.</span></li></ul><li><span style="font-size: medium;">Add a Card:</span></li><ul><li><span style="font-size: medium;">On the Data pane, expand fact_sales and check the box next to Profit. This selection creates a column chart and adds the field to the Y-axis.</span></li><ul><li><span style="font-size: medium;">With the bar chart selected, select the Card visual in the visualization pane.</span></li><li><span style="font-size: medium;">This selection converts the visual to a card. Place the card under the title.</span></li><li><span style="font-size: medium;">Click anywhere on the blank canvas (or press the Esc key) so the Card that we just placed is no longer selected.</span></li></ul></ul><li><span style="font-size: medium;">Add a Bar chart:</span></li><ul><li><span style="font-size: medium;">On the Data pane, expand fact_sales and check the box next to Profit. This selection creates a column chart and adds the field to the Y-axis.</span></li><li><span style="font-size: large;">On the Data pane, expand dimension_city and check the box for SalesTerritory. This selection adds the field to the Y-axis.</span><span style="font-size: large; white-space: pre;"> </span></li><li><span style="font-size: medium;">With the bar chart selected, select the Clustered bar chart visual in the visualization pane. This selection converts the column chart into a bar chart.</span></li><li><span style="font-size: large;">Resize the Bar chart to fill in the area under the title and Card.</span></li><li><span style="font-size: medium;">Click anywhere on the blank canvas (or press the Esc key) so the bar chart is no longer selected.</span></li></ul></ul></ul></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgfgX4YHD8EXtCLDyCjViQopggIEHKzAB2iotxVebY1bAvor5QaI0aEBku3uVxuj5zMrdgiGr2pHTBRalcxr2Z9xeZA6bPEYCZq2MqwEDpMeHyWQwmVxKH55nbVpX6W14x4NPkyiQRq-wp6y7N_ZK0kmEkU7MMQaTgiYHDDmjkRp0ZoQNNEzJTpXbbSeI4" style="margin-left: 1em; margin-right: 1em;"><img alt="Sinha" data-original-height="303" data-original-width="975" height="124" src="https://blogger.googleusercontent.com/img/a/AVvXsEgfgX4YHD8EXtCLDyCjViQopggIEHKzAB2iotxVebY1bAvor5QaI0aEBku3uVxuj5zMrdgiGr2pHTBRalcxr2Z9xeZA6bPEYCZq2MqwEDpMeHyWQwmVxKH55nbVpX6W14x4NPkyiQRq-wp6y7N_ZK0kmEkU7MMQaTgiYHDDmjkRp0ZoQNNEzJTpXbbSeI4=w400-h124" title="Saurabh" width="400" /></a></div><div class="separator" style="clear: both; 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text-align: left;"><b>Build a stacked area chart visual:</b></h3><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">On the Visualizations pane, select the Stacked area chart visual.</span></li><li><span style="font-size: medium;">Reposition and resize the stacked area chart to the right of the card and bar chart visuals created in the previous steps.</span></li><li><span style="font-size: medium;">On the Data pane, expand fact_sales and check the box next to Profit. Expand dimension_date and check the box next to FiscalMonthNumber. This selection creates a filled line chart showing profit by fiscal month.</span></li><li><span style="font-size: medium;">On the Data pane, expand dimension_stock_item and drag BuyingPackage into the Legend field well. This selection adds a line for each of the Buying Packages.</span></li><li><span style="font-size: medium;">Click anywhere on the blank canvas (or press the Esc key) so the stacked area chart is no longer selected.</span></li></ul><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjDPt2T-gvjFNozo8VYnVctUn9DqTQpPTVAZX9KBs4rauWI9K2EESLW3Hf_q3MzE_ZYOqJTU0h9Br36DIuUtXPgmIFK6bj-1jVpzQs07_LAM4DJxwOIfsDYBVYCuVq9majhyH90sjf03E4FdOVFgi5StROhdLz1VTY3w_6Zi8yiCPC3rdXA8Vhb9T86qig" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="750" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjDPt2T-gvjFNozo8VYnVctUn9DqTQpPTVAZX9KBs4rauWI9K2EESLW3Hf_q3MzE_ZYOqJTU0h9Br36DIuUtXPgmIFK6bj-1jVpzQs07_LAM4DJxwOIfsDYBVYCuVq9majhyH90sjf03E4FdOVFgi5StROhdLz1VTY3w_6Zi8yiCPC3rdXA8Vhb9T86qig" width="312" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh2S3b5dKz10k-fMJuaL-EJhKfLwv2i7UPlC1uR059uzPLQ_tdojEILo86VEqxWMdGENN63lO2-XhskQpIqua97M69Uhu4xLVlBNed3deMP6ORsHWiLldYTorsfHvZsaqi6SIb__2TGeoOyhvw2YvHg47oCeVNmTD6xzFcB_41d3sd5ZV4BgJLkPT7M5G4" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="596" data-original-width="975" height="196" src="https://blogger.googleusercontent.com/img/a/AVvXsEh2S3b5dKz10k-fMJuaL-EJhKfLwv2i7UPlC1uR059uzPLQ_tdojEILo86VEqxWMdGENN63lO2-XhskQpIqua97M69Uhu4xLVlBNed3deMP6ORsHWiLldYTorsfHvZsaqi6SIb__2TGeoOyhvw2YvHg47oCeVNmTD6xzFcB_41d3sd5ZV4BgJLkPT7M5G4" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiLXrthfcY7lilUpMQFiItGa76Z3dOHkJyDuyCXZVlbmN614QF27CotcHSxXmfGO-yOH99ngeroXFpfRtnKOo2XXb_nOQQ0PBo3D43Qyl0tsEG7iFap0nXyctNOjHsLHpFpRM5ppHRoyAPerUBkDWgVJbAIUBur4OtC8iz2QH4cUVd1XqMYl1HgXhOFECw" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="404" data-original-width="975" height="133" src="https://blogger.googleusercontent.com/img/a/AVvXsEiLXrthfcY7lilUpMQFiItGa76Z3dOHkJyDuyCXZVlbmN614QF27CotcHSxXmfGO-yOH99ngeroXFpfRtnKOo2XXb_nOQQ0PBo3D43Qyl0tsEG7iFap0nXyctNOjHsLHpFpRM5ppHRoyAPerUBkDWgVJbAIUBur4OtC8iz2QH4cUVd1XqMYl1HgXhOFECw" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiMBNEiUWbp9-zrk1Fov6cT9-pZLEFhUBYs35Ov_JZT4wftY3Vu7I8qwq-0USCKom3sDqpYY-XNbPw995B0W0olLAKd5YrszilivtwlurQupicN9rfxATllvYDz_uiCx-7W4p8ravKXQDtC9UGot1NOKLYi1l-bfb5d7YeG4dqhPTIYRNGsP0nqhT6fbu8" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="419" data-original-width="975" height="138" src="https://blogger.googleusercontent.com/img/a/AVvXsEiMBNEiUWbp9-zrk1Fov6cT9-pZLEFhUBYs35Ov_JZT4wftY3Vu7I8qwq-0USCKom3sDqpYY-XNbPw995B0W0olLAKd5YrszilivtwlurQupicN9rfxATllvYDz_uiCx-7W4p8ravKXQDtC9UGot1NOKLYi1l-bfb5d7YeG4dqhPTIYRNGsP0nqhT6fbu8" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhbxIY7p_OTj_cogDD0jooDqR8DjSz3CxC7xCdlIDFGp9ubAofX9ljO0Ipl4EFF9zuPb4gDy5ZIJeTiHTdykRF-w6w9V9jVH80sLE5yv0CE4egciB1QNOt3TrGl6wODQnOuAWjLp_JrC0RlHOSzOjz4hIctC8DjYkUJY8NcVg6A2bprOuj9VZTMH6vl_mk" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="483" data-original-width="975" height="318" src="https://blogger.googleusercontent.com/img/a/AVvXsEhbxIY7p_OTj_cogDD0jooDqR8DjSz3CxC7xCdlIDFGp9ubAofX9ljO0Ipl4EFF9zuPb4gDy5ZIJeTiHTdykRF-w6w9V9jVH80sLE5yv0CE4egciB1QNOt3TrGl6wODQnOuAWjLp_JrC0RlHOSzOjz4hIctC8DjYkUJY8NcVg6A2bprOuj9VZTMH6vl_mk=w640-h318" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div></div></div></div></div><div><br /></div><h3 style="text-align: left;"><b>Build a column chart:</b></h3><ul style="text-align: left;"><li><span style="font-size: medium;">On the Visualizations pane, select the Stacked column chart visual.</span></li><li><span style="font-size: medium;">On the Data pane, expand fact_sales and check the box next to Profit. This selection adds the field to the Y-axis.</span></li><li><span style="font-size: medium;">On the Data pane, expand dimension_employee and check the box next to Employee. This selection adds the field to the X-axis.</span></li><li><span style="font-size: medium;">Click anywhere on the blank canvas (or press the Esc key) so the chart is no longer selected.</span></li></ul><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh8f2QBVdiH8BuuFFvYU3LwTQ33-rVMZJvgKLmkUbEWsrlARK5OaupLlJi9lAY-WyeQyI-R01tAG5FTLcctNmM-09xguMPEHpYjMrRi5od7CmG2r21NWiJK1A1Dh7rJGByUjx6UHullpFYkpuu0YMAZ07PPErWJFExdNrmyOl2EipEWjRjJvPLd_Eim3vs" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="735" data-original-width="539" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEh8f2QBVdiH8BuuFFvYU3LwTQ33-rVMZJvgKLmkUbEWsrlARK5OaupLlJi9lAY-WyeQyI-R01tAG5FTLcctNmM-09xguMPEHpYjMrRi5od7CmG2r21NWiJK1A1Dh7rJGByUjx6UHullpFYkpuu0YMAZ07PPErWJFExdNrmyOl2EipEWjRjJvPLd_Eim3vs" width="176" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgs6ibfdXLI02iX2ULzYREDIcOb3ptRxQvvhV6yuO7bSXotA5JM1LL8UOKZDkSHsalEfYrmNc2Hyu-8trC6-2tTnokxiaeLNHa4_utT11uv5SQRkK5_blafqPIEJb--rG9o5YFbwIczq3MCl9r56jztBCE6_1VVC_2Lih8u_Q3BSTAZEt-HdyB5M3o6hZ8" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="460" data-original-width="975" height="151" src="https://blogger.googleusercontent.com/img/a/AVvXsEgs6ibfdXLI02iX2ULzYREDIcOb3ptRxQvvhV6yuO7bSXotA5JM1LL8UOKZDkSHsalEfYrmNc2Hyu-8trC6-2tTnokxiaeLNHa4_utT11uv5SQRkK5_blafqPIEJb--rG9o5YFbwIczq3MCl9r56jztBCE6_1VVC_2Lih8u_Q3BSTAZEt-HdyB5M3o6hZ8" width="320" /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgs6ibfdXLI02iX2ULzYREDIcOb3ptRxQvvhV6yuO7bSXotA5JM1LL8UOKZDkSHsalEfYrmNc2Hyu-8trC6-2tTnokxiaeLNHa4_utT11uv5SQRkK5_blafqPIEJb--rG9o5YFbwIczq3MCl9r56jztBCE6_1VVC_2Lih8u_Q3BSTAZEt-HdyB5M3o6hZ8" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgs6ibfdXLI02iX2ULzYREDIcOb3ptRxQvvhV6yuO7bSXotA5JM1LL8UOKZDkSHsalEfYrmNc2Hyu-8trC6-2tTnokxiaeLNHa4_utT11uv5SQRkK5_blafqPIEJb--rG9o5YFbwIczq3MCl9r56jztBCE6_1VVC_2Lih8u_Q3BSTAZEt-HdyB5M3o6hZ8" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgd0To-SbyvDRy0igEdUakwjKPvrOGJOYPYdTabxTBi_jAPV7XvaFiiGDHpUT1_XUFhu7yJgDnfLtn-65C0TKFn9OiWBM6dMrze4XnyKC0nhdctEpcBk2j1M1Zae7JgfnqfxgTlVaMDnLZe7geW-EV3xncnB-yWKozigYexegGRiniQfPsbs1f_biKZToY" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgd0To-SbyvDRy0igEdUakwjKPvrOGJOYPYdTabxTBi_jAPV7XvaFiiGDHpUT1_XUFhu7yJgDnfLtn-65C0TKFn9OiWBM6dMrze4XnyKC0nhdctEpcBk2j1M1Zae7JgfnqfxgTlVaMDnLZe7geW-EV3xncnB-yWKozigYexegGRiniQfPsbs1f_biKZToY" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a><ul style="color: black; text-align: left;"><li><span style="font-size: medium;">From the ribbon, select File > Save.</span></li><li><span style="font-size: medium;">Enter the name of your report as Profit Reporting. Select Save.</span></li><li><span style="font-size: medium;">You will get a notification stating that the report has been saved.</span></li></ul><div style="text-align: left;"><span style="font-size: medium;"><br /></span></div><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgd0To-SbyvDRy0igEdUakwjKPvrOGJOYPYdTabxTBi_jAPV7XvaFiiGDHpUT1_XUFhu7yJgDnfLtn-65C0TKFn9OiWBM6dMrze4XnyKC0nhdctEpcBk2j1M1Zae7JgfnqfxgTlVaMDnLZe7geW-EV3xncnB-yWKozigYexegGRiniQfPsbs1f_biKZToY" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="555" data-original-width="975" height="364" src="https://blogger.googleusercontent.com/img/a/AVvXsEgd0To-SbyvDRy0igEdUakwjKPvrOGJOYPYdTabxTBi_jAPV7XvaFiiGDHpUT1_XUFhu7yJgDnfLtn-65C0TKFn9OiWBM6dMrze4XnyKC0nhdctEpcBk2j1M1Zae7JgfnqfxgTlVaMDnLZe7geW-EV3xncnB-yWKozigYexegGRiniQfPsbs1f_biKZToY=w640-h364" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEixZ7tRwHP1XeBRSu7ay-ohp67KRllKTuMTjMyCkiRc3Z162pk0m-pFrAIHo2Im_dp2alCdqNk0wljFMCJmCcqjPvTQi0GCz9rw4V14NM2mv9K-X5fFdMAw3t5miB_MIh_TjH0byXZx-uzCaIOVJyXjrwuM3FQFif67HvIlsLqg_uQ2Tr5G_gxp9OdFpRo" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="713" data-original-width="945" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEixZ7tRwHP1XeBRSu7ay-ohp67KRllKTuMTjMyCkiRc3Z162pk0m-pFrAIHo2Im_dp2alCdqNk0wljFMCJmCcqjPvTQi0GCz9rw4V14NM2mv9K-X5fFdMAw3t5miB_MIh_TjH0byXZx-uzCaIOVJyXjrwuM3FQFif67HvIlsLqg_uQ2Tr5G_gxp9OdFpRo" width="318" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj6SmcwGkK6fOUBnmOIEzkrZQR9whGCcJEFqaeeWew_s3ZUp3rT_jNMAcDgTOUOPcTflsk84d22wAUq8Z9WmkocfIRV6JSZWSFerly9KcsZEw1V5JYXbceydsskZghg2xpqHTspx4kYiKePs1VYV5Xn32TIsS42gMBiWG3z_SxI6d9IluKHpgrs97BcqhA" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="436" data-original-width="975" height="286" src="https://blogger.googleusercontent.com/img/a/AVvXsEj6SmcwGkK6fOUBnmOIEzkrZQR9whGCcJEFqaeeWew_s3ZUp3rT_jNMAcDgTOUOPcTflsk84d22wAUq8Z9WmkocfIRV6JSZWSFerly9KcsZEw1V5JYXbceydsskZghg2xpqHTspx4kYiKePs1VYV5Xn32TIsS42gMBiWG3z_SxI6d9IluKHpgrs97BcqhA=w640-h286" width="640" /></a></div><br /><br /></div><br /><br /></div><br /><br /></div><br /><br /></div><br /><br /></div></div></div></div></div><div class="separator" style="clear: both; text-align: center;"></div></div></div></div></div><ul><li>Microsoft Fabric - Resource Cleanup in Lab -6 </li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</a></li></ul></ul>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0QXC4+R5 Galowali, Punjab, India31.7721162 74.955448931.742932912972918 74.921116624609368 31.80129948702708 74.989781175390618tag:blogger.com,1999:blog-830335965541290967.post-62349235721276247722024-02-11T09:13:00.002+05:302024-02-11T10:42:54.825+05:30Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4<p><span style="font-size: medium;"><span></span></span></p><a name='more'></a><span style="font-size: medium;"><br /></span><p></p><p><span style="font-size: medium;"><br /></span></p><h1 style="text-align: center;"><span style="font-size: x-large;">Prepare and Transform Data in the Lakehouse </span></h1><p><span style="font-size: medium;"><br /></span></p><p><br /></p><h3 style="text-align: left;"><span style="font-size: medium;">Objective:</span></h3><p></p><ul style="text-align: left;"><li><span style="font-size: large;">Task 1: Upload existing notebooks.</span></li><li><span style="font-size: large;">Task 2: Transform data and load to silver Delta table</span></li></ul><p></p><p><span style="font-size: large;"><br /></span></p><p><span style="font-size: large;">Please go through <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html" rel="nofollow" target="_blank">Lab -1</a> & <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html" rel="nofollow" target="_blank">Lab - 2</a> and Prepare the Machine and data</span></p><p><span style="font-size: medium;">From the previous exercise steps, </span></p><p><span style="font-size: medium;">We have raw data "wwi-raw-data" ingested from the source "<a href="https://azuresynapsestorage.blob.core.windows.net/sampledata">https://azuresynapsestorage.blob.core.windows.net/sampledata</a>" to the Files section of the lakehouse. Now you can transform that data and prepare it for creating delta tables.</span></p><p><span style="font-size: medium;"><br /></span></p><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><h4 style="clear: both;"><span style="font-size: xx-small;">Microsoft Fabric Labs</span></h4></div></div></div></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Lab -1 for Beginners:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a></span></li></ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Auto Power BI Reports Lab -2:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric and Power BI Reports Lab - 5:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Resource Cleanup in Lab -6 </span></li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html"><span style="font-size: xx-small;">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</span></a></li></ul></ul></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both;"><br /></div><p><span style="font-size: medium;">Steps to Upload the Notebook:</span></p><p></p><ul style="text-align: left;"><li><span style="font-size: medium;">Now, click on Fabric Lakehouse Tutorial-XX on the left-side navigation pane</span></li><li><span style="font-size: medium;">In the Fabric Lakehouse Tutorial-XX workspace page, click on the drop-down arrow in the +New button, then select Import notebook.</span></li><li><span style="font-size: medium;">Select Upload from the Import status pane that opens on the right side of the screen.</span></li><li><span style="font-size: medium;">Navigate to C:\LabFiles\Lakehouse Tutorial Source Code, select 01-Create Delta Tables, 02-Data Transformation-Business Aggregation notebook, and click on Open.</span></li><li><span style="font-size: medium;">You will see a notification stating Imported successfully.</span></li></ul><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><div class="separator" style="clear: both; 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text-align: center;"><br /></div></div></div></div></div></div></span></div><div><br /></div><div><span style="font-size: medium;"><br /></span></div><ul style="text-align: left;"><li><span style="font-size: medium;">After the import is successful, to see the newly imported notebooks select Fabric Lakehouse Tutorial-XX under the Recommended section.</span></li><li><span style="font-size: medium;">In the Fabric Lakehouse Tutorial-XX pane, Select wwilakehouse Lakehouse to open it.</span></li></ul><p></p><p><span style="font-size: medium;"></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj_znaAuOynIcQr8b07DR-fqgG4GKlUEmCUp1yvZNNztzwfWXwn2AGqNyFTjfdwnRUU0ufNzdd8SM0uoZk3cSyuZKSE5fjLAdwBpiPNooWEBT1tQ2PHWuN67CbqcpTYqGUZ1alpJN53OnKUH4dxFZXGsrlThUIuxtRDu--V38DI0MgjpYT9By2751-UIvY" style="clear: left; 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text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhMHRtKtR5afBHtBtItJI2atYCm_Kun9hmv8A9_P4sxHlzbZ4GfXKyWwlnZFKYk-LmB4HhQCkDonpWJp7YShky_aXOlEzg5Xcd4SlErVwQgNYqTlfgHyMsKXXiR9fHixZ6fhlSuv3wIPZIpjUv0ICnzPCgp3W6lH-2wYJrEH95O0elHwatapZ6n4p5N21c" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="845" data-original-width="975" height="347" src="https://blogger.googleusercontent.com/img/a/AVvXsEhMHRtKtR5afBHtBtItJI2atYCm_Kun9hmv8A9_P4sxHlzbZ4GfXKyWwlnZFKYk-LmB4HhQCkDonpWJp7YShky_aXOlEzg5Xcd4SlErVwQgNYqTlfgHyMsKXXiR9fHixZ6fhlSuv3wIPZIpjUv0ICnzPCgp3W6lH-2wYJrEH95O0elHwatapZ6n4p5N21c=w400-h347" width="400" /></a></span></div><span style="font-size: medium;"><br /><br /></span></div><span style="font-size: medium;"><br /><br /></span></div><span style="font-size: medium;"><br /><br /></span><p></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><h3 style="text-align: left;"><span style="font-size: large;">Task 2: Transform data and load to Delta table</span></h3><div><span style="font-size: medium;"><br /></span></div><p></p><ol style="text-align: left;"><li><span style="font-size: medium;">In the wwilakehouse page, select Open notebook > Existing notebook from the top navigation menu (You can also Build a new notebook, All codes are shared below).</span></li><li><span style="font-size: medium;">From the list of Open existing notebooks, select the 01 - Create Delta Tables notebook and select Open.</span></li><li><span style="font-size: medium;">In the opened notebook in Lakehouse Explorer, you see the notebook is already linked to your opened lakehouse.</span></li></ol><div><span style="font-size: medium;"><div class="separator" style="clear: both; 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float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="936" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjezbSZMZDq8vuJOY_2WEEq560pwR2cuq0KN4ASAUhVsTUNb5IGfIK1FcYeP_3z70qRZ-kpnyX5EyuH4paSYuKX68yx45TpVmw3JQQeqf9vGw2YI4zj6RhnUxjw5aEdYsYnStm6GYnolabtKS4WaZbsXuhxvfyJqZ-P7u7DNXJSftU4oxXE7F3jFug9iqM" width="250" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhyIYnJZTZUhFpyLfsGuOvhTlaar0uBU5H5PvNy8pVmhjxYDMMbtxJb79B2_X7LOPAi9r9XmF2YRRA6VcC6Mh-q2rmaL_3EA_c5m6gqCZ1x_cG-GN7-Ft6R1TGZrn5mApcHaoiGkdvob-C8bVn5QG138LBsIJ87mqz35lin0llYw0EQDE0nXhgqbjKK7zg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="477" data-original-width="975" height="314" src="https://blogger.googleusercontent.com/img/a/AVvXsEhyIYnJZTZUhFpyLfsGuOvhTlaar0uBU5H5PvNy8pVmhjxYDMMbtxJb79B2_X7LOPAi9r9XmF2YRRA6VcC6Mh-q2rmaL_3EA_c5m6gqCZ1x_cG-GN7-Ft6R1TGZrn5mApcHaoiGkdvob-C8bVn5QG138LBsIJ87mqz35lin0llYw0EQDE0nXhgqbjKK7zg=w640-h314" width="640" /></a></div><br /><br /></div><br /><br /></div><br /><br /></span></div><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><br /></span></div><p></p><p><span style="font-size: medium;"></span></p><p><span style="font-size: medium;"><br /></span></p><p><br /></p><p><b>Note</b>: Fabric provides the V-order capability to write optimized delta lake files. V-order often improves compression by three to four times and up to 10 times performance acceleration over the Delta Lake files that aren't optimized. Spark in Fabric dynamically optimizes partitions while generating files with a default 128 MB size. The target file size may be changed per workload requirements using configurations. With the optimized write capability, the Apache Spark engine reduces the number of files written and aims to increase the individual file size of the written data.</p><p><br /></p><p></p><ul style="text-align: left;"><li>Before you write data as delta lake tables in the Tables section of the lakehouse, you use two Fabric features (V-order and Optimize Write) for optimized data writing and for improved reading performance. To enable these features in your session, set these configurations in the first cell of your notebook.</li><li>To start the notebook and execute the cell, select the Run icon that appears to the left of the cell upon hover.</li><li>Next, you read raw data from the Files section of the lakehouse, and add more columns for different date parts as part of the transformation. you use partitionBy Spark API to partition the data before writing it as a delta table based on the newly created data part columns (Year and Quarter).</li><li>To execute the second cell, select the Run icon that appears to the left of the cell upon hover.</li></ul><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjhhprBmHc4UO71rOMrt0Sh5kW7yGaZaybMlxLKC-gVenow4QwBVowY2Vr58NU8NaTJFcDvbS6rOgyqIbo8gVzv18Rb2dCEMupUFRaGd37dDJ68JFDCh0G_UVTWz1tUc4mJpaOedyTtcA5F52-mkPhGliaunql4jjhepOmDD-vajqwWYqjEz9ycxsHjS2o" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="477" data-original-width="975" height="314" src="https://blogger.googleusercontent.com/img/a/AVvXsEjhhprBmHc4UO71rOMrt0Sh5kW7yGaZaybMlxLKC-gVenow4QwBVowY2Vr58NU8NaTJFcDvbS6rOgyqIbo8gVzv18Rb2dCEMupUFRaGd37dDJ68JFDCh0G_UVTWz1tUc4mJpaOedyTtcA5F52-mkPhGliaunql4jjhepOmDD-vajqwWYqjEz9ycxsHjS2o=w640-h314" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Note:</b> When running a cell, you don't have to specify the underlying Spark pool or cluster details because Fabric provides them through Live Pool. Every Fabric workspace comes with a default Spark pool, called Live Pool. This means when you create notebooks, you don't have to worry about specifying any Spark configurations or cluster details. When you execute the first notebook command, the live pool is up and running in a few seconds. And the Spark session is established and it starts executing the code. Subsequent code execution is almost instantaneous in this notebook while the Spark session is active.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div></div></div><p></p><div class="separator" style="clear: both;"><b>PythonCode</b></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">/**************************************************/</div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">from pyspark.sql.functions import col, year, month, quarter</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">table_name = 'fact_sale'</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">df = spark.read.format("parquet").load('Files/wwi-raw-data/full/fact_sale_1y_full')</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">df = df.withColumn('Year', year(col("InvoiceDateKey")))</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">df = df.withColumn('Quarter', quarter(col("InvoiceDateKey")))</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">df = df.withColumn('Month', month(col("InvoiceDateKey")))</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">df.write.mode("overwrite").format("delta").partitionBy("Year","Quarter").save("Tables/" + table_name)</span></div><div class="separator" style="clear: both;">/**************************************************/</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh-fy4GCRDZHaP-qN7wUb6b1x9bOQ3dglgOWsv_Qzc6vXguWkU_UZR_YDT4HMjz44CC0kNLhEs5elhraAomOEQyNHWwuQ1aeuehEtnGhhujzhka3svY_HVoSaPyrVrCy3wLN_7Co_aEwYCdzMCXsz14YfTpTck_rXdHJbjAMxDEUWiep8L3IRT-al38uDk" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="519" data-original-width="975" height="340" src="https://blogger.googleusercontent.com/img/a/AVvXsEh-fy4GCRDZHaP-qN7wUb6b1x9bOQ3dglgOWsv_Qzc6vXguWkU_UZR_YDT4HMjz44CC0kNLhEs5elhraAomOEQyNHWwuQ1aeuehEtnGhhujzhka3svY_HVoSaPyrVrCy3wLN_7Co_aEwYCdzMCXsz14YfTpTck_rXdHJbjAMxDEUWiep8L3IRT-al38uDk=w640-h340" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>After the fact tables load, you can move on to loading data for the rest of the dimensions. The following cell creates a function to read raw data from the Files section of the lakehouse for each of the table names passed as a parameter. Next, it creates a list of dimension tables. Finally, it loops through the list of tables and creates a delta table for each table name that's read from the input parameter.</li><li>Select the cell and select the Run icon that appears to the left of the cell upon hover.</li></ul><div><br /></div><div><div><b>PythonCode</b></div><div>/**************************************************/</div><div><span style="background-color: #fcff01;">from pyspark.sql.types import *</span></div><div><span style="background-color: #fcff01;">def loadFullDataFromSource(table_name):</span></div><div><span style="background-color: #fcff01;">df = spark.read.format("parquet").load('Files/wwi-raw-data/full/' + table_name)</span></div><div><span style="background-color: #fcff01;">df.write.mode("overwrite").format("delta").save("Tables/" + table_name)</span></div><div><span style="background-color: #fcff01;">full_tables = [</span></div><div><span style="background-color: #fcff01;"> 'dimension_city',</span></div><div><span style="background-color: #fcff01;"> 'dimension_date',</span></div><div><span style="background-color: #fcff01;"> 'dimension_employee',</span></div><div><span style="background-color: #fcff01;"> 'dimension_stock_item'</span></div><div><span style="background-color: #fcff01;"> ]</span></div><div><span style="background-color: #fcff01;">for table in full_tables:</span></div><div><span style="background-color: #fcff01;">loadFullDataFromSource(table)</span></div><div>/**************************************************/</div></div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj08JAAI2d0E2qXJnW8DcLvrzUqt_rvQSgUEJjyF59XNaz-flzBNcFTjJgSZSPy27HxdKR6c2IYbetDaZcnDAu4mFEecxb74ZstbRv8LrbnOHp5D_YAh79lKCsLS5TCxZtGx3QqHMH8HS9ZKbonbDLn0_bZ-PPNcwcAbOh4erGhdD6waK9sRqd3rWA_M1g" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="476" data-original-width="975" height="312" src="https://blogger.googleusercontent.com/img/a/AVvXsEj08JAAI2d0E2qXJnW8DcLvrzUqt_rvQSgUEJjyF59XNaz-flzBNcFTjJgSZSPy27HxdKR6c2IYbetDaZcnDAu4mFEecxb74ZstbRv8LrbnOHp5D_YAh79lKCsLS5TCxZtGx3QqHMH8HS9ZKbonbDLn0_bZ-PPNcwcAbOh4erGhdD6waK9sRqd3rWA_M1g=w640-h312" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><b>To validate the created tables, right-click on the Tables folder and choose Refresh. The tables appear.</b></div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgBHjDpfLBbmnHp-II7UEPACfXyrY73z_TlOHCuTKle44xXpySkBdF4fFHsy15GJkGmfzd3de1IsXdOv8-s-IGTR822GgAr7zv_dWmyIG6ncNz31cVQViiPQrSPFGBTePC89DjdoFauDlQBTxTbZwT0qA9bwmWtID9ETAlsxqJcxoGQZF_AUwYKagRd7Jo" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="860" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgBHjDpfLBbmnHp-II7UEPACfXyrY73z_TlOHCuTKle44xXpySkBdF4fFHsy15GJkGmfzd3de1IsXdOv8-s-IGTR822GgAr7zv_dWmyIG6ncNz31cVQViiPQrSPFGBTePC89DjdoFauDlQBTxTbZwT0qA9bwmWtID9ETAlsxqJcxoGQZF_AUwYKagRd7Jo" width="272" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh_csEIDXaxF0hhWm3z-nrHLQ0peFZdtaUxx_zTKxpr6E24Piw2bXIwzssALKkIUq2UEBT2N8g7StZvVUSMURol48xE0OTh6sjBaoa03XmngrNAOQYDzzlYNbdtVPu4v8OCOe3IgFX6aCar_mriwWlLwJnb-z7v2xjWurjvU6oVqzhJiVfNKvk53mAMARQ" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="870" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEh_csEIDXaxF0hhWm3z-nrHLQ0peFZdtaUxx_zTKxpr6E24Piw2bXIwzssALKkIUq2UEBT2N8g7StZvVUSMURol48xE0OTh6sjBaoa03XmngrNAOQYDzzlYNbdtVPu4v8OCOe3IgFX6aCar_mriwWlLwJnb-z7v2xjWurjvU6oVqzhJiVfNKvk53mAMARQ" width="269" /></a></div><br /><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><ul style="text-align: left;"><li>Go to the items view of the workspace again select Fabric Lakehouse Tutorial-XX and select the wwilakehouse lakehouse to open it.</li><li>Now, open the second notebook. In the lakehouse view, select Open notebook > Existing notebook from the ribbon.</li><li>From the list of Open existing notebooks, select the 02 - Data Transformation - Business Aggregation notebook and click on the Open.</li><li>In the open notebook in Lakehouse Explorer, you see the notebook is already linked to your opened lakehouse.</li><li>To start the notebook select the 1stcell and select the Run icon that appears to the left of the cell upon hover.</li></ul><div><br /></div></div><div><br /></div><div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjdYHKv_Kk8Na252sx8xZWLDm8R6_mNKlJL1JJRYlAIOzSXauyyeA6VGeKEsdcbx9EUczSQk-6jdTu3XNJerji8WDXne8E8XV80huzpoe4IGBjvb3sDizvOSYEtG-TuxG66z6haU4out2xmqnUgNOqSLhQE0c_3LUJehGNeWriTIwXM2uECv_8S5i5Q0sM" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="825" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjdYHKv_Kk8Na252sx8xZWLDm8R6_mNKlJL1JJRYlAIOzSXauyyeA6VGeKEsdcbx9EUczSQk-6jdTu3XNJerji8WDXne8E8XV80huzpoe4IGBjvb3sDizvOSYEtG-TuxG66z6haU4out2xmqnUgNOqSLhQE0c_3LUJehGNeWriTIwXM2uECv_8S5i5Q0sM" width="284" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEic8MsyFLCDBh4e9tvz9HrvWRF8uTZtFXbtUHAsw-VsqPcsZYo2lZFf11z0wbvn352d_DvSxpxPTmtj72Z-Y1eIshVRXLjFoPxlGxaJ8OOhIXbqqU5Vd9TyZft4IWoSoyFrE1ZypIw428zscLO8rNtslTAyJWH300Ua5fsOoqGiSfZ1jpVMM0RGcYg4-Jk" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="845" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEic8MsyFLCDBh4e9tvz9HrvWRF8uTZtFXbtUHAsw-VsqPcsZYo2lZFf11z0wbvn352d_DvSxpxPTmtj72Z-Y1eIshVRXLjFoPxlGxaJ8OOhIXbqqU5Vd9TyZft4IWoSoyFrE1ZypIw428zscLO8rNtslTAyJWH300Ua5fsOoqGiSfZ1jpVMM0RGcYg4-Jk" width="277" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgMuF5c78zGHFUvRG2MsXtE7agAjFd9cJlpulIZCPoZfaqIXxvq11fkcVz-s9ieFev8Fig3_4Zyw5Q896baBkouD3LUisb5qGJWOsmJ1cIbbW-DO-vx1x8TlOZt4PoGpZ4DJHoPJWbm9srNkQzl5daTsyFEU2AI2by0AE5zSHZ0tfk7iGMSLn8of7vRheI" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="713" data-original-width="975" height="234" src="https://blogger.googleusercontent.com/img/a/AVvXsEgMuF5c78zGHFUvRG2MsXtE7agAjFd9cJlpulIZCPoZfaqIXxvq11fkcVz-s9ieFev8Fig3_4Zyw5Q896baBkouD3LUisb5qGJWOsmJ1cIbbW-DO-vx1x8TlOZt4PoGpZ4DJHoPJWbm9srNkQzl5daTsyFEU2AI2by0AE5zSHZ0tfk7iGMSLn8of7vRheI" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiszmfa-z29UXMSuqZ4oc8o21Pon9B9wfVqXIjIKALkLAe_c8gTJzm1V9zDiHeQC7vgwxnZZputWQAulJDxPLr2cSaU20JL4cpHEZCGi0lsoC9-Aou9nHCBEm9eSdIyMU7CYW0wX4NmeKm38X5JZFKM2qzpsvQ_EJmtBULXQptTVyAFiNOKtgYMZg6hJf0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="939" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiszmfa-z29UXMSuqZ4oc8o21Pon9B9wfVqXIjIKALkLAe_c8gTJzm1V9zDiHeQC7vgwxnZZputWQAulJDxPLr2cSaU20JL4cpHEZCGi0lsoC9-Aou9nHCBEm9eSdIyMU7CYW0wX4NmeKm38X5JZFKM2qzpsvQ_EJmtBULXQptTVyAFiNOKtgYMZg6hJf0" width="249" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiuTSbsIpCMhhdK8L-MjH2NSBSxmy7GUEWnlBHAJCVc59QrL6FHeddmpLZxTy85OihhJzanXNLgeCIRNklKqpqLvojzoEcz7Ef8dmcp8FEJtx8J046DikPOBex-TdYjz-nYn9-LGcJi2O0yDDrpv5O6igp4MoYtmExIl2CpxlpDm8vLR5gl4yH-e64s_i4" style="margin-left: 1em; margin-right: 1em;"><img alt="Saurabh Microsoftt Fabric" data-original-height="348" data-original-width="975" height="143" src="https://blogger.googleusercontent.com/img/a/AVvXsEiuTSbsIpCMhhdK8L-MjH2NSBSxmy7GUEWnlBHAJCVc59QrL6FHeddmpLZxTy85OihhJzanXNLgeCIRNklKqpqLvojzoEcz7Ef8dmcp8FEJtx8J046DikPOBex-TdYjz-nYn9-LGcJi2O0yDDrpv5O6igp4MoYtmExIl2CpxlpDm8vLR5gl4yH-e64s_i4=w400-h143" title="Sinha Azure AI" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><ul style="text-align: left;"><li>An organization might have data engineers working with Scala/Python and other data engineers working with SQL (Spark SQL or T-SQL), all working on the same copy of the data. Fabric makes it possible for these different groups, with varied experiences and preferences, to work and collaborate. The two different approaches transform and generate business aggregates. You can pick the one suitable for you or mix and match these approaches based on your preference without compromising on the performance:</li><ul><li><b>Approach #1 </b>- Use PySpark to join and aggregate data for generating business aggregates. This approach is preferable to someone with a programming (Python or PySpark) background.</li><li><b>Approach #2</b> - Use Spark SQL to join and aggregate data for generating business aggregates. This approach is preferable to someone with an SQL background, transitioning to Spark.</li></ul></ul><div><br /></div><div><br /></div><div><div><b>Approach #1</b> (sale_by_date_city) - </div><div><ul style="text-align: left;"><li>Use PySpark to join and aggregate data for generating business aggregates. </li><li>With the following code, you create three different Spark dataframes, each referencing an existing delta table. </li><li>Then you join these tables using the dataframes, do group by to generate aggregation, rename a few of the columns, and finally write it as a delta table in the Tables section of the lakehouse to persist with the data.</li><li>In this cell, you create three different Spark dataframes, each referencing an existing delta table.</li><li>Execute the cell by clicking on the Run icon.</li></ul></div><div><br /></div><div><b>PythonCode</b></div><div>/**************************************************/</div><div><span style="background-color: #fcff01;">df_fact_sale = spark.read.table("wwilakehouse.fact_sale")</span></div><div><span style="background-color: #fcff01;">df_dimension_date = spark.read.table("wwilakehouse.dimension_date")</span></div><div><span style="background-color: #fcff01;">df_dimension_city = spark.read.table("wwilakehouse.dimension_city")</span></div><div>/**************************************************/</div></div><div><br /></div><div><div><br /></div><div><ul style="text-align: left;"><li>In this cell, you join these tables using the dataframes created earlier, do group by to generate aggregation, rename a few of the columns, and finally write it as a delta table in the Tables section of the lakehouse.</li><li>Execute the cell by clicking on the Run icon.</li></ul></div><div><br /></div><div><b>PythonCode</b></div><div>/**************************************************/</div><div><span style="background-color: #fcff01;">sale_by_date_city = df_fact_sale.alias("sale") \</span></div><div><span style="background-color: #fcff01;">.join(df_dimension_date.alias("date"), df_fact_sale.InvoiceDateKey == df_dimension_date.Date, "inner") \</span></div><div><span style="background-color: #fcff01;">.join(df_dimension_city.alias("city"), df_fact_sale.CityKey == df_dimension_city.CityKey, "inner") \</span></div><div><span style="background-color: #fcff01;">.select("date.Date", "date.CalendarMonthLabel", "date.Day", "date.ShortMonth", "date.CalendarYear", "city.City", "city.StateProvince", "city.SalesTerritory", "sale.TotalExcludingTax", "sale.TaxAmount", "sale.TotalIncludingTax", "sale.Profit")\</span></div><div><span style="background-color: #fcff01;">.groupBy("date.Date", "date.CalendarMonthLabel", "date.Day", "date.ShortMonth", "date.CalendarYear", "city.City", "city.StateProvince", "city.SalesTerritory")\</span></div><div><span style="background-color: #fcff01;">.sum("sale.TotalExcludingTax", "sale.TaxAmount", "sale.TotalIncludingTax", "sale.Profit")\</span></div><div><span style="background-color: #fcff01;">.withColumnRenamed("sum(TotalExcludingTax)", "SumOfTotalExcludingTax")\</span></div><div><span style="background-color: #fcff01;">.withColumnRenamed("sum(TaxAmount)", "SumOfTaxAmount")\</span></div><div><span style="background-color: #fcff01;">.withColumnRenamed("sum(TotalIncludingTax)", "SumOfTotalIncludingTax")\</span></div><div><span style="background-color: #fcff01;">.withColumnRenamed("sum(Profit)", "SumOfProfit")\</span></div><div><span style="background-color: #fcff01;">.orderBy("date.Date", "city.StateProvince", "city.City")</span></div><div><span style="background-color: #fcff01;">sale_by_date_city.write.mode("overwrite").format("delta").option("overwriteSchema", "true").save("Tables/aggregate_sale_by_date_city")</span></div></div><div>/**************************************************/</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a 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class="separator" style="clear: both;"><b>Approach #2</b> (sale_by_date_employee) - </div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Use Spark SQL to join and aggregate data for generating business aggregates. </li><li>With the following code, you create a temporary Spark view by joining three tables, do group by to generate aggregation, and rename a few of the columns. </li><li>Finally, you read from the temporary Spark view and finally write it as a delta table in the Tables section of the lakehouse to persist with the data.</li><li>In this cell, you create a temporary Spark view by joining three tables, do group by to generate aggregation, and rename a few of the columns.</li><li>Execute the cell.</li></ul></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><b>PythonCode</b></div><div class="separator" style="clear: both;">/**************************************************/</div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">%%sql</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">CREATE OR REPLACE TEMPORARY VIEW sale_by_date_employee</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">AS</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">SELECT</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">DD.Date, DD.CalendarMonthLabel</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">, DD.Day, DD.ShortMonth Month, CalendarYear Year</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">,DE.PreferredName, DE.Employee</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">,SUM(FS.TotalExcludingTax) SumOfTotalExcludingTax</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">,SUM(FS.TaxAmount) SumOfTaxAmount</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">,SUM(FS.TotalIncludingTax) SumOfTotalIncludingTax</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">,SUM(Profit) SumOfProfit</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">FROM wwilakehouse.fact_sale FS</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">INNER JOIN wwilakehouse.dimension_date DD ON FS.InvoiceDateKey = DD.Date</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">INNER JOIN wwilakehouse.dimension_Employee DE ON FS.SalespersonKey = DE.EmployeeKey</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">GROUP BY DD.Date, DD.CalendarMonthLabel, DD.Day, DD.ShortMonth, DD.CalendarYear, DE.PreferredName, DE.Employee</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">ORDER BY DD.Date ASC, DE.PreferredName ASC, DE.Employee ASC</span></div><div class="separator" style="clear: both;">/**************************************************/</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>In this cell, you read from the temporary Spark view created in the previous cell and finally write it as a delta table in the Tables section of the lakehouse.</li><li>Execute the cell by clicking on the Run icon.</li></ul></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><b>PythonCode</b></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">/**************************************************/</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">sale_by_date_employee = spark.sql("SELECT * FROM sale_by_date_employee")</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">sale_by_date_employee.write.mode("overwrite").format("delta").option("overwriteSchema", "true").save("Tables/aggregate_sale_by_date_employee")</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01;">/**************************************************/</span></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjyeNVJ-0kB3m0gsf3O4n-dvT0nU1n_3IDGdlaStSN0CrHcAIvvLae2kCyKMf4DQQhr0qh7BRB_lfzz_uVOM61lZq6dAi4XkW9O1YPKyBaWRylXvceQYE8dvnkHngbDE8eJrmYiT4tG5MscZbbA5SuJe54QACv4jZvpk4YkO7v9s7IwrZzoF8UdjzjfFtg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="underlying Spark pool or cluster details because Fabric provides them through Live Pool." data-original-height="502" data-original-width="975" height="206" src="https://blogger.googleusercontent.com/img/a/AVvXsEjyeNVJ-0kB3m0gsf3O4n-dvT0nU1n_3IDGdlaStSN0CrHcAIvvLae2kCyKMf4DQQhr0qh7BRB_lfzz_uVOM61lZq6dAi4XkW9O1YPKyBaWRylXvceQYE8dvnkHngbDE8eJrmYiT4tG5MscZbbA5SuJe54QACv4jZvpk4YkO7v9s7IwrZzoF8UdjzjfFtg=w400-h206" title="Fabric Pyspark algaestudy" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhaCaxmqhSXlNvcBAFJ0vkSneFvcYwGqFUVeKvfjQzEUEnV8vK0H5GNN5dsFyCKjB7WLEqHpcDlNQKD_GeF6cY87yNcB8cxPG39tmA4DNZPeR6_BnyX0tpQTQ3A7TDBRXdxssM3zRWMZxVuo0gzk4l_KBcodKdR8MullfwdVmZE5bx-7CIQGtQdvph71R4" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Microsoft Fabric Azure AI" data-original-height="283" data-original-width="975" height="186" src="https://blogger.googleusercontent.com/img/a/AVvXsEhaCaxmqhSXlNvcBAFJ0vkSneFvcYwGqFUVeKvfjQzEUEnV8vK0H5GNN5dsFyCKjB7WLEqHpcDlNQKD_GeF6cY87yNcB8cxPG39tmA4DNZPeR6_BnyX0tpQTQ3A7TDBRXdxssM3zRWMZxVuo0gzk4l_KBcodKdR8MullfwdVmZE5bx-7CIQGtQdvph71R4=w640-h186" title="Algae Services" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><span style="font-size: large;">To validate the created tables, right-click on the Tables folder and choose Refresh. The tables appear.</span></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><b>Note</b>: Both approaches produce a similar outcome. You can choose based on your background and preference, to minimize the need for you to learn a new technology or compromise on the performance.</div><div class="separator" style="clear: both;">Also, you may notice that you're writing data as delta lake files. The automatic table discovery and registration feature of Fabric pick up and registers them in the metastore. You don't need to explicitly call CREATE TABLE statements to create tables to use with SQL.</div></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiDttuMLQX2yHdw71aAZQRfZEIWht1mcW8tQ7jeem6BOCocG11aO70y6KXB2OOPQ8E-MYob-F_T_JLqK4sGyIaZh3t0EEbg6Dqf5Bo5WohhgwFxdE9ZQRSGz-gcucLLZN0EZ93XaDdmPRApaon8aL7C7F-XvrUubOw2lVjXmxjovB-HeWEp5vdrdQmflnI" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="underlying Spark pool or cluster details because Fabric provides them through Live Pool." data-original-height="801" data-original-width="975" height="526" src="https://blogger.googleusercontent.com/img/a/AVvXsEiDttuMLQX2yHdw71aAZQRfZEIWht1mcW8tQ7jeem6BOCocG11aO70y6KXB2OOPQ8E-MYob-F_T_JLqK4sGyIaZh3t0EEbg6Dqf5Bo5WohhgwFxdE9ZQRSGz-gcucLLZN0EZ93XaDdmPRApaon8aL7C7F-XvrUubOw2lVjXmxjovB-HeWEp5vdrdQmflnI=w640-h526" title="Algae Study Microsoft Fabric" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhcvDhd7haEeyGZmLmBJ5w9-AWlj50XuUe1Rm5qTtoJlXsG8cDzzUX5KJ0GCk_4QLF_f0sPrFGujo4JaO1e9KM5llCrFbD6bKtXjyrsseGcFt93sC83zT55dJkqdBtAYyybLEqKgdQ66zkC-LL5s6s8S5tH5_IIp8BsSJUEkggB0gJ8reNRDXYMIfMqDwQ" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Microsoft fabric Algae Services" data-original-height="906" data-original-width="975" height="595" src="https://blogger.googleusercontent.com/img/a/AVvXsEhcvDhd7haEeyGZmLmBJ5w9-AWlj50XuUe1Rm5qTtoJlXsG8cDzzUX5KJ0GCk_4QLF_f0sPrFGujo4JaO1e9KM5llCrFbD6bKtXjyrsseGcFt93sC83zT55dJkqdBtAYyybLEqKgdQ66zkC-LL5s6s8S5tH5_IIp8BsSJUEkggB0gJ8reNRDXYMIfMqDwQ=w640-h595" title="underlying Spark pool or cluster details because Fabric provides them through Live Pool." width="640" /></a></div><br /><br /></div><br /><br /><br /></div></div><br /><br /></div><br /><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div></div><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div></div></div></div></div></div></div></div></div></div><ul><li>Microsoft Fabric and Power BI Reports Lab - 5:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></li></ul></ul><p><br /></p>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com05P73+F5X, Bhutnath, Guwahati, Assam 781010, India26.1637329 91.70297780000001426.148325041377873 91.6858116623047 26.179140758622125 91.720143937695326tag:blogger.com,1999:blog-830335965541290967.post-33589968951791545192024-02-10T20:16:00.001+05:302024-02-11T10:42:00.641+05:30Microsoft Fabric - Ingest data into the Lakehouse Lab - 3<p><span></span></p><a name='more'></a><span style="font-size: medium;"><br /></span><p></p><h1 style="text-align: center;"><span style="font-size: x-large;">Ingest data into the Lakehouse using Fabric</span></h1><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><br /></span></p><h2 style="text-align: left;"><span style="font-size: large;">In this exercise, you ingest additional dimensional and fact tables from the Wide World Importers (WWI) into the lakehouse.</span></h2><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><h4 style="clear: both;"><span style="font-size: xx-small;">Microsoft Fabric Labs</span></h4></div></div></div></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Lab -1 for Beginners:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a></span></li></ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Auto Power BI Reports Lab -2:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric and Power BI Reports Lab - 5:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Resource Cleanup in Lab -6 </span></li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html"><span style="font-size: xx-small;">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</span></a></li></ul></ul></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="text-align: left;"><span style="font-size: large;">Task 1: Ingest data</span></h3><p><span style="font-size: medium;">In this task, you use the Copy data activity of the Data Factory pipeline to ingest sample data from an Azure storage account to the Files section of the lakehouse you created earlier.</span></p><p><span style="font-size: medium;">Now, click on Fabric Lakehouse Tutorial-XX on the left-sided navigation pane.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="1350" data-original-width="826" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEgXPqM47DUmzoS-AI5FCfuWiaPJNdXjczeYcPujV-Dee2fN17gGQpcezB7qiJiLJL4KTqu5lGcmuGx0_GymnLRFRn8u4064I8Dy5_wZRigMFd_3YYhkBohxxHEgjbmCDxTA9JWpbl6nSBmRH7wT0lgzo1imNjxGyWx5ASFVoxDmRNI82Be3vUDSdNGxD3o=w245-h400" width="245" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">In the Fabric Lakehouse Tutorial-XX workspace page, click on the drop-down arrow in the +New button, then select Data pipeline .</span></li><li><span style="font-size: medium;">In the New pipeline dialog box, specify the name as IngestDataFromSourceToLakehouse and select Create. A new data factory pipeline is created and opened</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: left; float: left; font-size: medium; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="563" data-original-width="821" height="274" src="https://blogger.googleusercontent.com/img/a/AVvXsEgO-2NA56oM4pwksgnPuBiMu7bgirY7Hnvpt13Z4I4mDkK5M0PrN6Ztd6ZWVbOgu86v3BcSPtJoi4rtq7T2Z1YJb2hqFwR6HeSv8a_kKCrYYGFurXBCst_FxNpZSYvIM02zewr3EFZjTmqQ7FjoGD_9PEG3AcISvMWvQAv5DPMV4VcIXxAxoKdxtGumqDQ=w400-h274" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="500" data-original-width="647" height="247" src="https://blogger.googleusercontent.com/img/a/AVvXsEhQqm9_astaZK9C4DOV8oKaJGuKVRrhA4KMBiNCS4bZdgWc0ZIA1qEqPECf7piqt2D2X9qbwakf49tDeMGYI0UHAd3fDJ72iLUKQqTTvV3GoSHgp9iX2iQR_l60hqCpsur83W7OmxY8SIRbXO7-Uqg7-R1qebKK_2gp3d332CYHvREjfRzdivOILLL3GTc=w320-h247" width="320" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: left; float: left; font-size: medium; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="474" data-original-width="805" height="235" src="https://blogger.googleusercontent.com/img/a/AVvXsEiVv63w0SGXAzdpQqGNt93OkoM0QAjUdsQEEvCNa9wrlv9PBhIPfGH3RS0bBYBDmsJvylKROyubYiVniDS_brckkGvRyRGuQSNvwrOZXj_vO7KJucl1dqHbI5sRXSVTO26CuSuPzlNH4mzJ9lkYNeWLCGmF9evUG9YTxxTTnN9e4Zhk1icG9VRB-DK4Hyo=w400-h235" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">On newly created data factory pipeline i.e IngestDataFromSourceToLakehouse, select Add pipeline activity to add an activity to the pipeline and select Copy data. </span></li><li><span style="font-size: medium;">This action adds copy data activity to the pipeline canvas.</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="650" data-original-width="893" height="291" src="https://blogger.googleusercontent.com/img/a/AVvXsEiBWHpsYgx3Q70v55peNM4TWXhq5auIyhmpXdVFWrPPgQxWi4zau2-X1XKddfXN8MeJTyG4aLZE1QbFrN9FJlBmUG0HVviyhHYya8hyeVscRLEVdaWyrSaKWY5d_Forv1R0WHsS6SUIY18iNKnuEZIew_IPadzWwjguVEo_weVvzaIDLoppwdIxJmwrsg8=w400-h291" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">Select the newly added copy data activity from the canvas. </span></li><li><span style="font-size: medium;">Activity properties appear in a pane below the canvas. </span></li><li><span style="font-size: medium;">Select Expand(upward arrow) in the Properties bar as in the below Screenshot.</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg6byfnDbiKSDVVwYZHwct3sw0nd_rFhrKP_AFjenvCKt5JdYnGNg2p4Jzs38MCz89W_bfCB8IfLjlb8HOOvCmCBczuOE5IQwwr0O2W5Umf6-cjraFQ_b5URKGL7UT2bxLQf1MWSOHZ6_6nFl25ea3myhzZaT0JxjudvZw4vQwh6qXzw5YldpinHZozGKY" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img data-original-height="829" data-original-width="975" height="340" src="https://blogger.googleusercontent.com/img/a/AVvXsEg6byfnDbiKSDVVwYZHwct3sw0nd_rFhrKP_AFjenvCKt5JdYnGNg2p4Jzs38MCz89W_bfCB8IfLjlb8HOOvCmCBczuOE5IQwwr0O2W5Umf6-cjraFQ_b5URKGL7UT2bxLQf1MWSOHZ6_6nFl25ea3myhzZaT0JxjudvZw4vQwh6qXzw5YldpinHZozGKY=w400-h340" width="400" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">Under the General tab in the properties pane, specify the name for the copy data activity as Data Copy to Lakehouse .</span></li><li><span style="font-size: medium;">Under Source tab of the selected copy data activity, select External as Data store type and then select + New to create a new connection to data source.</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: left; float: left; font-size: medium; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="713" data-original-width="671" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEgG5D70jsiPkC15rkjgiXbjxsO7w3BnQ-owdy8bNRnK2PVeb_FmjcUk3707GXuL8Syf867tuYOGGL2msD16Rj6ff-mNPHsuggKud1IIenvtlcQps5viUWwxbXfcLNGCrVSJk725m7dMc3WncojP9GJHgAK_7F02Xg9AOaTKFOVba7pYbuglia3XsTPrgWI=w377-h400" width="377" /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgDX5CCHWZ8m-v4T1KsLXHUjXl1Fz82nvwN_UoiNY9nXdTKrvSs7hrco70J2F3ZniFjt6htvnzN0kc6ISeNkpQjig4gbWIbVhRMEUFrdM98rFNPOtivuhtHYj-05nI9gGbx1OOfEUFMs4pO_71_x9VdVMTETmeEfSAogrKqbm3vzeBO3zfJEa9HspJQpuc" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img data-original-height="649" data-original-width="832" height="312" src="https://blogger.googleusercontent.com/img/a/AVvXsEgDX5CCHWZ8m-v4T1KsLXHUjXl1Fz82nvwN_UoiNY9nXdTKrvSs7hrco70J2F3ZniFjt6htvnzN0kc6ISeNkpQjig4gbWIbVhRMEUFrdM98rFNPOtivuhtHYj-05nI9gGbx1OOfEUFMs4pO_71_x9VdVMTETmeEfSAogrKqbm3vzeBO3zfJEa9HspJQpuc=w400-h312" width="400" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">For this task, all the sample data is available in a public container of Azure blob storage. You connect to this container to copy data from it. </span></li><li><span style="font-size: medium;">On the New connection wizard, select Azure Blob Storage and then select Continue.</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg0_iBGOaI0n1oysv6dWwZsvaG5RbPRINqSRfKlbpKMsoJqEeH8bogtsCKudQUmlDUvU3t-988fpVzr_oHwjKjDmAXWSEjQq4b9NEpQMw1_aWLg6mqazEhqBD8ZC4dPOGj1yFOjC92zcwIuvRKR1RsYaj8HDwaviMe2Xhiq3Vw3pZvi6ZVPV6nGDm5X-x8" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img data-original-height="481" data-original-width="975" height="316" src="https://blogger.googleusercontent.com/img/a/AVvXsEg0_iBGOaI0n1oysv6dWwZsvaG5RbPRINqSRfKlbpKMsoJqEeH8bogtsCKudQUmlDUvU3t-988fpVzr_oHwjKjDmAXWSEjQq4b9NEpQMw1_aWLg6mqazEhqBD8ZC4dPOGj1yFOjC92zcwIuvRKR1RsYaj8HDwaviMe2Xhiq3Vw3pZvi6ZVPV6nGDm5X-x8=w640-h316" width="640" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><b>On the next screen of the New Connection wizard, enter the following details and select Create to create the connection to the data source.</b></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div></div></div></div></div></div></div></div></div></div><p></p><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-yfti-tbllook: 1184;">
<thead>
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<td style="border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; padding: 6pt 9pt;">
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0in; text-align: center;"><b><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Property<o:p></o:p></span></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 6pt 9pt;">
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0in; text-align: center;"><b><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Value<o:p></o:p></span></span></b></p>
</td>
</tr>
</thead>
<tbody><tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Account name or
URI<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-size: medium;"><span style="background: rgb(239, 239, 239); font-family: Consolas;">https</span><span style="background: rgb(239, 239, 239); color: #666600; font-family: Consolas;">:</span><span style="background: rgb(239, 239, 239); color: #880000; font-family: Consolas;">//azuresynapsestorage.blob.core.windows.net/sampledata</span><span style="font-family: "Times New Roman", serif;"><o:p></o:p></span></span></p>
</td>
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<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Connection<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Create new
connection<o:p></o:p></span></span></p>
</td>
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<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Connection name<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-size: medium;"><span style="background: rgb(239, 239, 239); font-family: Consolas;">wwisampledata</span><span style="font-family: "Times New Roman", serif;"><o:p></o:p></span></span></p>
</td>
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<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Authentication
kind<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Anonymous<o:p></o:p></span></span></p>
</td>
</tr>
</tbody></table><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="472" data-original-width="597" height="316" src="https://blogger.googleusercontent.com/img/a/AVvXsEhYbLN35Lm9pGlNXnOBMeHpFNHP3QJrtdWttjGTCGRtOaZ6YXKirSz5J3LOpr_QluhGKs7tZvFLMqEe0ePDc2CvVyzEIqQ2q55yrtJb_ly0WAzXabSCz3qNzyuHQ6yAMWlzGeZmXUzHNhaOlbGngQP7EGCyh6cdLXeXBOPCO35ZjnQnJvhq_7jLi2JKMTA=w400-h316" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><b>Once the new connection is created, return to the Source tab of the copy data activity, and the newly created connection is selected by default. Specify the following properties before moving to the destination settings.</b></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 0.5in; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-yfti-tbllook: 1184;">
<thead>
<tr>
<td style="border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; padding: 6pt 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Property<o:p></o:p></span></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 6pt 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Value<o:p></o:p></span></span></b></p>
</td>
</tr>
</thead>
<tbody><tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Data store type<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">External<o:p></o:p></span></span></p>
</td>
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<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Connection<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">wwisampledata<o:p></o:p></span></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">File path type<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">File path<o:p></o:p></span></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">File path<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-size: medium;"><span style="font-family: "Times New Roman", serif;">Container name
(first text box): </span><span style="background: rgb(239, 239, 239); font-family: Consolas;">sampledata</span><span style="font-family: "Times New Roman", serif;"><o:p></o:p></span></span></p>
</td>
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<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">File path<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-size: medium;"><span style="font-family: "Times New Roman", serif;">Directory name
(second text box): </span><span style="background: rgb(239, 239, 239); color: #660066; font-family: Consolas;">WideWorldImportersDW</span><span style="background: rgb(239, 239, 239); color: #666600; font-family: Consolas;">/</span><span style="background: rgb(239, 239, 239); font-family: Consolas;">parquet</span><span style="font-family: "Times New Roman", serif;"><o:p></o:p></span></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Recursively<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Checked<o:p></o:p></span></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">File Format<o:p></o:p></span></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt; width: 102.6pt;" width="137">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Binary<o:p></o:p></span></span></p>
</td>
</tr>
</tbody></table></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="582" data-original-width="805" height="289" src="https://blogger.googleusercontent.com/img/a/AVvXsEh8r7MNhB5lnaLISpG2t2E_Vp_8a_MrJw-euZ2V32g18mKgb7GqvYItjko79VggjERj7TAFYAB-QsOzY2XRLlt2JG8-tQ6t99JEvBMwknpAgS0ucPHP6Wmj4MX39DBlD1eAJulyHbkqPfrfYWXETMZtXHwg1kPhMScNghUmzdt4ffx4kjdD2qbNtpZUjVg=w400-h289" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><b>Under the Destination tab of the selected copy data activity, specify the following properties:</b></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 0.5in; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-yfti-tbllook: 1184;">
<thead>
<tr>
<td style="border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; padding: 6pt 9pt;">
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0in; text-align: center;"><b><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Property<o:p></o:p></span></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 6pt 9pt;">
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0in; text-align: center;"><b><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Value<o:p></o:p></span></span></b></p>
</td>
</tr>
</thead>
<tbody><tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Data store type<o:p></o:p></span></span></p>
</td>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Workspace<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Workspace data
store type<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Lakehouse<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Lakehouse<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">wwilakehouse<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Root Folder<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Files<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">File path<o:p></o:p></span></span></p>
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<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 9pt;">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-size: medium;"><span style="font-family: "Times New Roman", serif;">Directory name
(first text box): </span><span style="background: rgb(239, 239, 239); font-family: Consolas;">wwi</span><span style="background: rgb(239, 239, 239); color: #666600; font-family: Consolas;">-</span><span style="background: rgb(239, 239, 239); font-family: Consolas;">raw</span><span style="background: rgb(239, 239, 239); color: #666600; font-family: Consolas;">-</span><span style="background: rgb(239, 239, 239); font-family: Consolas;">data</span><span style="font-family: "Times New Roman", serif;"><o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">File Format<o:p></o:p></span></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: "Times New Roman", serif;"><span style="font-size: medium;">Binary<o:p></o:p></span></span></p>
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</tbody></table></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="668" data-original-width="927" height="289" src="https://blogger.googleusercontent.com/img/a/AVvXsEiUGhf1Y2hogjDlHQM-hBs9yMOlx91gQ5XUxApKP3GU3IwNac6OQo8PerVGcvVY3-eLPN7HD4EsZwUpqsFAz5jj5tv6Is0k0pq2mCoa6WG7VCZQIp4Thg6GWIhntbQNvdjDwRclIHPNzGEDyHsBRAlpESJYOFkVw3CAC8IloeQoiemhmbyChatKIG6dCj8=w400-h289" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">You have finished configuring the copy data activity. Select the Save button on the top ribbon (under Home) to save your changes.</span></li><li><span style="font-size: medium;">You will see a notification stating Saving is completed.</span></li><li><span style="font-size: medium;">In the IngestDataFromSourceToLakehouse page select Run to execute your pipeline and its activity.</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEht2jZj21w_ihCwqym4bdtjlLwX40safWNAa1wt_xGOVp2_BNbc_KoBsUi6Zq9S-dSngq74nED5mbCQrVzb04QLX-riVl-prvctzOZZ9bit2HkiP2_pnL41uQdQ3mxKTeDGKWPxvcL9190GJPtT-7-lm39xPaDQ1ED1BKK_IZzjPTqvtAfoly1GP5MNzI0" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img data-original-height="695" data-original-width="713" height="390" src="https://blogger.googleusercontent.com/img/a/AVvXsEht2jZj21w_ihCwqym4bdtjlLwX40safWNAa1wt_xGOVp2_BNbc_KoBsUi6Zq9S-dSngq74nED5mbCQrVzb04QLX-riVl-prvctzOZZ9bit2HkiP2_pnL41uQdQ3mxKTeDGKWPxvcL9190GJPtT-7-lm39xPaDQ1ED1BKK_IZzjPTqvtAfoly1GP5MNzI0=w400-h390" width="400" /></span></a> </div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="343" data-original-width="518" height="212" src="https://blogger.googleusercontent.com/img/a/AVvXsEhJAsJ4sL_C0hSrzNgyNGwEwbzYx-I4JvKF_9p0Sp25xVdLgGAPj3FtRcabquyJ_4YtQRocUmNxd47CR-2QwRD5OUgOm1FEQOpOs_4iSE9Bio1Lw8t7zIl573l0wXOp3rStUbpSEgU1JWyUiJ7Dknh3OcerKq8XaJsNQo_Vwm3RF7T6S9JERY5gkJWLm3k" width="320" /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: left; float: left; font-size: medium; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="683" data-original-width="659" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEgjULCNN5AEpxkcIqOoINt-MkMKCZ3D-yQ1Q6NqbCL7NQvhDnL9bxWvHJ0oUcMEiyNBjR-1GjiRbRbNiTaDfZbP_r7r_wQjMhJ-7FqqO1rnDYd80UprNY3Dj-InulFi0I6VVZ25CcLBB-RrULeWMqX3E2e_QscxDkvCjwce8LZOq2Q2Hl7Y-2ImZyH3EA0=w387-h400" width="387" /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><span style="font-size: medium;"><ul style="text-align: left;"><li><span style="font-size: medium;">This action triggers data copy from the underlying data source to the specified lakehouse and might take up to a minute to complete. </span></li><li><span style="font-size: medium;">You can monitor the execution of the pipeline and its activity under the Output tab, which appears when you click anywhere on the canvas.</span></li><li><span style="font-size: medium;">Under the Output tab, hover your mouse to Data Copy to Lakehouse row, select Data Copy to Lakehouse to look at the details of the data transfer. After seeing the Status as Succeeded, click on the Close button.</span></li></ul></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: left; float: left; font-size: medium; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="579" data-original-width="975" height="238" src="https://blogger.googleusercontent.com/img/a/AVvXsEjb0MbLP7OBrfHPauNaNV8kDk2x-vJ1kh3hJpkNkw9f18LglWWW6knOHIU7XVYP1k5lQsBgTJQDHJg7KtemIwiUnfaQb5RHwNDwUZnW9Ek3xfipm0QtLi2REcg9h-NKxoxVcAMaGdOoxGJkcohTV1CmMN-hUb7W5cutkJfQu1z40KseB4s1upaZ1tF_Yrc=w400-h238" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="508" data-original-width="975" height="209" src="https://blogger.googleusercontent.com/img/a/AVvXsEi3jsufLCK39nRW-i2qA0R8XwnTZRUOIrNSjE1FC3eSCWQrLV1LRnQ5T3zVqJ68f_D8r85LEyjbBgjULVsK_DArvw92SDnbNcNykRssoU59LHVqky_jj8gI4oYwG_chuNG7M40URh1gIW_5ZehNdu4zaKQPmsV4P0QbO6DvBB4q1TFvwPQqsmBVNLMBC84=w400-h209" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="clear: left; float: left; font-size: medium; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="508" data-original-width="975" height="209" src="https://blogger.googleusercontent.com/img/a/AVvXsEgJrENB0VKvcbeQ02HHYPuggvtIVQaLSS0NLzdraWK1Km3MkHLRPG0PgGEPKpi9wq-ATtrZ5AM8kc8X2Abhp-ZzByfkZOi_psaQTiX5ZPBOelSL7SpaOM8FOBjWr1oP9oYquZyU8aYOc1G86lCC4sUPUGdBUTH8ajwBZLIQ8wbOh4sEnTFoSluaFNv2KMc=w400-h209" width="400" /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: right; float: right; font-size: medium; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="1058" data-original-width="975" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEhDaWfd82Zy8-2oWxhOjAfUSxiCV3MWu7ZEfxWhTKfoBMOyn9AckuPujAtIE5JSpQz5KBguyH8r44cfoL5_yfSNHQpvwG2IirCzJfst6Pp9We3-PiHGHH4W2EJ7MYTGxNFgRf9zlw0PlZltYzxdyW8Go5Wgvy5t-HuiR01tVb8GKDdNJaggn-HMQFxiyqU=w368-h400" width="368" /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="clear: left; float: left; font-size: medium; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="690" data-original-width="975" height="452" src="https://blogger.googleusercontent.com/img/a/AVvXsEgpakVZhKXK0sF4bcH7BcD6uI59QsYQnl589evS_aSruL_YdQkEL-i2YdPh6_5e5GkPRt9mIItXPIEKOfebDXH-vmbtyvpl1n5HdeIof39KT3X_i0So1wcM8HbnM5EXbLj6sAQ0AnzdNcqImvQp7G9zQtfmDWiai4zCmqjoqdlRcFTmfuqXYHaYSxN-6xs=w640-h452" width="640" /></span></div><span style="font-size: medium;"><br /><br /></span></div><div style="text-align: left;"><span style="font-size: medium;"><br /></span></div><span style="font-size: medium;"><br /></span></div><span style="font-size: medium;"><br /><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">Now, click on Fabric Lakehouse Tutorial-XX on the left-side navigation pane and select your new lakehouse (wwilakehouse) to launch the Lakehouse explorer as shown in the below image.</span></li><li><span style="font-size: medium;">Validate that in the Lakehouse explorer view, a new folder wwi-raw-data has been created. Now expand the wwi-raw-date select full folder then select fact_sale_1y_full and data for all the files have been copied there.</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; font-size: large; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjwI86HPNybMckBgba5bmDvK5RSM2qmlPudZ6daFJYbbY79t2_bPlKr4RwMtnA9Qrvy6Agj42Jt9kcwtAgIBmTmtc_Chlh55KLUXrKJIuWGDo7gXm9ds22VKiKZtROki9q1KRdFT5HwKMfYYGiW1VRzjSFuXwdMzhqnQseWlKzasGx0p37c0r2cOr1YkT8" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="817" data-original-width="975" height="336" src="https://blogger.googleusercontent.com/img/a/AVvXsEjwI86HPNybMckBgba5bmDvK5RSM2qmlPudZ6daFJYbbY79t2_bPlKr4RwMtnA9Qrvy6Agj42Jt9kcwtAgIBmTmtc_Chlh55KLUXrKJIuWGDo7gXm9ds22VKiKZtROki9q1KRdFT5HwKMfYYGiW1VRzjSFuXwdMzhqnQseWlKzasGx0p37c0r2cOr1YkT8=w400-h336" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; font-size: large; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhKijwUC0cpyQgjfSvtpwAfcdcpaXwdZsW6iTcD0YW32A7bzRq3kuXzGBLCOTOaVV1w-dEJJlXXOE4m5f8Sh8ih-Vgc0JAeWTppnK4fhUB25Bqr1-vggYYGUCzCLxntoGX9RS5IFZi0V2pRxKl_yUjEqru4f4OsP3_spC8oRuVQxtiyWP4j3i1pgPiSQgQ" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="642" data-original-width="975" height="264" src="https://blogger.googleusercontent.com/img/a/AVvXsEhKijwUC0cpyQgjfSvtpwAfcdcpaXwdZsW6iTcD0YW32A7bzRq3kuXzGBLCOTOaVV1w-dEJJlXXOE4m5f8Sh8ih-Vgc0JAeWTppnK4fhUB25Bqr1-vggYYGUCzCLxntoGX9RS5IFZi0V2pRxKl_yUjEqru4f4OsP3_spC8oRuVQxtiyWP4j3i1pgPiSQgQ=w400-h264" width="400" /></a></div><div class="separator" style="clear: both; font-size: large; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhNl3_Rynuk6BUrfrMHPL6qV-iQy4wu_n6O2f01f12VNvnYl6EcMPPwaRQDHR4D-Lys3i6w1EjipcIEGZLku6OZ6F54he83S1pJ6gQ9vp1at6zdbfJ8LaIjJm6cEGOfeEJpHsfVtiAToQumpirsHaSHZk4JFzOoSCABYI9IK5tylI7oor6gLNQ0d5AS1Wk" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="536" data-original-width="975" height="352" src="https://blogger.googleusercontent.com/img/a/AVvXsEhNl3_Rynuk6BUrfrMHPL6qV-iQy4wu_n6O2f01f12VNvnYl6EcMPPwaRQDHR4D-Lys3i6w1EjipcIEGZLku6OZ6F54he83S1pJ6gQ9vp1at6zdbfJ8LaIjJm6cEGOfeEJpHsfVtiAToQumpirsHaSHZk4JFzOoSCABYI9IK5tylI7oor6gLNQ0d5AS1Wk=w640-h352" width="640" /></a></div><br /></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: x-large;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: x-large;">Now data is Ready for Further Consumption</span></div><div class="separator" style="clear: both; font-size: large; text-align: center;"><br /></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><p><span style="font-size: medium;"></span></p><ul><li>Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></li></ul></ul>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com09P4G3GM5+W652.0847893 110.508052239.435437434043578 92.9299272 64.734141165956416 128.0861772tag:blogger.com,1999:blog-830335965541290967.post-78290093972932932852024-02-10T19:10:00.001+05:302024-02-11T10:41:10.850+05:30Azure Microsoft Fabric - Auto Power BI Reports Lab -2<p></p><div><span><a name='more'></a></span><br /></div><h1 style="text-align: center;">Automatic Report Creation in MS Fabric</h1><div><br /></div><div><br /></div><div><br /></div><div><span style="font-size: medium;">To build the Aut report we will continue from <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html" rel="nofollow" target="_blank">Lab-1</a> "<a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a>". So our Data set is ready</span></div><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><br /></span></div><div><span><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><h4 style="clear: both;"><span style="font-size: xx-small;">Microsoft Fabric Labs</span></h4></div></div></div></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Lab -1 for Beginners:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a></span></li></ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Auto Power BI Reports Lab -2:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric and Power BI Reports Lab - 5:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Resource Cleanup in Lab -6 </span></li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html"><span style="font-size: xx-small;">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</span></a></li></ul></ul></div></div></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: xx-small;"><br /></span></div><div class="separator" style="clear: both; font-size: large;"><br /></div><div class="separator" style="clear: both; font-size: large;"><br style="font-size: medium;" /></div></span></div><div><span style="font-size: medium;"><br /></span></div><h2 style="text-align: left;"><span style="font-size: large;">Steps to Building the Report</span></h2><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: large;">Click on Fabric Lakehouse Tutorial-XX on the left-sided navigation pane.<br /></span><div><span style="font-size: large;"><br /></span></div><div></div></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="font-size: large;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjfEKHW84s-npRh_CTmw2jIIZq3bmhdf8KqcAdjzi1SOPnxR262Q_uwQytiWEs4Xgd_PBVkyKkPhonp-2AS67EdPR484REMC7oD9zSiCHGeGIXNSCYT29Kj_3fnVMWANkdX8wGQm9U3Cv2u9ZTMVkSVBoZioezfOBbIEkwlT5pD5QQh_tyGBKnGYtaeImI" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-size: large;"><img data-original-height="1178" data-original-width="876" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEjfEKHW84s-npRh_CTmw2jIIZq3bmhdf8KqcAdjzi1SOPnxR262Q_uwQytiWEs4Xgd_PBVkyKkPhonp-2AS67EdPR484REMC7oD9zSiCHGeGIXNSCYT29Kj_3fnVMWANkdX8wGQm9U3Cv2u9ZTMVkSVBoZioezfOBbIEkwlT5pD5QQh_tyGBKnGYtaeImI=w475-h640" width="475" /></span></a></div><span style="font-size: large;"><br /></span><p style="clear: both; text-align: center;"><span style="font-size: large;"><br /></span></p><p style="clear: both; text-align: center;"><span style="font-size: large;"><br /><span style="text-align: left;"><br /></span></span></p><div style="text-align: justify;"><span style="font-size: large;">In the Fabric Lakehouse Tutorial-XX view, select wwilakehouse of Type Semantic model(default).</span></div><p></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: large;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhoUnLO-x_9KskSWDJqMuXFp7LEiwQhP7One88zo287mo19yn4JKt1xdD9oJg7z4vvolNCqUOnPDTQ4woOEkORrb34SaHyeINWSGfYeiS0P8iOPvL2R_U1G9yLFjC9O_4Nu5wfFXoxwun_WoXrcC2OWBess1mU_Nhfp0y2Tiji_9L_ipGr0eFndambgjBQ" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: right;"><span style="font-size: large;"><img data-original-height="383" data-original-width="975" height="252" src="https://blogger.googleusercontent.com/img/a/AVvXsEhoUnLO-x_9KskSWDJqMuXFp7LEiwQhP7One88zo287mo19yn4JKt1xdD9oJg7z4vvolNCqUOnPDTQ4woOEkORrb34SaHyeINWSGfYeiS0P8iOPvL2R_U1G9yLFjC9O_4Nu5wfFXoxwun_WoXrcC2OWBess1mU_Nhfp0y2Tiji_9L_ipGr0eFndambgjBQ=w640-h252" width="640" /></span></a><span style="font-size: large;"> </span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><span style="font-size: large;"><br /></span></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: large;"><span style="text-align: left;"><br /></span></span></div><div class="separator" style="clear: both; text-align: justify;"><span style="font-size: large;"><span style="text-align: left;"> </span><span style="text-align: left;">This dataset is automatically created and has the same name as the lakehouse.</span></span></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><ul><li style="text-align: justify;"><span style="text-align: left;"><span style="font-size: large;">From the semantic model pane, you can view all the tables. You have options to create reports either from scratch, paginated report or let Power BI automatically create a report based on your data. </span></span></li><li style="text-align: justify;"><span style="text-align: left;"><span style="font-size: large;">For this task, navigate to the Discover business insights section, then click on Explore this data and select Auto-create a report as shown in the below image.</span></span></li></ul></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhoUnLO-x_9KskSWDJqMuXFp7LEiwQhP7One88zo287mo19yn4JKt1xdD9oJg7z4vvolNCqUOnPDTQ4woOEkORrb34SaHyeINWSGfYeiS0P8iOPvL2R_U1G9yLFjC9O_4Nu5wfFXoxwun_WoXrcC2OWBess1mU_Nhfp0y2Tiji_9L_ipGr0eFndambgjBQ" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><br /></span></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjvZT8O-qpVJ5brdHTT_iNNA84DYzxIdn9Ep24qkM6mzb8dspkgsJ7SGaVE6D3D403rSlgCMcVxuNC6IxNQFtytZZnC-qFKt4zssVpZhXfniYlTOZ4j8Gr2QoKYyNFGYXWIT9JdqIdc9nh3MNXCp5kJ-S9c0M17XI4cNFy7OC15pSDQ3_zC0m3gC8YILB8" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><img data-original-height="544" data-original-width="975" height="358" src="https://blogger.googleusercontent.com/img/a/AVvXsEjvZT8O-qpVJ5brdHTT_iNNA84DYzxIdn9Ep24qkM6mzb8dspkgsJ7SGaVE6D3D403rSlgCMcVxuNC6IxNQFtytZZnC-qFKt4zssVpZhXfniYlTOZ4j8Gr2QoKYyNFGYXWIT9JdqIdc9nh3MNXCp5kJ-S9c0M17XI4cNFy7OC15pSDQ3_zC0m3gC8YILB8=w640-h358" width="640" /></span></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjvZT8O-qpVJ5brdHTT_iNNA84DYzxIdn9Ep24qkM6mzb8dspkgsJ7SGaVE6D3D403rSlgCMcVxuNC6IxNQFtytZZnC-qFKt4zssVpZhXfniYlTOZ4j8Gr2QoKYyNFGYXWIT9JdqIdc9nh3MNXCp5kJ-S9c0M17XI4cNFy7OC15pSDQ3_zC0m3gC8YILB8" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><br /></span></a><div class="separator" style="clear: both; color: black;"><span style="font-size: large;"><br /></span></div><div class="separator" style="clear: both; color: black;"><div style="text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: large;">Expand dimension_customer, check the box next to BuyingGroup, and check the box next to wwwCustomerID .<br /><ul style="text-align: left;"><li><span style="font-size: large;">Since the table is a dimension and there are no measures in it, Power BI creates a measure for the row count aggregates it across different columns, and creates different charts as shown in the following image.</span></li></ul><br /></span></div></div><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjvZT8O-qpVJ5brdHTT_iNNA84DYzxIdn9Ep24qkM6mzb8dspkgsJ7SGaVE6D3D403rSlgCMcVxuNC6IxNQFtytZZnC-qFKt4zssVpZhXfniYlTOZ4j8Gr2QoKYyNFGYXWIT9JdqIdc9nh3MNXCp5kJ-S9c0M17XI4cNFy7OC15pSDQ3_zC0m3gC8YILB8" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><br /></span></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh_d9OcPQOn6UG8kt8cLIbu6MXDkCTFE2trclh_BQfUNUkNgfka1tnEk5Fy7M_rsm8Ee9VVozfFNEhdsux-aYQr9QUS7o2dB78Evil31effUFkQn2RIpCTX8jsweAIcnRMo1bATX8vtn9MY1POl-h235cW-UMRhPBmAN_E0MYgQllESqbqjUlhpG7GNt58" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><img data-original-height="476" data-original-width="975" height="312" src="https://blogger.googleusercontent.com/img/a/AVvXsEh_d9OcPQOn6UG8kt8cLIbu6MXDkCTFE2trclh_BQfUNUkNgfka1tnEk5Fy7M_rsm8Ee9VVozfFNEhdsux-aYQr9QUS7o2dB78Evil31effUFkQn2RIpCTX8jsweAIcnRMo1bATX8vtn9MY1POl-h235cW-UMRhPBmAN_E0MYgQllESqbqjUlhpG7GNt58=w640-h312" width="640" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjPE8s4Ipm_MuxzGahUnamDp0RbpyOc1QQkMkMWfnmEjTKxjjiUZ4kS4g1cYaadNHrVmU0xiExG0L3rP1qd-daBM14tDzvNWa1zh9XmMHAjkbYu61xb2JiAz38dht_Ow9Xt-ir-LFrmhBWvBgD87M67P9pf5V9TXXhTMcSNAhqqyoqinezFf_UrdnOmQUI" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><img data-original-height="482" data-original-width="975" height="316" src="https://blogger.googleusercontent.com/img/a/AVvXsEjPE8s4Ipm_MuxzGahUnamDp0RbpyOc1QQkMkMWfnmEjTKxjjiUZ4kS4g1cYaadNHrVmU0xiExG0L3rP1qd-daBM14tDzvNWa1zh9XmMHAjkbYu61xb2JiAz38dht_Ow9Xt-ir-LFrmhBWvBgD87M67P9pf5V9TXXhTMcSNAhqqyoqinezFf_UrdnOmQUI=w640-h316" width="640" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><span style="font-size: large;"><br /><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: large;">Save this report for future use by selecting Save at the top ribbon.</span></li><li><span style="font-size: large;">You will see a notification stating Report saved.</span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: large;"><img data-original-height="474" data-original-width="645" height="470" src="https://blogger.googleusercontent.com/img/a/AVvXsEi7HxkIjGzS-T1n7oDqUm0cED6SF6Vi7qHrX2zTMLbxxVLZKvjdEqmZBCJomHvxLZthbvy6I-VIzMJ_DbOuYOD6_aqI_6eUcmh-P8cliqlPvxDprL3-w-v6A8LDyU13Z-0w30aUosfwZp1XCDI5CJlasS97DB3xQKmSRLikLwHBatcw3FpnNUDiinw_6d0=w640-h470" width="640" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: black; text-align: left;"><span style="font-size: large;"><br /></span></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: large;"><span style="color: black; text-align: left;">You will see a notification stating Report saved.</span><ol style="color: black; display: inline; text-align: left;"><li style="display: inline;"><div class="separator" style="clear: both; text-align: center;"><div style="text-align: left;"><br /></div></div></li><li style="display: inline;"><div style="text-align: left;"><br /></div></li></ol></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjmwaPx_6LCtjxn_JqM8Vfnq5aucyp_r-pSPlGV46zToR70aL_oFw5CWeRUwQOxyokpywU4hrYUVltniCB2Ubl8Z-dBel66jpIgPIIX8e6zWg2MT-IrgDzDaG5IKQC-UBBPXXZa0FgXNud2PlBQoSEsg_Jh5Q4QYg1_KvB9-K-jB4lfvq7d7pxj0sSNN-o" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><img data-original-height="488" data-original-width="665" height="470" src="https://blogger.googleusercontent.com/img/a/AVvXsEjmwaPx_6LCtjxn_JqM8Vfnq5aucyp_r-pSPlGV46zToR70aL_oFw5CWeRUwQOxyokpywU4hrYUVltniCB2Ubl8Z-dBel66jpIgPIIX8e6zWg2MT-IrgDzDaG5IKQC-UBBPXXZa0FgXNud2PlBQoSEsg_Jh5Q4QYg1_KvB9-K-jB4lfvq7d7pxj0sSNN-o=w640-h470" width="640" /></span></a></div><span style="font-size: large;"><br /><br /></span></div><span style="font-size: large;"><br /><br /></span></div><span style="font-size: large;"><br /><br /></span></div><span style="font-size: large;"><br /><br /></span></div><span style="font-size: large;"><br /><br /></span></div><span style="font-size: large;"><br /><br /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="font-size: large;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><b><span style="font-size: large;">Now you can use this report to share users just like another Power BI</span></b></div><div class="separator" style="clear: both; text-align: left;"><b><span style="font-size: large;"><br /></span></b></div><div class="separator" style="clear: both; text-align: left;"><ul><li><span style="font-size: xx-small;">Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></span></li></ul></ul></div></div></div></div></div></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com08QGP+45 Vulvoz, France46.3253685 5.785481499999998633.108676467178 -11.7926435 59.542060532822006 23.3636065tag:blogger.com,1999:blog-830335965541290967.post-90425699167672000922024-02-10T14:37:00.003+05:302024-02-11T10:39:45.131+05:30Azure Microsoft Fabric - Lab -1 for Beginners<p><span></span></p><a name='more'></a><p></p><p><br /></p><p></p><h1 style="text-align: center;"><span style="font-size: 22px;"><b>Creating a Lakehouse, Ingesting Sample Data</b></span></h1><p><span style="font-size: 22px;"><b><br /></b></span></p><div style="text-align: left;">Fabric with its unification of data store and standardization on Delta Lake format allows you to eliminate silos, remove data duplicity, and drastically reduce total cost of ownership.</div><div style="text-align: left;">With the flexibility offered by Fabric, you can implement either lakehouse or data warehouse architectures or combine them together to get the best of both with simple implementation. <br /><br />This lab explains how a developer at the fictional Wide World Importers company from the retail domain completes the following steps:</div><p style="text-align: left;"><br /></p><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><h4 style="clear: both;"><span style="font-size: xx-small;">Microsoft Fabric Labs</span></h4></div></div></div></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Lab -1 for Beginners:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a></span></li></ul><li><span style="font-size: xx-small;">Azure Microsoft Fabric - Auto Power BI Reports Lab -2:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric and Power BI Reports Lab - 5:</span></li><ul><li><span style="font-size: xx-small;"> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></span></li></ul><li><span style="font-size: xx-small;">Microsoft Fabric - Resource Cleanup in Lab -6 </span></li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html"><span style="font-size: xx-small;">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</span></a></li></ul></ul></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both;"><br style="font-size: 14px; font-weight: 700;" /></div><p style="text-align: left;"><br /></p><h4 style="text-align: left;"><span style="font-size: 22px;"><b>Objectives</b></span></h4><ol start="1" style="margin-top: 0in;" type="1">
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Sign in to
Power BI account and initiate a free Microsoft Fabric trial.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Start the
Microsoft Fabric (Preview) trial within Power BI.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Configure
OneDrive sign-up for the Microsoft 365 admin center.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Build and
implement an end-to-end lakehouse for the organization, including creating
a Fabric workspace and a lakehouse.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Ingest sample
data into the lakehouse and prepare it for further processing.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Transform and
prepare the data using Python/PySpark and SQL notebooks.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Create business
aggregate tables using different approaches.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Establish
relationships between tables for seamless reporting.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 3.75pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Build a Power
BI report with visualizations based on the prepared data.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 7.5pt; margin-top: 3.75pt;"><span face=""Segoe UI",sans-serif" style="font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Save and store
the created report for future reference and analysis.</span></li></ol><div><span face="Segoe UI, sans-serif"><span style="font-size: 14px;"><br /></span></span></div><div><span face="Segoe UI, sans-serif"><span><h3 style="text-align: left;"><span style="font-size: medium;">Exercise 1: Setup Lakehouse end-to-end scenario</span></h3><h4 style="text-align: left;"><span style="font-size: medium;">Task 1: </span></h4><div><ul style="text-align: left;"><li><span style="font-size: medium;">Sign in to Power BI account and sign up for the free Microsoft Fabric trial</span></li><li><span style="font-size: medium;">Open your browser, navigate to the address bar, and type or paste the following URL: https://app.fabric.microsoft.com/ then press Enter.</span></li></ul></div><div style="font-size: 14px;"><br /></div></span></span></div><div><span face="Segoe UI, sans-serif"><span style="font-size: 14px;"><br /></span></span></div><div><span face="Segoe UI, sans-serif"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgruUUiqfeXa8HGh-O87-jNdynXnYRIR_QJiF78274th5pZtZ8ESMHNipWDqImw7u4YWk9F23aFTwvRrXT8xKmq-wQ-cZrpgY7Lv2QcOEhdBu5IMhJrUysOkBgXt_6yZ8Y9u2rM92Xxuaogl1OYIHsdcS1FijBW4DXiqD0Nv79gYPV-_1ag89N01zjJieA" style="clear: right; float: right; font-size: 14px; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="148" data-original-width="955" height="63" src="https://blogger.googleusercontent.com/img/a/AVvXsEgruUUiqfeXa8HGh-O87-jNdynXnYRIR_QJiF78274th5pZtZ8ESMHNipWDqImw7u4YWk9F23aFTwvRrXT8xKmq-wQ-cZrpgY7Lv2QcOEhdBu5IMhJrUysOkBgXt_6yZ8Y9u2rM92Xxuaogl1OYIHsdcS1FijBW4DXiqD0Nv79gYPV-_1ag89N01zjJieA=w400-h63" width="400" /></a><span style="font-size: 14px;"><div class="separator" style="clear: both; text-align: center;"><span style="font-size: 14px;"><br /></span></div><div style="text-align: left;">2. In the Microsoft Fabric window, enter your Microsoft 365 credentials from the Resources tab, and click on the Submit button. </div><div style="text-align: left;"><br /></div></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: 14px;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: 14px;"><br /></span><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgruUUiqfeXa8HGh-O87-jNdynXnYRIR_QJiF78274th5pZtZ8ESMHNipWDqImw7u4YWk9F23aFTwvRrXT8xKmq-wQ-cZrpgY7Lv2QcOEhdBu5IMhJrUysOkBgXt_6yZ8Y9u2rM92Xxuaogl1OYIHsdcS1FijBW4DXiqD0Nv79gYPV-_1ag89N01zjJieA" style="clear: right; float: right; font-size: 14px; margin-bottom: 1em; margin-left: 1em;"></a><img data-original-height="364" data-original-width="622" height="117" src="https://blogger.googleusercontent.com/img/a/AVvXsEjYo6kYd7uEl9sllebBE8jSOw6GrmqLH55jP8mhSthlpy5Xc4YEMItxIqA0cNSvkemiF3v_gdc4QnuwA0OFFLNfQ88Dlkai26-morP_-iMEnoAbgRheKi0I_J49H2XtTVvheI3el5CtPjNoG00SVn9XEs5gMR9NIFa_j5f9_iJInDvogDvk2lewzDJWYPo=w200-h117" width="200" /> <span style="font-size: 14px;"> </span><img data-original-height="419" data-original-width="659" height="127" src="https://blogger.googleusercontent.com/img/a/AVvXsEhFjI8PC5Al7evEuwaXy1__ELsfeZ8da6KQDz00Ts9sxHw3pUx3PrahF1XjrdGU5fcdycBVcw7jPbP4A3MO93CoPVjBC3A39T7iON5ZCozCx_EQJIL0j7H5v99CRm-jriDRmcC5i98_5TZModw7czXp-d4BBHeKpTEQ8Ro4pE63EPkqSY3jXl8a1d_OKvg=w200-h127" style="font-size: 14px;" width="200" /><span style="font-size: 14px;"> </span><img data-original-height="575" data-original-width="768" height="150" src="https://blogger.googleusercontent.com/img/a/AVvXsEg7GCM5-zr22WRHi-he0w4VHmfUZj9qz6kRq4ph53R3UnRe2EKVTbHPXvRGy3kdbb-gAUGBDBOdKYJe3qKhvd1OgiVM7jRWVP5QgwjmISHevOhDWghYpxwLoel1p_TM6obhkXeQBu68ahnbPcVJu360W02R1brrR2nAAXDUhC_oTJF-U-meKGpxXVV5Ujo=w200-h150" style="font-size: 14px;" width="200" /><span style="font-size: 14px;"> </span><a href="https://blogger.googleusercontent.com/img/a/AVvXsEggLSwCuMcQVp9R3zvC8x1bErPg5CVBhO8y42Z4xuA-8WtrBQOPr1s3UzDFvTKDtlCCUIa0FNtHLDcCnI682TU_8XokwvXSucdaE3HDtbfopc39o35xfY0mD3rb40PzLp_zoYhaW_TFP1lx5COwjoBc5rb2GiSEr4cb8dKRC46A0SsjE-AHSRedPczq6Z8" style="clear: left; display: inline; font-size: 14px; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="548" data-original-width="722" height="152" src="https://blogger.googleusercontent.com/img/a/AVvXsEggLSwCuMcQVp9R3zvC8x1bErPg5CVBhO8y42Z4xuA-8WtrBQOPr1s3UzDFvTKDtlCCUIa0FNtHLDcCnI682TU_8XokwvXSucdaE3HDtbfopc39o35xfY0mD3rb40PzLp_zoYhaW_TFP1lx5COwjoBc5rb2GiSEr4cb8dKRC46A0SsjE-AHSRedPczq6Z8=w200-h152" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhVk2UERKgc9LYK0EHymPI9ILEjWnXQULzlWftBu4_x_YI0EeZwQGFpyJSL4f8FqjQRODgbin3H0nGWY2EiGgtTPkx3ceEL4Vs01ygiAzeLm38PIjr1qdwp2GxzNvyz77D4NNq5ZO-YuUem_U83ZOt9yGpnKxACkIEgJY6bYk8iywmxJOTbd8hRUeIiGG4" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="410" data-original-width="942" height="278" src="https://blogger.googleusercontent.com/img/a/AVvXsEhVk2UERKgc9LYK0EHymPI9ILEjWnXQULzlWftBu4_x_YI0EeZwQGFpyJSL4f8FqjQRODgbin3H0nGWY2EiGgtTPkx3ceEL4Vs01ygiAzeLm38PIjr1qdwp2GxzNvyz77D4NNq5ZO-YuUem_U83ZOt9yGpnKxACkIEgJY6bYk8iywmxJOTbd8hRUeIiGG4=w640-h278" width="640" /></a></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><h3 style="clear: both; text-align: left;"><span style="font-size: medium;">Task 2: Start the Microsoft Fabric (Preview) trial</span></h3><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;">Follow these steps to start your Fabric (Preview) trial.</span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: medium;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-size: medium;">On the Power BI Home page, click on the Account Manager for Administrator icon on the top right corner of the page. </span></li><li><span style="font-size: medium;">In the Account Manager blade, navigate and select Start Trial as shown in the below image.</span></li></ul></div><div style="font-size: 14px; text-align: left;"><br /></div><div style="text-align: left;"><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjCiIZkiXEDstf4jqr8ox4BPuJwVwV-Y5AH3xffsxexi5io43kRKd1cUBa1tLzegL6Pxjx_QZuDDYBJxlRtnxtYMlbavYBuz2RiMkXupTTPJVpkyYBUTp5JX6YDVGeWdqPmmWBO0mJp4aGmj_SeaGhxaZZlM5DQfp_nJpnMMntkfFrV-n8WUh6qeRn1J8U" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="259" data-original-width="975" height="85" src="https://blogger.googleusercontent.com/img/a/AVvXsEjCiIZkiXEDstf4jqr8ox4BPuJwVwV-Y5AH3xffsxexi5io43kRKd1cUBa1tLzegL6Pxjx_QZuDDYBJxlRtnxtYMlbavYBuz2RiMkXupTTPJVpkyYBUTp5JX6YDVGeWdqPmmWBO0mJp4aGmj_SeaGhxaZZlM5DQfp_nJpnMMntkfFrV-n8WUh6qeRn1J8U" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEgtA5ZiderrSGOb0IYMjrp3CWrDA8xlWvzyHRTg50_xgH2pK20DGApvvQn8f3btTzssq39Df_QU0wd2-tYqQwpK83JJ_hKtJLnE_9-F2W6k1r6q5ERxFn6S14oW5QE5YZeffmFAmVMcFJtCep2mn_Acf_X1VhPTynhqRNb5xvBYRFdbMVacHY4_LOkcB6A" style="margin-left: 1em; margin-right: 1em; text-align: right;"><img alt="" data-original-height="292" data-original-width="975" height="96" src="https://blogger.googleusercontent.com/img/a/AVvXsEgtA5ZiderrSGOb0IYMjrp3CWrDA8xlWvzyHRTg50_xgH2pK20DGApvvQn8f3btTzssq39Df_QU0wd2-tYqQwpK83JJ_hKtJLnE_9-F2W6k1r6q5ERxFn6S14oW5QE5YZeffmFAmVMcFJtCep2mn_Acf_X1VhPTynhqRNb5xvBYRFdbMVacHY4_LOkcB6A" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEjt7UZnHyq8BdMYNg0Ztjiyt5tgkiIf7xXe8FBsLRDPrW9SjmsepM6Q2icB96ZkN5EJjS1qC627cwGRyyHJIOR1tJzoFnn1wmyR1oLpaBcf-xZmL5asc--39mJQeVFvYEM5Kt-569juOIeoSrmiz2bBLyZZNa9T2SnN6NzGss93bCwhZTeAZKuvqGyRRqk" style="clear: left; display: inline; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="309" data-original-width="930" height="106" src="https://blogger.googleusercontent.com/img/a/AVvXsEjt7UZnHyq8BdMYNg0Ztjiyt5tgkiIf7xXe8FBsLRDPrW9SjmsepM6Q2icB96ZkN5EJjS1qC627cwGRyyHJIOR1tJzoFnn1wmyR1oLpaBcf-xZmL5asc--39mJQeVFvYEM5Kt-569juOIeoSrmiz2bBLyZZNa9T2SnN6NzGss93bCwhZTeAZKuvqGyRRqk" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEj4CsT_xFPAF0Lg-f0oIBODlwTiCJx8vsC_2STJgYJqfxjVYFbNpXY7loyxx8t_Wo3vn7_VNxBncq__YVXkL7D-1OkgoZHxw0VQhsR_tCf5okWldOGvMp0zsz8fmVvcTPqQ4qYDSsUx0tCGah1Ktu24j8-0J-IL_rS1l7Ur_PSbALiFTI2dUVpIYUpbV9w" style="clear: right; display: inline; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img alt="" data-original-height="358" data-original-width="975" height="117" src="https://blogger.googleusercontent.com/img/a/AVvXsEj4CsT_xFPAF0Lg-f0oIBODlwTiCJx8vsC_2STJgYJqfxjVYFbNpXY7loyxx8t_Wo3vn7_VNxBncq__YVXkL7D-1OkgoZHxw0VQhsR_tCf5okWldOGvMp0zsz8fmVvcTPqQ4qYDSsUx0tCGah1Ktu24j8-0J-IL_rS1l7Ur_PSbALiFTI2dUVpIYUpbV9w" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEjjo2x6bW_eIEH2JHFTt3VT44GiUIHxwuWgTYpbBUC1C0lV5bA-h7h1KmaDep0l8eutdO5A2n1YiWnWdVUX6T0Qo6dLRv6jMOtvkjTAml1qSdDI7EQVdCeBXWsSzMpU_zEuJZMUuVnufKdPHrC0uSdE_XXGsiIARRAKFkIco1r2M-L8714G7_ZLS3nzsCo" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img data-original-height="440" data-original-width="975" height="180" src="https://blogger.googleusercontent.com/img/a/AVvXsEjjo2x6bW_eIEH2JHFTt3VT44GiUIHxwuWgTYpbBUC1C0lV5bA-h7h1KmaDep0l8eutdO5A2n1YiWnWdVUX6T0Qo6dLRv6jMOtvkjTAml1qSdDI7EQVdCeBXWsSzMpU_zEuJZMUuVnufKdPHrC0uSdE_XXGsiIARRAKFkIco1r2M-L8714G7_ZLS3nzsCo=w400-h180" width="400" /></a></div><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;"><span style="font-size: medium;">Task 3: Ingest First Dimension</span></h3><div class="separator" style="clear: both;"><ol style="text-align: left;"><li><span style="font-size: medium;">Open your browser, navigate to the address bar, and type or paste the following URL: <a href="https://admin.microsoft.com/AdminPortal/Home#/homepage">https://admin.microsoft.com/AdminPortal/Home#/homepage</a> then press the Enter button.</span></li><li><span style="font-size: medium;">Click on the App launcher from the top left corner of the Microsoft 365 admin center page.</span></li><li><span style="font-size: medium;">In the Microsoft 365 page from the Apps pane select OneDrive</span></li><li><span style="font-size: medium;">In One Drive page, under Securely store and share files select Your One Drive is ready</span></li></ol></div><div class="separator" style="clear: both;"><span style="font-size: 14px;"><br /></span></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjIy9z10WmSFi1Z6aM0FeoaCRTCwj6Krx4tzQAWzFjlAIcjZDllK43K8TIF_LFWmpxbygptoxn1R7m7oxcXKUKOn8olo-vna_hRhFb5vGRkBI3PJyI7MVHp6hjXzmuqh7pk2pPo6ShV1qftE6rbgwph_B2AJKUgo_2mFurPjs0qo6nAzF2GSIqtwSV8tsc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="249" data-original-width="799" height="100" src="https://blogger.googleusercontent.com/img/a/AVvXsEjIy9z10WmSFi1Z6aM0FeoaCRTCwj6Krx4tzQAWzFjlAIcjZDllK43K8TIF_LFWmpxbygptoxn1R7m7oxcXKUKOn8olo-vna_hRhFb5vGRkBI3PJyI7MVHp6hjXzmuqh7pk2pPo6ShV1qftE6rbgwph_B2AJKUgo_2mFurPjs0qo6nAzF2GSIqtwSV8tsc" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEhkYOZygoii5_aEsHpGd2bCsb_hq5mmOi6WDS-TUOjDW_vxbFOaojJOBrkRMnc1SbMLOtSspQ2LSq33NMJemRkREkny_65Aav4GBe4RC4Z90VGOo9pHWE0WqbCkZOBNoMrZBkiJiDLtMKryOKtps6Fs6EMEvZ4Puis2D3rcftW5w0s6Lc62mLyRUTqFRfw" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="805" data-original-width="972" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEhkYOZygoii5_aEsHpGd2bCsb_hq5mmOi6WDS-TUOjDW_vxbFOaojJOBrkRMnc1SbMLOtSspQ2LSq33NMJemRkREkny_65Aav4GBe4RC4Z90VGOo9pHWE0WqbCkZOBNoMrZBkiJiDLtMKryOKtps6Fs6EMEvZ4Puis2D3rcftW5w0s6Lc62mLyRUTqFRfw" width="290" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEhWlIoEzR8zVBR4xRAvRdsZGnDT-6_FG72EChEwBQxyVEMchroGOxmCm6UeoG5rcmMFICOijRx4BXBw1-M0celRzWbDPiV1U05oqs7ShJkA60M2ycsz5ZiRWWTwMAqhGz4l4zF_xbpo-UKVPMEp8PFiNfwn29st0_Vq5PCmTZa4cMKxUOePTA0omORtcDM" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="1059" data-original-width="617" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEhWlIoEzR8zVBR4xRAvRdsZGnDT-6_FG72EChEwBQxyVEMchroGOxmCm6UeoG5rcmMFICOijRx4BXBw1-M0celRzWbDPiV1U05oqs7ShJkA60M2ycsz5ZiRWWTwMAqhGz4l4zF_xbpo-UKVPMEp8PFiNfwn29st0_Vq5PCmTZa4cMKxUOePTA0omORtcDM" width="140" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEhJkHfeOk228clSilmGT4UEUqefmXnVlruY76ft30yEBfRYQ5rGkTR04x-wcldd-M1qlEibTlW2hTmFokqOxhYOpmZa4QpKDoVLJ6j--kqc9CLE9tUfQUMEiraVRXtVHlGvsBwea_UADFEWxnP9oqRxrE0fa4y2QJq85HH-kgti0JgO6mu4fzxZuxeR5cU" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="604" data-original-width="975" height="198" src="https://blogger.googleusercontent.com/img/a/AVvXsEhJkHfeOk228clSilmGT4UEUqefmXnVlruY76ft30yEBfRYQ5rGkTR04x-wcldd-M1qlEibTlW2hTmFokqOxhYOpmZa4QpKDoVLJ6j--kqc9CLE9tUfQUMEiraVRXtVHlGvsBwea_UADFEWxnP9oqRxrE0fa4y2QJq85HH-kgti0JgO6mu4fzxZuxeR5cU" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEgDkicc6p_YL_Z8Q3Iee8Wm8ckzGPQVs6FBgbyZnXB8WZVf4UbZwkjoSESKyidUzDr6Fk8ewuK4Nk_RGn-f2Cllk8iRqqVT6UOuHF_JlycJY_e1jQGZgU4lxf_GpZNHXEUGaoTIGBzztvtUnh6KO4nCdmO9VJsHee365Tu1QWzY14Jt4ApFLMAqqun4yZk" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="555" data-original-width="975" height="182" src="https://blogger.googleusercontent.com/img/a/AVvXsEgDkicc6p_YL_Z8Q3Iee8Wm8ckzGPQVs6FBgbyZnXB8WZVf4UbZwkjoSESKyidUzDr6Fk8ewuK4Nk_RGn-f2Cllk8iRqqVT6UOuHF_JlycJY_e1jQGZgU4lxf_GpZNHXEUGaoTIGBzztvtUnh6KO4nCdmO9VJsHee365Tu1QWzY14Jt4ApFLMAqqun4yZk" width="320" /></a></div><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /><div style="text-align: left;"><h2 style="text-align: left;"><span style="font-size: medium;">Exercise 2: Build and implement an end-to-end lakehouse for your organization</span></h2><div><span style="font-size: medium;"><br /></span></div><h3 style="text-align: left;"><span style="font-size: medium;">Task 1: Create a Fabric workspace</span></h3><div><span style="font-size: medium;">In this task, you create a Fabric workspace. The workspace contains all the items needed for this lakehouse tutorial, which includes </span></div><div><ul style="text-align: left;"><li><span style="font-size: medium;">Lakehouse</span></li><li><span style="font-size: medium;">Dataflows</span></li><li><span style="font-size: medium;">Data Factory pipelines</span></li><li><span style="font-size: medium;">the notebooks</span></li><li><span style="font-size: medium;">Power BI datasets</span></li><li><span style="font-size: medium;">Reports</span></li></ul><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;">Steps:</span></div><ul style="text-align: left;"><li><span style="font-size: medium;">Back in the Power BI page, select Workspaces from the left side navigation menu.</span></li><li><span style="font-size: medium;">In the Workspaces pane Select + New workspace.</span></li><li><span style="font-size: medium;">In the Create a workspace tab, enter the following details and click on the Apply button.</span></li><li><span style="font-size: medium;">Wait for the deployment to complete. It takes 2-3 minutes to complete</span></li></ul><div><span style="font-size: 14px;"><br /></span></div><div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-yfti-tbllook: 1184;">
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Name<o:p></o:p></span></b></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="background: rgb(239, 239, 239); color: #660066; font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Fabric</span></b><b><span style="background: rgb(239, 239, 239); font-size: 10pt;"> </span></b><b><span style="background: rgb(239, 239, 239); color: #660066; font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Lakehouse</span></b><b><span style="background: rgb(239, 239, 239); font-size: 10pt;"> </span></b><b><span style="background: rgb(239, 239, 239); color: #660066; font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Tutorial</span></b><b><span style="background: rgb(239, 239, 239); color: #666600; font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">-</span></b><b><span style="background: rgb(239, 239, 239); font-size: 10pt;">XX</span></b><b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"> (XX can be a unique number) (here, we
entered Fabric Lakehouse Tutorial-29)<o:p></o:p></span></b></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Description</span></b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"><o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="background: rgb(239, 239, 239); color: #660066; font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">This</span></b><b><span style="background: rgb(239, 239, 239); font-size: 10pt;"> workspace contains all the
items </span></b><b><span style="background: rgb(239, 239, 239); color: #000088; font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">for</span></b><b><span style="background: rgb(239, 239, 239); font-size: 10pt;"> the lakehouse tutorial</span></b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"><o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Advanced</span></b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"><o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Under <b>License mode</b>, select <b>Trial</b><o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Default storage format</span></b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"><o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Small dataset storage format</span></b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"><o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">Template apps</span></b><span style="font-size: 10pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"><o:p></o:p></span></p>
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font-size: 14px; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiFhR1Gp-0NzIjpWzodS7BBaLtKzaKjzhp6TZAdAQs8t9Z4boTaZzaZ_MPUBYzzBkiKWzdm3zLSh3qJtTOU8LpV8JnQCPV9dHZs9YixjqHojGtvUni3Hfrd8_hEDYY311MCi4m_Yh2WACx3vempiraBPLNdPWNNUhp52gtKpylE4AYLdo02tO8Wk-K87oo" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1158" data-original-width="975" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiFhR1Gp-0NzIjpWzodS7BBaLtKzaKjzhp6TZAdAQs8t9Z4boTaZzaZ_MPUBYzzBkiKWzdm3zLSh3qJtTOU8LpV8JnQCPV9dHZs9YixjqHojGtvUni3Hfrd8_hEDYY311MCi4m_Yh2WACx3vempiraBPLNdPWNNUhp52gtKpylE4AYLdo02tO8Wk-K87oo" width="202" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEhVArfGEbr0Ptr--Va67yRkp1KAyY2ey5tzkInxS0n9YMMmfiJsqHq1KxtshlkfjpKEjYqItA9GtyrRLba8Y0RLuOHQuW4WiH5XorJOwTWw0b6bRBMfEPqct7KXXpCynR_sE3ZAWvRBxHx1y55rJj5G4Nk-VxsEhwKemZjLAHclIdH78NoZNUMMvc3CEuE" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1143" data-original-width="523" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEhVArfGEbr0Ptr--Va67yRkp1KAyY2ey5tzkInxS0n9YMMmfiJsqHq1KxtshlkfjpKEjYqItA9GtyrRLba8Y0RLuOHQuW4WiH5XorJOwTWw0b6bRBMfEPqct7KXXpCynR_sE3ZAWvRBxHx1y55rJj5G4Nk-VxsEhwKemZjLAHclIdH78NoZNUMMvc3CEuE" width="110" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEjMHRhmn4JUkLConqfltiNm0QmU0WNaMb0xX5M2-3IYfi5jnZK_8y5TsU7ACtWS9w1b8boyZn5mj0IneJx3pgg0V9ZLSLrM2LjtjNE0Plr6Sj-98RcQHtlZ-c06oF3S4pxCRzbQToejmSK453DT18CLsoty_tFeel_KwmwArDAI6INeF_etRUilrwXvRDk" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="691" data-original-width="569" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjMHRhmn4JUkLConqfltiNm0QmU0WNaMb0xX5M2-3IYfi5jnZK_8y5TsU7ACtWS9w1b8boyZn5mj0IneJx3pgg0V9ZLSLrM2LjtjNE0Plr6Sj-98RcQHtlZ-c06oF3S4pxCRzbQToejmSK453DT18CLsoty_tFeel_KwmwArDAI6INeF_etRUilrwXvRDk" width="198" /></a> </div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div style="text-align: left;"><h3 style="text-align: left;"><span style="font-size: medium;">Task 2: Create a lakehouse</span></h3><div><ul style="text-align: left;"><li><span style="font-size: medium;">In the Power BI Fabric Lakehouse Tutorial-XX page, click on the Power BI icon located at the bottom left and select Data Engineering under Synapse.</span></li><li><span style="font-size: medium;">In the Synapse Data Engineering Home page, select Lakehouse(Preview) to create a lakehouse.</span></li><li><span style="font-size: medium;">In the New lakehouse dialog box, enter wwilakehouse in the Name field, click on the Create button.</span></li><li><span style="font-size: medium;">You will see a notification stating Successfully created SQL endpoint.</span></li></ul><div><span style="font-size: 14px;"><br /></span></div><div><span style="font-size: 14px;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><div style="font-size: 14px; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg5k_UHJe2J-eZgh81LZD_cydjreuEMjx0EbdefZJYJgQnsLRO9Ka9P1lqzPthUF_EhV9uN_kTuuszUuUQ0Ktuy15_0fdTuaxPylDyzWyG4SmzjIr1PoiQXkFpMx56ADL6tLbbr-1NM7A3AwbUiGldwmPSfWcXy1QlZ_siGH3tuvx1FrWn4mIDlzR-MxfU" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1179" data-original-width="655" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEg5k_UHJe2J-eZgh81LZD_cydjreuEMjx0EbdefZJYJgQnsLRO9Ka9P1lqzPthUF_EhV9uN_kTuuszUuUQ0Ktuy15_0fdTuaxPylDyzWyG4SmzjIr1PoiQXkFpMx56ADL6tLbbr-1NM7A3AwbUiGldwmPSfWcXy1QlZ_siGH3tuvx1FrWn4mIDlzR-MxfU" width="133" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEgQTUI6jQD-tNveFsdro2s1Ey-S-1gPgPCaGRJy8KqbjNTxcTUe_priT_GGvxNwlCxwaRfMEu34Rr5N6YiMEdqPF6UcAlWKU91MaIHD7mdyY1dI8KtEACejNrVnTjR-F_xJyha5prMchmCjN8j2rra88eiRltoMxYDKrm8nKeEEJ86fUkqvNIP0SCvL_6E" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="655" data-original-width="975" height="215" src="https://blogger.googleusercontent.com/img/a/AVvXsEgQTUI6jQD-tNveFsdro2s1Ey-S-1gPgPCaGRJy8KqbjNTxcTUe_priT_GGvxNwlCxwaRfMEu34Rr5N6YiMEdqPF6UcAlWKU91MaIHD7mdyY1dI8KtEACejNrVnTjR-F_xJyha5prMchmCjN8j2rra88eiRltoMxYDKrm8nKeEEJ86fUkqvNIP0SCvL_6E" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEiJ6ra6Xbslu1WPFokhKEmopByq78I2BYTj7cTr3vcYODv3U-5AYLHHpdDBASvsAVo2UyskAjgZYV4DoGSbBAZkc2znRmzvWAJ5AMbl8kmvqUT6Q0tOHOnaRea4WDiquzWKISArPzOIy-ey3U79tB9LKozJlMnKiZm48JnPeKwH3xz5XN4nY2xtOJe8kwU" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="371" data-original-width="604" height="86" src="https://blogger.googleusercontent.com/img/a/AVvXsEiJ6ra6Xbslu1WPFokhKEmopByq78I2BYTj7cTr3vcYODv3U-5AYLHHpdDBASvsAVo2UyskAjgZYV4DoGSbBAZkc2znRmzvWAJ5AMbl8kmvqUT6Q0tOHOnaRea4WDiquzWKISArPzOIy-ey3U79tB9LKozJlMnKiZm48JnPeKwH3xz5XN4nY2xtOJe8kwU=w140-h86" width="140" /></a> </div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh-xaO0mE2iRQXtCrd4a2kqW6RZGqeLarVcYkcD01EQTztCXKEqjVl-Q1ISdls-9_-_BwmzeMaVl4RZmOCudahR9pkDn0OIQF4sg__3z6YEQqRnAysDQ645ar8yjIikiJoXRw1RoInwEXzLRNcZt2XKBBStvmd-9UEgz-pyGnRQnh0YLcGGH0y2gexDBp0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="511" data-original-width="975" height="168" src="https://blogger.googleusercontent.com/img/a/AVvXsEh-xaO0mE2iRQXtCrd4a2kqW6RZGqeLarVcYkcD01EQTztCXKEqjVl-Q1ISdls-9_-_BwmzeMaVl4RZmOCudahR9pkDn0OIQF4sg__3z6YEQqRnAysDQ645ar8yjIikiJoXRw1RoInwEXzLRNcZt2XKBBStvmd-9UEgz-pyGnRQnh0YLcGGH0y2gexDBp0" width="320" /></a> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEgP1vrteYkA7ibsIm-jKGP86u6Cr97nN85TU8RJJI9pE2taVRKoR6ZF9B7QOV8aiv4g9_U94dBuwU-oXiQZ_-DkhqqzpSn3CjU6HqV9Vz5TJOHA4_LQlo4GeivgaGqJtvfRREcin75b1SKMtcet6FImVP0aAEQPgRjTxsfHEAqDm2m6ppobLk1VrinocHM" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="540" data-original-width="603" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgP1vrteYkA7ibsIm-jKGP86u6Cr97nN85TU8RJJI9pE2taVRKoR6ZF9B7QOV8aiv4g9_U94dBuwU-oXiQZ_-DkhqqzpSn3CjU6HqV9Vz5TJOHA4_LQlo4GeivgaGqJtvfRREcin75b1SKMtcet6FImVP0aAEQPgRjTxsfHEAqDm2m6ppobLk1VrinocHM" width="268" /></a></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;"><span style="font-size: medium;">Task 3: Ingest sample data</span></h3><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">In the wwilakehouse page, under Get data in your lakehouse section, click on New Dataflow Gen2 as shown in the below image.</span></li><li><span style="font-size: medium;">On the Dataflow canvas, navigate and click on Import from a Text/CSV file.</span></li><li><span style="font-size: medium;">On the Connect to data source pane, select the Upload file(Preview) radio button. Click on Browse button and browse your VM to C:\LabFiles and then select dimension_customer.csv file. Select Open.</span></li><li><span style="font-size: medium;">In the Connect to data source pane select Next.</span></li><li><span style="font-size: medium;">From the Preview file data page, preview the data and select Create to proceed and return back to the dataflow canvas.</span></li><li><span style="font-size: medium;">In the Query settings pane on the right side of the Dataflow canvas, ensure that dimension_customer is selected under the Name field. Similarly, ensure that Lakehouse is selected under the Data destination field.</span></li></ul><div><span style="font-size: medium;"><br /></span></div><div><div><span style="font-size: medium;"><b>Note:</b></span></div><div><span style="font-size: medium;">o<span style="white-space: pre;"> </span>If needed, from the Connect to data destination screen, sign into your account. Select Next.</span></div><div><span style="font-size: medium;">o<span style="white-space: pre;"> </span>Navigate to the wwilakehouse in your workspace.</span></div><div><span style="font-size: medium;">o<span style="white-space: pre;"> </span>If the dimension_customer table doesn't exist, select the New table setting and enter the table name dimension_customer. If the table already exists, select the Existing table setting and choose dimension_customer from the list of tables in the object explorer. Select Next.</span></div><div><span style="font-size: medium;">Fabric adds a space and number at the end of the table name by default. Table names must be lower case and must not contain spaces. Please rename it appropriately and remove any spaces from the table name.*</span></div></div><div><span style="font-size: 14px;"><br /></span></div><div><span style="font-size: 14px;"><br /></span></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /><div style="text-align: left;"><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgRAk0_qOZl2Zf18aubxC1dckelUbAVAftTDB1P4qsF1vZGaMKoYjh5yt8eQ1p2PQc9-H1b9c1QQFnK_tshwpJW3zng6lud_zPQbGrbWqCg14uVTmEDI6w3bS78WAR2aeNYxrg-GvAsDG_CKSxgK2DUozSiduB5eyFk3LDVQWGnOurprztYDZ9j4JNrhV8" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="497" data-original-width="975" height="163" src="https://blogger.googleusercontent.com/img/a/AVvXsEgRAk0_qOZl2Zf18aubxC1dckelUbAVAftTDB1P4qsF1vZGaMKoYjh5yt8eQ1p2PQc9-H1b9c1QQFnK_tshwpJW3zng6lud_zPQbGrbWqCg14uVTmEDI6w3bS78WAR2aeNYxrg-GvAsDG_CKSxgK2DUozSiduB5eyFk3LDVQWGnOurprztYDZ9j4JNrhV8" width="320" /></a></div><div class="separator" style="clear: both; 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margin-right: 1em;"><img alt="" data-original-height="715" data-original-width="975" height="235" src="https://blogger.googleusercontent.com/img/a/AVvXsEgcsB7BziRFPKovyqLmV2FOYjaEuH-xZ8nilpi4KBLcZt5Fy0xgTmrMvr6prIF_US-ZMNxq05NdUr84WgzjJGt4vGIrzewbqfhGTsd1SRU5UgH9dnG8t9t6UwtcK9RI1D31bY5ncijmh3xGteu9UwQsKld_It8A_t0Q3sgdE3OFwJW3vykLTMCQ2WGkZtA" width="320" /></a></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">Refreshing data will take around 5-6 min.</span></li><li><span style="font-size: medium;">Once the dataflow is refreshed, select wwilakehouse in the left navigation panel to view the dimension_customer delta table. Select the table to preview its data.</span></li><li><span style="font-size: medium;">You can also use the SQL endpoint of the lakehouse to query the data with SQL statements. Select SQL endpoint from the Lakehouse drop-down menu at the top right of the screen.</span></li></ul></div></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; font-size: 14px; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgSwElCtAkYvUGG93jtNf_S5XKvzeruHMg5enC9WmrPWbZOgi5pQ4X3qCkFfsnmAvDI9tDz49XTtBaWVyw6bSF6X-7C53eX9EohW20n0vGMNJuFg16AkgF1NuUDbY81jq8eLX-eCbXU5xWRmspJJ-tof2jO8ab61dKGX8XoGD9x1r-pKAGwD_kMkNyovP8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="651" data-original-width="975" height="214" src="https://blogger.googleusercontent.com/img/a/AVvXsEgSwElCtAkYvUGG93jtNf_S5XKvzeruHMg5enC9WmrPWbZOgi5pQ4X3qCkFfsnmAvDI9tDz49XTtBaWVyw6bSF6X-7C53eX9EohW20n0vGMNJuFg16AkgF1NuUDbY81jq8eLX-eCbXU5xWRmspJJ-tof2jO8ab61dKGX8XoGD9x1r-pKAGwD_kMkNyovP8" width="320" /></a></div><div class="separator" style="clear: both; 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text-align: center;"><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhvIBGF1KqCWkZKIN7DLuhVY2ooeQ6p-FLF3_-olYJF36rs_7wdDGskjqsyAt6HRiqb7tz-TKFVETHd3eqHv7MB-UZHhTSbRDmnkn_0_Q6gMvUMKqINnn5TkT1wXZpilqocevNseV6gZsNwITji5Xf4QyWt3tUIpT-d1V-pFK2831Y2AorHcULB4DdBxP4" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="696" data-original-width="975" height="228" src="https://blogger.googleusercontent.com/img/a/AVvXsEhvIBGF1KqCWkZKIN7DLuhVY2ooeQ6p-FLF3_-olYJF36rs_7wdDGskjqsyAt6HRiqb7tz-TKFVETHd3eqHv7MB-UZHhTSbRDmnkn_0_Q6gMvUMKqINnn5TkT1wXZpilqocevNseV6gZsNwITji5Xf4QyWt3tUIpT-d1V-pFK2831Y2AorHcULB4DdBxP4" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgK-NOGj-epyTT_LWgOtkNGBNdecr1_X0_o2by86tjPHlcG6-Gg7_1XwiL9bD6V1x9-plbwqo82x5QNZaz3DdB6us8DqrwPG5Rtn78tN7B8aA0W9J4OGbAc0V2NLhw2u0g9nd21NQbXJyVQrnuPqefRynkQHP3KtwjeCt5LAWmx3_vi0F18_CaoqSOnmiY" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="643" data-original-width="975" height="211" src="https://blogger.googleusercontent.com/img/a/AVvXsEgK-NOGj-epyTT_LWgOtkNGBNdecr1_X0_o2by86tjPHlcG6-Gg7_1XwiL9bD6V1x9-plbwqo82x5QNZaz3DdB6us8DqrwPG5Rtn78tN7B8aA0W9J4OGbAc0V2NLhw2u0g9nd21NQbXJyVQrnuPqefRynkQHP3KtwjeCt5LAWmx3_vi0F18_CaoqSOnmiY" width="320" /></a></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><span style="font-size: medium;">In the wwilakehouse page, under Explorer select the dimension_customer table to preview its data and select New SQL query to write your SQL statements.</span></li><li><span style="font-size: medium;">The following sample query aggregates the row count based on the BuyingGroup column of the dimension_customer table. SQL query files are saved automatically for future reference, and you can rename or delete these files based on your need. Paste the code as shown in the below image, then click on the play icon to Run the script.</span></li></ul></div><div class="separator" style="clear: both;"><span style="font-size: 14px;">/***********************/</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01; font-size: 14px;">SELECT BuyingGroup, Count(*) AS Total</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01; font-size: 14px;">FROM dimension_customer</span></div><div class="separator" style="clear: both;"><span style="background-color: #fcff01; font-size: 14px;">GROUP BY BuyingGroup</span></div><div class="separator" style="clear: both;"><span style="font-size: 14px;">/***********************/</span></div></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-size: 14px; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgSM4E6cI8KmyyBYK08KqjunZ1PgNtbBqHKGPbJF5dIM-bvLZ-bgojtOQKaD9ugPtTreGMf1_2UxMQdIhsqYGafeNjZJleLcRpgsEJo3-abV9CMq-J6gRri8kc_O6NFrvX9V2FWsmSOjOJ3NnT_Y510WBpSRk4LpodgS5GScxOyQuspkq2uAxwco4xe2D4" style="clear: left; 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text-align: center;"><br /></div><br /><br /></div><br /><b>Proceed to the next lab to build the report on the Database</b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><b>Summary: </b>This practical lab focuses on setting up and configuring essential components within Microsoft Fabric and Power BI for data management and reporting. It includes tasks like activating trials, configuring OneDrive, creating workspaces, and setting up lakehouses. The lab also covers tasks related to ingesting sample data, optimizing delta tables, and building reports in Power BI for effective data analysis. The objectives aim to provide hands-on experience in utilizing Microsoft Fabric and Power BI for data management and reporting purposes.</div><div style="font-weight: bold;"><br /></div><div style="font-weight: bold;"><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><h4 style="clear: both;"><span style="font-size: large;">Microsoft Fabric Labs</span></h4></div></div></div></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul><li>Azure Microsoft Fabric - Lab -1 for Beginners:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-lab-1-for.html</a></li></ul><li>Azure Microsoft Fabric - Auto Power BI Reports Lab -2:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html">https://saurabhsinhainblogs.blogspot.com/2024/02/azure-microsoft-fabric-auto-power-bi.html</a></li></ul><li>Microsoft Fabric - Ingest data into the Lakehouse Lab - 3:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-ingest-data-into.html</a></li></ul><li>Microsoft Fabric - Lakehouse and Data Transformation - Lab - 4:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-lakehouse-and-data.html</a></li></ul><li>Microsoft Fabric and Power BI Reports Lab - 5:</li><ul><li> <a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-and-power-bi-reports.html</a></li></ul><li>Microsoft Fabric - Resource Cleanup in Lab -6 </li><ul><li><a href="https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html">https://saurabhsinhainblogs.blogspot.com/2024/02/microsoft-fabric-resource-cleanup-in.html</a></li></ul></ul></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br style="font-size: medium; font-weight: 400;" /></div></div></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></span></div><ol start="9" type="1">
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</ol>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0tag:blogger.com,1999:blog-830335965541290967.post-35005383067535924482024-01-31T00:52:00.003+05:302024-01-31T00:52:21.728+05:30Use Apache Spark in - Azure Databricks Lab 2<p><span></span></p><a name='more'></a><br /><p></p><h1 style="text-align: center;">Use Apache Spark in Azure Databricks</h1><p><br /></p><p>One of the benefits of Spark is support for a wide range of programming languages, including Java, Scala, Python, and SQL; making Spark a very flexible solution for data processing workloads including data cleansing and manipulation, statistical analysis and machine learning, and data analytics and visualization. Azure Databricks is built on Apache Spark and offers a highly scalable solution for data engineering and analysis tasks that involve working with data in files.</p><p><br /></p><h3 style="text-align: left;">Step 1. Setup Azure Databricks Workspace and open notebook</h3><p>Steps are available: <a href="https://saurabhsinhainblogs.blogspot.com/2024/01/azure-databricks-lab-how-to-start-with.html">https://saurabhsinhainblogs.blogspot.com/2024/01/azure-databricks-lab-how-to-start-with.html</a></p><p></p><ul style="text-align: left;"><li>Connect to Azure Portal</li><li>Setup Azure Datbricks</li><li>Setup Cluster for Azure Databricks</li><li>Open Notebook</li></ul><p></p><p><br /></p><h3 style="text-align: left;">Step 2. Prepare data to consume</h3><p>Shell commands can also use to download data files from GitHub into the Databricks file system (DBFS)</p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>%sh</div><div> rm -r /dbfs/spark_lab</div><div> mkdir /dbfs/spark_lab</div><div> wget -O /dbfs/spark_lab/2019.csv https://raw.githubusercontent.com/MicrosoftLearning/mslearn-databricks/main/data/2019.csv</div><div> wget -O /dbfs/spark_lab/2020.csv https://raw.githubusercontent.com/MicrosoftLearning/mslearn-databricks/main/data/2020.csv</div><div> wget -O /dbfs/spark_lab/2021.csv https://raw.githubusercontent.com/MicrosoftLearning/mslearn-databricks/main/data/2021.csv</div></div><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgZ4o7ONMTFsJUdpK4oNWyECJwka7gYLUA44uRr_cS9TP1PqN-QZfWZTZQ9cf1IP9LnAgu2C8TLkR6jWGqPBDPR6t9kORL--8ew96ak_ZWqqu3-7KxESEu2W-xBLBVUVfa7TEigiXpLAmfiNmW23qlTRe1GX8D0WQzm7Vu-uvjjJOViaKXWZenyOm3krHg" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="590" data-original-width="1045" height="181" src="https://blogger.googleusercontent.com/img/a/AVvXsEgZ4o7ONMTFsJUdpK4oNWyECJwka7gYLUA44uRr_cS9TP1PqN-QZfWZTZQ9cf1IP9LnAgu2C8TLkR6jWGqPBDPR6t9kORL--8ew96ak_ZWqqu3-7KxESEu2W-xBLBVUVfa7TEigiXpLAmfiNmW23qlTRe1GX8D0WQzm7Vu-uvjjJOViaKXWZenyOm3krHg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 3. Load the data frame and view the data</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">Data is loaded and visible here but</div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Data doesn't include the column headers</li><li>Information about the data types is missing</li></ul></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Code:</div><div class="separator" style="clear: both; text-align: left;"><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>df <span style="color: #687687;">=</span> spark.read.<span style="color: #795e26;">load</span>(<span style="color: #c72e0f;">'spark_lab/*.csv'</span>, <span style="color: #001080;">format</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'csv'</span>) </div><div><span style="color: #795e26;">display</span>(df.<span style="color: #795e26;">limit</span>(<span style="color: #098658;">100</span>))</div></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgCM5_Oh2CVuts0-7h1Cjz_n94BIY1yE1lvwG82ajmdOR1kToh3MCgeH99Xhv4Wultz8ZfAeDlaIxX7SfiyVFiLJQEiiftYVxXmYg394NKEo9KwbkxAeh6bZirOT2U3F2TVwNf2K-F63WQFHGdM0vMNTy9j8YiJdE3PX_JPkwrYurSpOFG0kkYNjlrvlEA" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Load the data frame and view the data in Azure Databricks" data-original-height="386" data-original-width="803" height="308" src="https://blogger.googleusercontent.com/img/a/AVvXsEgCM5_Oh2CVuts0-7h1Cjz_n94BIY1yE1lvwG82ajmdOR1kToh3MCgeH99Xhv4Wultz8ZfAeDlaIxX7SfiyVFiLJQEiiftYVxXmYg394NKEo9KwbkxAeh6bZirOT2U3F2TVwNf2K-F63WQFHGdM0vMNTy9j8YiJdE3PX_JPkwrYurSpOFG0kkYNjlrvlEA=w640-h308" title="df = spark.read.load('spark_lab/*.csv', format='csv')" width="640" /></a></div><br /><br /></div><br /><br /><p></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><h3 style="text-align: left;">Step 3. Define a schema for the data frame</h3><p>Observe that this time, our below problems are solved</p><p></p><ul style="text-align: left;"><li>The data frame includes column headers</li><li>Information about the data types is also available</li></ul><p></p><p><br /></p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div><span style="color: blue;">from</span> pyspark.sql.types <span style="color: blue;">import</span> <span style="color: #687687;">*</span></div><div><span style="color: blue;">from</span> pyspark.sql.functions <span style="color: blue;">import</span> <span style="color: #687687;">*</span></div><div>orderSchema <span style="color: #687687;">=</span> <span style="color: #795e26;">StructType</span>([ </div><div> <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"SalesOrderNumber"</span>, <span style="color: #795e26;">StringType</span>()), <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"SalesOrderLineNumber"</span>, <span style="color: #795e26;">IntegerType</span>()), <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"OrderDate"</span>, <span style="color: #795e26;">DateType</span>()),</div><div> <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"CustomerName"</span>, <span style="color: #795e26;">StringType</span>()), <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"Email"</span>, <span style="color: #795e26;">StringType</span>()), <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"Item"</span>, <span style="color: #795e26;">StringType</span>()),</div><div> <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"Quantity"</span>, <span style="color: #795e26;">IntegerType</span>()), <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"UnitPrice"</span>, <span style="color: #795e26;">FloatType</span>()), <span style="color: #795e26;">StructField</span>(<span style="color: #c72e0f;">"Tax"</span>, <span style="color: #795e26;">FloatType</span>()) ])</div><div>df <span style="color: #687687;">=</span> spark.read.<span style="color: #795e26;">load</span>(<span style="color: #c72e0f;">'/spark_lab/*.csv'</span>, <span style="color: #001080;">format</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'csv'</span>, <span style="color: #001080;">schema</span><span style="color: #687687;">=</span>orderSchema)</div><div><span style="color: #795e26;">display</span>(df.<span style="color: #795e26;">limit</span>(<span style="color: #098658;">100</span>))</div><div><br /></div><div><div style="line-height: 20px;">df.<span style="color: #795e26;">printSchema</span>()</div></div></div><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhQ3n54EQm3kiJUP05TextybCYPLG5-RyaCx_nMVGzuG4fjnWi_AJIjYcWJ6tay8ymuVXIP_TTemFhRchoYtJbHWJ5yLAocAN5ec1TfiQsm8jQaQVTBIcVF1P8Dk0WTLpoI9LxZG6_2ydq7WsOLfQZeVExDVzwu-bq4yeZWzKMGNVIJ_vs7vAFZiDgWTAI" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Pyspark define schema" data-original-height="674" data-original-width="1117" height="386" src="https://blogger.googleusercontent.com/img/a/AVvXsEhQ3n54EQm3kiJUP05TextybCYPLG5-RyaCx_nMVGzuG4fjnWi_AJIjYcWJ6tay8ymuVXIP_TTemFhRchoYtJbHWJ5yLAocAN5ec1TfiQsm8jQaQVTBIcVF1P8Dk0WTLpoI9LxZG6_2ydq7WsOLfQZeVExDVzwu-bq4yeZWzKMGNVIJ_vs7vAFZiDgWTAI=w640-h386" title="StructType([ StructField(" width="640" /></a></div><br /><br /><p></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgvKiMVziP7mztl90A7-VVu5TL_hGdWwkMtpILU1sNab1RLQH9GJatiHkgqD965I9hNEQMlhgBkCFA_pm6UGzrZKsT3HbDT9trk8xSohaBKsHN9vjm_nMOeefZmjMrylv8Faz5Tkou7Aiq-SJB4LaxTNu2FBFifvGA_QnjIDBApIT_7SIE5CmrlRvqIfIw" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="print datatyping spark databricks" data-original-height="335" data-original-width="533" height="402" src="https://blogger.googleusercontent.com/img/a/AVvXsEgvKiMVziP7mztl90A7-VVu5TL_hGdWwkMtpILU1sNab1RLQH9GJatiHkgqD965I9hNEQMlhgBkCFA_pm6UGzrZKsT3HbDT9trk8xSohaBKsHN9vjm_nMOeefZmjMrylv8Faz5Tkou7Aiq-SJB4LaxTNu2FBFifvGA_QnjIDBApIT_7SIE5CmrlRvqIfIw=w640-h402" title="df.printSchema" width="640" /></a></div><br /><br /><p></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><h3 style="text-align: left;">Step 4. Filter a data frame</h3><ul style="text-align: left;"><li>Filter the columns of the sales orders data frame to include only the customer name and email address.</li><ul><li>When you perform an operation on a data frame, the result is a new data frame (in this case, a new customer data frame is created by selecting a specific subset of columns from the df data frame)</li><li>The dataframe['Field1', 'Field2', ...] syntax is a shorthand way of defining a subset of column. You can also use select method, so the first line of the code above could be written as customers = df.select("CustomerName", "Email")</li></ul><li>Count the total number of order records</li><li>Count the number of distinct customers</li><li>Display the distinct customers</li><ul><li>Dataframes provide functions such as count and distinct that can be used to summarize and filter the data they contain.</li></ul></ul><ul style="text-align: left;"></ul><ul style="text-align: left;"></ul><ul style="text-align: left;"></ul><ul style="text-align: left;"></ul><ul style="text-align: left;"></ul><p><br /></p><p>Code: </p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>customers <span style="color: #687687;">=</span> df[<span style="color: #c72e0f;">'CustomerName'</span>, <span style="color: #c72e0f;">'Email'</span>]</div><div><span style="color: #795e26;">print</span>(customers.<span style="color: #795e26;">count</span>())</div><div><span style="color: #795e26;">print</span>(customers.<span style="color: #795e26;">distinct</span>().<span style="color: #795e26;">count</span>())</div><div><span style="color: #795e26;">display</span>(customers.<span style="color: #795e26;">distinct</span>())</div></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg_dfgdeZgj3OFE503lu_foJCuLthz7Pu_-E6zN4khy6F7WIVIwhI7Sx9xmjzLmNA70Ia2ITkG6dMf1e_50HhZl_lSMkiUlDIbSpROpCG_-aDkvsyx1ETSOLTdM9eyT6wRiI5wWq_aNm2PILzDYNMIiMutOEpgZnC8Qokc6zs-rx3gtyQKFHVX3IUuLsH4" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Filter a dataframe" data-original-height="488" data-original-width="794" height="394" src="https://blogger.googleusercontent.com/img/a/AVvXsEg_dfgdeZgj3OFE503lu_foJCuLthz7Pu_-E6zN4khy6F7WIVIwhI7Sx9xmjzLmNA70Ia2ITkG6dMf1e_50HhZl_lSMkiUlDIbSpROpCG_-aDkvsyx1ETSOLTdM9eyT6wRiI5wWq_aNm2PILzDYNMIiMutOEpgZnC8Qokc6zs-rx3gtyQKFHVX3IUuLsH4=w640-h394" title="customers = df['CustomerName', 'Email'] print(customers.count()) print(customers.distinct().count()) display(customers.distinct())" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Let’s apply a filter to include only the customers who have placed an order for a specific product by running the following code</div><div class="separator" style="clear: both; text-align: left;">Code:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><p></p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>customers <span style="color: #687687;">=</span> df.<span style="color: #795e26;">select</span>(<span style="color: #c72e0f;">"CustomerName"</span>, <span style="color: #c72e0f;">"Email"</span>)<span style="color: #795e26;">.where</span>(df[<span style="color: #c72e0f;">'</span><span style="color: black;">Item</span><span style="color: #c72e0f;">'</span>]==<span style="color: #c72e0f;">'</span><span style="color: black;">Road</span><span style="color: #687687;">-</span><span style="color: #098658;">250</span><span style="color: black;"> Red, </span><span style="color: #098658;">52</span><span style="color: #c72e0f;">'</span>)</div><div><span style="color: #795e26;">print</span>(customers.<span style="color: #795e26;">count</span>())</div><div><span style="color: #795e26;">print</span>(customers.<span style="color: #795e26;">distinct</span>().<span style="color: #795e26;">count</span>())</div><div><span style="color: #795e26;">display</span>(customers.<span style="color: #795e26;">distinct</span>())</div></div><div class="separator" style="clear: both; text-align: left;"></div><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi35IO2l82MD5Wckdw2OyTSk1AJdS3tycDtCbUfVV5ioZowWmutMznlbxdZLdYt6j5UCrv5OLdGIO4bL-aygqrtyo4sCKZh-pOUz2f-SjpxK8h0UnYfjrGhsjmrnbNMtHybQMIWffLcK7tT0Uy1P9_ysw14T0dFo723i0BKS_97LVt_XzQXjnvU6tVy2gc" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Selec and where in pyspark databricks" data-original-height="470" data-original-width="974" height="308" src="https://blogger.googleusercontent.com/img/a/AVvXsEi35IO2l82MD5Wckdw2OyTSk1AJdS3tycDtCbUfVV5ioZowWmutMznlbxdZLdYt6j5UCrv5OLdGIO4bL-aygqrtyo4sCKZh-pOUz2f-SjpxK8h0UnYfjrGhsjmrnbNMtHybQMIWffLcK7tT0Uy1P9_ysw14T0dFo723i0BKS_97LVt_XzQXjnvU6tVy2gc=w640-h308" title="customers = df.select("CustomerName", "Email").where(df['Item']=='Road-250 Red, 52') print(customers.count()) print(customers.distinct().count()) display(customers.distinct())" width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 5. Aggregate and group data in a data frame</h3><div class="separator" style="clear: both; text-align: center;"><br /></div>Show the sum of order quantities grouped by product. The groupBy method groups the rows by Item, and the subsequent sum aggregate function is applied to all of the remaining numeric columns<p></p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>productSales <span style="color: #687687;">=</span> df.<span style="color: #795e26;">select</span>(<span style="color: #c72e0f;">"Item"</span>, <span style="color: #c72e0f;">"Quantity"</span>).<span style="color: #795e26;">groupBy</span>(<span style="color: #c72e0f;">"Item"</span>).<span style="color: #795e26;">sum</span>()</div><div><span style="color: #795e26;">display</span>(productSales)</div></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEin8BMDDiOfhb1mqrcopfRnUw0VE12OZP_FfashF_kMjmeTRwr2IErm85joMQQ-75_7RS_CLpNVFm2J1jbNnoi63I_SOBcZXoo0JNi0U3l83tWJtL9ItEhP0jSEjGSvdYSOBbKLLl7Rvy7_R1Lh8Uqjw4E3razsEw_AHPfLL8btn6Ye3iuMg6Valwgsgl0" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Aggregate databricks pyspark" data-original-height="344" data-original-width="800" height="276" src="https://blogger.googleusercontent.com/img/a/AVvXsEin8BMDDiOfhb1mqrcopfRnUw0VE12OZP_FfashF_kMjmeTRwr2IErm85joMQQ-75_7RS_CLpNVFm2J1jbNnoi63I_SOBcZXoo0JNi0U3l83tWJtL9ItEhP0jSEjGSvdYSOBbKLLl7Rvy7_R1Lh8Uqjw4E3razsEw_AHPfLL8btn6Ye3iuMg6Valwgsgl0=w640-h276" title="productSales = df.select("Item", "Quantity").groupBy("Item").sum() display(productSales)" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p></p><p>Show the number of sales orders per year. Note that the select method includes a SQL year function to extract the year component of the OrderDate field, and then an alias method is used to assign a column name to the extracted year value. The data is then grouped by the derived Year column and the count of rows in each group is calculated before finally the orderBy method is used to sort the resulting dataframe.</p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>yearlySales <span style="color: #687687;">=</span> df.<span style="color: #795e26;">select</span>(<span style="color: #795e26;">year</span>(<span style="color: #c72e0f;">"OrderDate"</span>).<span style="color: #795e26;">alias</span>(<span style="color: #c72e0f;">"Year"</span>)).<span style="color: #795e26;">groupBy</span>(<span style="color: #c72e0f;">"Year"</span>).<span style="color: #795e26;">count</span>().<span style="color: #795e26;">orderBy</span>(<span style="color: #c72e0f;">"Year"</span>)</div><div><span style="color: #795e26;">display</span>(yearlySales)</div></div><p></p><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjUZ6vRBjA_h1nVzGhjGMBb0TG1jCgrv6WPRy1N15f9GRdQN-Rr4uNIdjPce08YfYfBQFMWIg8zC9ZuB5vw6-Nh_gNmZUJCmJKHMyhYdJgJettEVkqbiDsl-FySB-B7V9Jxa6u5QX27mXfcwd6p0jKOTUlzr4RAIoe8eQx9Omm64-ZOELxBIbjaUmwxq-c" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="databricks pyspark function using sql" data-original-height="331" data-original-width="1139" height="186" src="https://blogger.googleusercontent.com/img/a/AVvXsEjUZ6vRBjA_h1nVzGhjGMBb0TG1jCgrv6WPRy1N15f9GRdQN-Rr4uNIdjPce08YfYfBQFMWIg8zC9ZuB5vw6-Nh_gNmZUJCmJKHMyhYdJgJettEVkqbiDsl-FySB-B7V9Jxa6u5QX27mXfcwd6p0jKOTUlzr4RAIoe8eQx9Omm64-ZOELxBIbjaUmwxq-c=w640-h186" title="yearlySales = df.select(year("OrderDate").alias("Year")).groupBy("Year").count().orderBy("Year") display(yearlySales)" width="640" /></a></div><br /><br /><p></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p>Step 6. Query data using Spark SQL</p><p></p><ul style="text-align: left;"><li>The native methods of the data frame object you used previously enable you to query and analyze data quite effectively. However, many data analysts are more comfortable working with SQL syntax. </li><li>Spark SQL is a SQL language API in Spark that you can use to run SQL statements, or even persist data in relational tables. </li><li>The code you just ran creates a relational view of the data in a data frame, and then uses the spark.sql library to embed Spark SQL syntax within your Python code query the view and return the results as a data frame.</li></ul><p></p><p>Code: </p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>df.<span style="color: #795e26;">createOrReplaceTempView</span>(<span style="color: #c72e0f;">"salesorders"</span>)</div><div>spark_df <span style="color: #687687;">=</span> spark<span style="color: #795e26;">.sql</span>(<span style="color: #c72e0f;">"</span><span style="color: blue;">SELECT</span><span style="color: black;"> </span><span style="color: #687687;">*</span><span style="color: black;"> </span><span style="color: blue;">FROM</span><span style="color: black;"> salesorders</span><span style="color: #c72e0f;">"</span>)</div><div><span style="color: #795e26;">display</span>(spark_df)</div></div><p></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhK79EBPSN3cOTydzuNXiwHoUBEC50vCEzA9shhgxB7GyNSrlW1PHiw1quneIYlrtaHUzlMKthWPLLkgwZghiv864CB2Qb6y2KXgyiUQSV_xWU-_r2lJVCEQ_d5bmOp5URXFyFtKJDH-dhtXBdcuDQmKALW9mkM6Jioid1tTSSG3ZKXsA_fSckciwu-kNQ" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="SQL API in pyspark pysql, databricks" data-original-height="373" data-original-width="709" height="336" src="https://blogger.googleusercontent.com/img/a/AVvXsEhK79EBPSN3cOTydzuNXiwHoUBEC50vCEzA9shhgxB7GyNSrlW1PHiw1quneIYlrtaHUzlMKthWPLLkgwZghiv864CB2Qb6y2KXgyiUQSV_xWU-_r2lJVCEQ_d5bmOp5URXFyFtKJDH-dhtXBdcuDQmKALW9mkM6Jioid1tTSSG3ZKXsA_fSckciwu-kNQ=w640-h336" title="df.createOrReplaceTempView("salesorders") spark_df = spark.sql("SELECT * FROM salesorders") display(spark_df)" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div></div><p></p><div class="separator" style="clear: both;">Execute SQL code in datbricks</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>The ``%sql` line at the beginning of the cell (called a magic) indicates that the Spark SQL language runtime should be used to run the code in this cell instead of PySpark.</li><li>The SQL code references the salesorder view that you created previously.</li><li>The output from the SQL query is automatically displayed as the result under the cell.</li></ul></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Code:</div></div><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>%sql</div><div><span style="color: blue;">SELECT</span> <span style="color: #795e26;">YEAR</span>(OrderDate) <span style="color: blue;">AS</span> OrderYear,</div><div> <span style="color: #795e26;">SUM</span>((UnitPrice <span style="color: #687687;">*</span> Quantity) <span style="color: #687687;">+</span> Tax) <span style="color: blue;">AS</span> GrossRevenue</div><div><span style="color: blue;">FROM</span> salesorders</div><div><span style="color: blue;">GROUP BY</span> <span style="color: #795e26;">YEAR</span>(OrderDate)</div><div><span style="color: blue;">ORDER BY</span> OrderYear;</div></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"></div><div class="separator" style="clear: both; text-align: left;"><br /></div></div><p></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgUE2a8e4A3aRMlqRzu7Fi79uPAJVeud5DUZOumLYn5sfrUGc0FJP0nVEYeu8le_oKMHt6V5AwYyfxxZ1a0hltjBmHLkVYlWb-6_GTJpUXmZrMjefs4oCsLAFWySXuFKpQye9c4XAjmYCsdAPMBLI58vOSX53TlH6s5hBCdzTtm3o1WKT6SaktRPA_qVX4" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="SQL code in Azure AI databricks pyspark" data-original-height="448" data-original-width="677" height="424" src="https://blogger.googleusercontent.com/img/a/AVvXsEgUE2a8e4A3aRMlqRzu7Fi79uPAJVeud5DUZOumLYn5sfrUGc0FJP0nVEYeu8le_oKMHt6V5AwYyfxxZ1a0hltjBmHLkVYlWb-6_GTJpUXmZrMjefs4oCsLAFWySXuFKpQye9c4XAjmYCsdAPMBLI58vOSX53TlH6s5hBCdzTtm3o1WKT6SaktRPA_qVX4=w640-h424" title="%sql SELECT YEAR(OrderDate) AS OrderYear, SUM((UnitPrice * Quantity) + Tax) AS GrossRevenue FROM salesorders GROUP BY YEAR(OrderDate) ORDER BY OrderYear;" width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 7. Visualize data with Spark</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Azure Databricks include support for visualizing data from a data frame or Spark SQL query.</li><li>It is not designed for comprehensive charting.</li><li>You can use Python graphics libraries like Matplotlib and Seaborn to create charts from data in data frames.</li></ul></div><div class="separator" style="clear: both;">Code:</div><div class="separator" style="clear: both;"><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>%sql </div><div><span style="color: blue;">SELECT</span> <span style="color: #687687;">*</span> <span style="color: blue;">FROM</span> salesorders</div></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Table of results, select + and then select Visualization to view the visualization editor, and then apply the following options:</div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Visualization type: Bar</li><li>X Column: Item</li><li>Y Column: Add a new column and select Quantity. Apply the Sum aggregation.</li><li>Save the visualization and then re-run the code cell to view the resulting chart in the notebook.</li></ul></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEibJJN9g6o9POotQuryFYUQVIFXY8QMX01g8iTv0gYOb8XbUywYxsm6sTQDkOABjnw8sBW9TLmaIeW5Q9oTTc8sww0zq51B60MuKpXZMoPku0e7mGsJeS1fuDXmhtqcJQbCAAK4t8ndpnDXXUFSAdlZ2FbkLK8HBeXvKMdO6zyaxpEevxWragl6otD6J5E" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="pyspark-databricks visualization" data-original-height="670" data-original-width="700" height="612" src="https://blogger.googleusercontent.com/img/a/AVvXsEibJJN9g6o9POotQuryFYUQVIFXY8QMX01g8iTv0gYOb8XbUywYxsm6sTQDkOABjnw8sBW9TLmaIeW5Q9oTTc8sww0zq51B60MuKpXZMoPku0e7mGsJeS1fuDXmhtqcJQbCAAK4t8ndpnDXXUFSAdlZ2FbkLK8HBeXvKMdO6zyaxpEevxWragl6otD6J5E=w640-h612" title="%sql SELECT * FROM salesorders" width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><h3 style="clear: both; text-align: left;">Step 8. Use Matplotlib in Databricks</h3><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Let's utilize the Python Visualization Library for the same'</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;">Code:</div><div class="separator" style="clear: both;"><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>sqlQuery <span style="color: #687687;">=</span> <span style="color: #c72e0f;">"SELECT CAST(YEAR(OrderDate) AS CHAR(4)) AS OrderYear, </span><span style="color: blue;">\</span></div><div><span style="color: #c72e0f;"> SUM((UnitPrice * Quantity) + Tax) AS GrossRevenue </span><span style="color: blue;">\</span></div><div><span style="color: #c72e0f;"> FROM salesorders </span><span style="color: blue;">\</span></div><div><span style="color: #c72e0f;"> GROUP BY CAST(YEAR(OrderDate) AS CHAR(4)) </span><span style="color: blue;">\</span></div><div><span style="color: #c72e0f;"> ORDER BY OrderYear"</span></div><div>df_spark <span style="color: #687687;">=</span> spark<span style="color: #795e26;">.sql</span>(sqlQuery)</div><div>df_spark.<span style="color: #795e26;">show</span>()</div></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjKUWG8RskU0v47dNVlDps1OSYjBD6CJfYezimEBfIvPo3F3sc1U-Xw-kqsETRUC7byGEJYi3dUqMXBDfgqUHe6p8TXqS6kyEtbADhZQjEdJaIPgix8WtAlmrZxgJFjOYtqJkh9DSarTAyrmtu19Ji6IhEZLdWGQRd7VAbmlHqUme42C6BBxcQTObjxs8M" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><img alt="Pyspark and matplotlib" data-original-height="503" data-original-width="824" height="390" src="https://blogger.googleusercontent.com/img/a/AVvXsEjKUWG8RskU0v47dNVlDps1OSYjBD6CJfYezimEBfIvPo3F3sc1U-Xw-kqsETRUC7byGEJYi3dUqMXBDfgqUHe6p8TXqS6kyEtbADhZQjEdJaIPgix8WtAlmrZxgJFjOYtqJkh9DSarTAyrmtu19Ji6IhEZLdWGQRd7VAbmlHqUme42C6BBxcQTObjxs8M=w640-h390" title="Let's utilize the Python Visualization Library for the same" width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;">Results, which consist of a column chart with the total gross revenue for each year. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Note the following features of the code used to produce this chart:</div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>The matplotlib library requires a Pandas dataframe, so you need to convert the Spark dataframe returned by the Spark SQL query to this format.</li><li>At the core of the matplotlib library is the pyplot object. This is the foundation for most plotting functionality.</li></ul></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Code:</div><div class="separator" style="clear: both;"><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div><span style="color: blue;">from</span> matplotlib <span style="color: blue;">import</span> pyplot <span style="color: blue;">as</span> plt</div><div><span style="color: green;"># matplotlib requires a Pandas dataframe, not a Spark one</span></div><div>df_sales <span style="color: #687687;">=</span> df_spark.<span style="color: #795e26;">toPandas</span>()</div><div><span style="color: green;"># Create a bar plot of revenue by year</span></div><div>plt.<span style="color: #795e26;">bar</span>(<span style="color: #001080;">x</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'OrderYear'</span>], <span style="color: #001080;">height</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'GrossRevenue'</span>])</div><div><span style="color: green;"># Display the plot</span></div><div>plt.<span style="color: #795e26;">show</span>()</div></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiwvrwY3fADKnQGA-FeasOXTFsjTGrpUFu05wCurZMUNqt6TN3HZ0cFE6Ffa3ynbJwPrsv9W0nlgK72besXVubmaLR6f5DPS200vd0AN9_Y94WVDyp49n4bslDuxB50vqoadfOV9eGTuT21y91M2tJfwT1010rsKQC9_fwZWyC7oCBMxpC8yrcfNDpnzfk" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="matplotlib databricks" data-original-height="622" data-original-width="557" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEiwvrwY3fADKnQGA-FeasOXTFsjTGrpUFu05wCurZMUNqt6TN3HZ0cFE6Ffa3ynbJwPrsv9W0nlgK72besXVubmaLR6f5DPS200vd0AN9_Y94WVDyp49n4bslDuxB50vqoadfOV9eGTuT21y91M2tJfwT1010rsKQC9_fwZWyC7oCBMxpC8yrcfNDpnzfk=w573-h640" title="from matplotlib import pyplot as plt # matplotlib requires a Pandas dataframe, not a Spark one df_sales = df_spark.toPandas() # Create a bar plot of revenue by year plt.bar(x=df_sales['OrderYear'], height=df_sales['GrossRevenue']) # Display the plot plt.show()" width="573" /></a></div><br /><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Lets Customize the plot </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Code:</div><div class="separator" style="clear: both;"><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div><span style="color: green;"># Clear the plot area</span></div><div>plt.<span style="color: #795e26;">clf</span>()</div><div><span style="color: green;"># Create a bar plot of revenue by year</span></div><div>plt.<span style="color: #795e26;">bar</span>(<span style="color: #001080;">x</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'OrderYear'</span>], <span style="color: #001080;">height</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'GrossRevenue'</span>], <span style="color: #001080;">color</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'orange'</span>)</div><div><span style="color: green;"># Customize the chart</span></div><div>plt.<span style="color: #795e26;">title</span>(<span style="color: #c72e0f;">'Revenue by Year'</span>)</div><div>plt.<span style="color: #795e26;">xlabel</span>(<span style="color: #c72e0f;">'Year'</span>)</div><div>plt.<span style="color: #795e26;">ylabel</span>(<span style="color: #c72e0f;">'Revenue'</span>)</div><div>plt.<span style="color: #795e26;">grid</span>(<span style="color: #001080;">color</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'#95a5a6'</span>, <span style="color: #001080;">linestyle</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'--'</span>, <span style="color: #001080;">linewidth</span><span style="color: #687687;">=</span><span style="color: #098658;">2</span>, <span style="color: #001080;">axis</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'y'</span>, <span style="color: #001080;">alpha</span><span style="color: #687687;">=</span><span style="color: #098658;">0.7</span>)</div><div>plt.<span style="color: #795e26;">xticks</span>(<span style="color: #001080;">rotation</span><span style="color: #687687;">=</span><span style="color: #098658;">45</span>)</div><div><span style="color: green;"># Show the figure</span></div><div>plt.<span style="color: #795e26;">show</span>()</div></div></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEijrLuOyP-3_rmn8AocZGx32_DnPZRhupUqhdAoebpWl9mq9Hyo3osiUZHTqlc1yrLecmsdubdaG23DLHTL-5jpGsZSmR0Cyp0X8eBXd3YulbvmZLKYZ1t-KYbfot3ExfXbMRQZipsqTfcOqtF2Ps7VBCHYhHT36peowzkVauaNhNCsrelhlg5KbGy4Q8Q" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Customize the subplot in Azure Synapses" data-original-height="697" data-original-width="635" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEijrLuOyP-3_rmn8AocZGx32_DnPZRhupUqhdAoebpWl9mq9Hyo3osiUZHTqlc1yrLecmsdubdaG23DLHTL-5jpGsZSmR0Cyp0X8eBXd3YulbvmZLKYZ1t-KYbfot3ExfXbMRQZipsqTfcOqtF2Ps7VBCHYhHT36peowzkVauaNhNCsrelhlg5KbGy4Q8Q=w584-h640" title="plt.bar(x=df_sales['OrderYear'], height=df_sales['GrossRevenue'], color='orange') # Customize the chart plt.title('Revenue by Year') plt.xlabel('Year') plt.ylabel('Revenue') plt.grid(color='#95a5a6', linestyle='--', linewidth=2, axis='y', alpha=0.7) plt.xticks(rotation=45)" width="584" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"> </div>The figure was created implicitly for you; but you can create it explicitly.<br /><br />Code:<div><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div><span style="color: green;"># Clear the plot area</span></div><div>plt.<span style="color: #795e26;">clf</span>()</div><div><span style="color: green;"># Create a Figure</span></div><div>fig <span style="color: #687687;">=</span> plt.<span style="color: #795e26;">figure</span>(<span style="color: #001080;">figsize</span><span style="color: #687687;">=</span>(<span style="color: #098658;">8</span>,<span style="color: #098658;">3</span>))</div><div><span style="color: green;"># Create a bar plot of revenue by year</span></div><div>plt.<span style="color: #795e26;">bar</span>(<span style="color: #001080;">x</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'OrderYear'</span>], <span style="color: #001080;">height</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'GrossRevenue'</span>], <span style="color: #001080;">color</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'orange'</span>)</div><div><span style="color: green;"># Customize the chart</span></div><div>plt.<span style="color: #795e26;">title</span>(<span style="color: #c72e0f;">'Revenue by Year'</span>)</div><div>plt.<span style="color: #795e26;">xlabel</span>(<span style="color: #c72e0f;">'Year'</span>)</div><div>plt.<span style="color: #795e26;">ylabel</span>(<span style="color: #c72e0f;">'Revenue'</span>)</div><div>plt.<span style="color: #795e26;">grid</span>(<span style="color: #001080;">color</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'#95a5a6'</span>, <span style="color: #001080;">linestyle</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'--'</span>, <span style="color: #001080;">linewidth</span><span style="color: #687687;">=</span><span style="color: #098658;">2</span>, <span style="color: #001080;">axis</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'y'</span>, <span style="color: #001080;">alpha</span><span style="color: #687687;">=</span><span style="color: #098658;">0.7</span>)</div><div>plt.<span style="color: #795e26;">xticks</span>(<span style="color: #001080;">rotation</span><span style="color: #687687;">=</span><span style="color: #098658;">45</span>)</div><div><span style="color: green;"># Show the figure</span></div><div>plt.<span style="color: #795e26;">show</span>()</div></div><p></p><p></p><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgzxNXfAwf4gLpfefviVIXbes7HkqKneCzG34A4c9JgXsJmGqF_C65zrLZ32W1S9znbjaxTZrCwBb1Hs_RsN8R7v8cwskblXgOnCZSX7tMmcrGHSpRgC6nQapQfc09M0nNUtCj2_Q17MmwFFbJKgaJclcfy0zOQ9poUDkBuaEAtYoxZFf9kITfxdH7eR7o" style="margin-left: 1em; margin-right: 1em;"><img alt="Implicit and explicit subplots in data bricks" data-original-height="641" data-original-width="698" height="589" src="https://blogger.googleusercontent.com/img/a/AVvXsEgzxNXfAwf4gLpfefviVIXbes7HkqKneCzG34A4c9JgXsJmGqF_C65zrLZ32W1S9znbjaxTZrCwBb1Hs_RsN8R7v8cwskblXgOnCZSX7tMmcrGHSpRgC6nQapQfc09M0nNUtCj2_Q17MmwFFbJKgaJclcfy0zOQ9poUDkBuaEAtYoxZFf9kITfxdH7eR7o=w640-h589" title="# Create a Figure fig = plt.figure(figsize=(8,3)) # Create a bar plot of revenue by year plt.bar(x=df_sales['OrderYear'], height=df_sales['GrossRevenue'], color='orange') # Customize the chart plt.title('Revenue by Year') plt.xlabel('Year') plt.ylabel('Revenue') plt.grid(color='#95a5a6', linestyle='--', linewidth=2, axis='y', alpha=0.7) plt.xticks(rotation=45) # Show the figure" width="640" /></a></div><br /><br /><p></p><p><br /></p><p><br /></p><p>A figure can contain multiple subplots, each on its own axis</p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div><span style="color: green;"># Clear the plot area</span></div><div>plt.<span style="color: #795e26;">clf</span>()</div><div><span style="color: green;"># Create a figure for 2 subplots (1 row, 2 columns)</span></div><div>fig, ax <span style="color: #687687;">=</span> plt.<span style="color: #795e26;">subplots</span>(<span style="color: #098658;">1</span>, <span style="color: #098658;">2</span>, <span style="color: #001080;">figsize</span> <span style="color: #687687;">=</span> (<span style="color: #098658;">10</span>,<span style="color: #098658;">4</span>))</div><div><span style="color: green;"># Create a bar plot of revenue by year on the first axis</span></div><div>ax[<span style="color: #098658;">0</span>].<span style="color: #795e26;">bar</span>(<span style="color: #001080;">x</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'OrderYear'</span>], <span style="color: #001080;">height</span><span style="color: #687687;">=</span>df_sales[<span style="color: #c72e0f;">'GrossRevenue'</span>], <span style="color: #001080;">color</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">'orange'</span>)</div><div>ax[<span style="color: #098658;">0</span>].<span style="color: #795e26;">set_title</span>(<span style="color: #c72e0f;">'Revenue by Year'</span>)</div><div><span style="color: green;"># Create a pie chart of yearly order counts on the second axis</span></div><div>yearly_counts <span style="color: #687687;">=</span> df_sales[<span style="color: #c72e0f;">'OrderYear'</span>].<span style="color: #795e26;">value_counts</span>()</div><div>ax[<span style="color: #098658;">1</span>].<span style="color: #795e26;">pie</span>(yearly_counts)</div><div>ax[<span style="color: #098658;">1</span>].<span style="color: #795e26;">set_title</span>(<span style="color: #c72e0f;">'Orders per Year'</span>)</div><div>ax[<span style="color: #098658;">1</span>].<span style="color: #795e26;">legend</span>(yearly_counts.<span style="color: #795e26;">keys</span>().<span style="color: #795e26;">tolist</span>())</div><div><span style="color: green;"># Add a title to the Figure</span></div><div>fig.<span style="color: #795e26;">suptitle</span>(<span style="color: #c72e0f;">'Sales Data'</span>)</div><div><span style="color: green;"># Show the figure</span></div><div>plt.<span style="color: #795e26;">show</span>()</div></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgIpsHzUiDxfYU_h3WzdDVkMDQimvy9mTZcWWGRrtPnMXzlo_VKvh8OgcShSSewGBQTrJOvFKpGe73Y8ZVBhnk7RdYhm7bqPb9NeGqq874Z1xHZ2a2XljIhBR-oM37zSMjo1EpNYtGsUOf64qn4JkSdGXkcVlcmxRqlWgwNunNq3KhNX9NGThygtPXVjWw" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="multiple subplots Azure databricks" data-original-height="571" data-original-width="608" height="600" src="https://blogger.googleusercontent.com/img/a/AVvXsEgIpsHzUiDxfYU_h3WzdDVkMDQimvy9mTZcWWGRrtPnMXzlo_VKvh8OgcShSSewGBQTrJOvFKpGe73Y8ZVBhnk7RdYhm7bqPb9NeGqq874Z1xHZ2a2XljIhBR-oM37zSMjo1EpNYtGsUOf64qn4JkSdGXkcVlcmxRqlWgwNunNq3KhNX9NGThygtPXVjWw=w640-h600" title="# Clear the plot area plt.clf() # Create a figure for 2 subplots (1 row, 2 columns) fig, ax = plt.subplots(1, 2, figsize = (10,4)) # Create a bar plot of revenue by year on the first axis ax[0].bar(x=df_sales['OrderYear'], height=df_sales['GrossRevenue'], color='orange') ax[0].set_title('Revenue by Year') # Create a pie chart of yearly order counts on the second axis yearly_counts = df_sales['OrderYear'].value_counts() ax[1].pie(yearly_counts) ax[1].set_title('Orders per Year') ax[1].legend(yearly_counts.keys().tolist()) # Add a title to the Figure fig.suptitle('Sales Data') # Show the figure" width="640" /></a></div><br /><br /><p></p><p><br /></p><p><br /></p><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;">Step 9. Use the Seaborn Library</h3><p>Using the seaborn library (which is built on matplotlib and abstracts some of its complexity) to create a chart:</p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div><span style="color: blue;">import</span> seaborn <span style="color: blue;">as</span> sns</div><div>plt.<span style="color: #795e26;">clf</span>() <span style="color: green;"># Clear the plot area</span></div><div><span style="color: green;"># Create a bar chart</span></div><div>ax <span style="color: #687687;">=</span> sns.<span style="color: #795e26;">barplot</span>(<span style="color: #001080;">x</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">"OrderYear"</span>, <span style="color: #001080;">y</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">"GrossRevenue"</span>, <span style="color: #001080;">data</span><span style="color: #687687;">=</span>df_sales)</div><div>plt.<span style="color: #795e26;">show</span>()</div></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhYM5_r5M59JhP-uzTEI599H9h-fKBI9LZzROGwYak5J9-7GNp8URJ4XuPJTxN5cn6SQbtneDfFtkEO9GUCZtLOR0TsKXiDJmUCWzWALQQHWxJvdZ2F0GSngERZs7HExRyV0HPZEtDBG4FfPZJRK5yzayS7Q1prJDI7THdkkJ5wr381jYFtUlhytC6_eEM" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Seaborn library makes it simpler to create complex plots of statistical data, and enables you to control the visual theme for consistent data visualizations." data-original-height="635" data-original-width="653" height="622" src="https://blogger.googleusercontent.com/img/a/AVvXsEhYM5_r5M59JhP-uzTEI599H9h-fKBI9LZzROGwYak5J9-7GNp8URJ4XuPJTxN5cn6SQbtneDfFtkEO9GUCZtLOR0TsKXiDJmUCWzWALQQHWxJvdZ2F0GSngERZs7HExRyV0HPZEtDBG4FfPZJRK5yzayS7Q1prJDI7THdkkJ5wr381jYFtUlhytC6_eEM=w640-h622" title="import seaborn as sns plt.clf() # Clear the plot area # Create a bar chart ax = sns.barplot(x="OrderYear", y="GrossRevenue", data=df_sales) plt.show()" width="640" /></a></div><br /><br /><p></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p>Seaborn library makes it simpler to create complex plots of statistical data, and enables you to control the visual theme for consistent data visualizations.</p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>plt.<span style="color: #795e26;">clf</span>() <span style="color: green;"># Clear the plot area</span></div><div><span style="color: green;"># Set the visual theme for seaborn</span></div><div>sns.<span style="color: #795e26;">set_theme</span>(<span style="color: #001080;">style</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">"whitegrid"</span>)</div><div><span style="color: green;"># Create a bar chart</span></div><div>ax <span style="color: #687687;">=</span> sns.<span style="color: #795e26;">barplot</span>(<span style="color: #001080;">x</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">"OrderYear"</span>, <span style="color: #001080;">y</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">"GrossRevenue"</span>, <span style="color: #001080;">data</span><span style="color: #687687;">=</span>df_sales)</div><div>plt.<span style="color: #795e26;">show</span>()</div></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgrEetzj9OrOLz6m1mSW3KMG3WphseFcD0V-BEuiBzVrvpOFDnBrLwWRqI1uKQnVzhc_HFG8UYvl1t79Y7vPlhjig-kfbVBBB5iy9zH3-7EZDEmZKOi_mh4F1crvDYYB_vVSF0ObEsjgL1O2YwJfKdbyWEzy0JG5GYFgPZlwUDK4BTeA9j3CtbfAMCNdQE" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Azure Synapses and seaborn" data-original-height="667" data-original-width="664" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEgrEetzj9OrOLz6m1mSW3KMG3WphseFcD0V-BEuiBzVrvpOFDnBrLwWRqI1uKQnVzhc_HFG8UYvl1t79Y7vPlhjig-kfbVBBB5iy9zH3-7EZDEmZKOi_mh4F1crvDYYB_vVSF0ObEsjgL1O2YwJfKdbyWEzy0JG5GYFgPZlwUDK4BTeA9j3CtbfAMCNdQE=w637-h640" title="plt.clf() # Clear the plot area # Set the visual theme for seaborn sns.set_theme(style="whitegrid") # Create a bar chart ax = sns.barplot(x="OrderYear", y="GrossRevenue", data=df_sales) plt.show()" width="637" /></a></div><br /><br /><p></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p>Like matplotlib. seaborn supports multiple chart types</p><p>Code:</p><div style="background-color: #fafafa; color: #3b3b3b; font-family: Menlo, Monaco, Consolas, "Ubuntu Mono", "Source Code Pro", monospace, Consolas, "Courier New", monospace; font-size: 13px; line-height: 20px; white-space: pre;"><div>plt.<span style="color: #795e26;">clf</span>() <span style="color: green;"># Clear the plot area</span></div><div><span style="color: green;"># Create a bar chart</span></div><div>ax <span style="color: #687687;">=</span> sns.<span style="color: #795e26;">lineplot</span>(<span style="color: #001080;">x</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">"OrderYear"</span>, <span style="color: #001080;">y</span><span style="color: #687687;">=</span><span style="color: #c72e0f;">"GrossRevenue"</span>, <span style="color: #001080;">data</span><span style="color: #687687;">=</span>df_sales)</div><div>plt.<span style="color: #795e26;">show</span>()</div></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgSs4UBreH8CiaFDMGe1Fax2jDHZCNkyEfG0tjSZXlhC2mG-N7jWT96Tp-i7W_i62jkuq3qzlXiwRZztglkcS4V1mPu61sig4buDjGHq1iB8m1a-b5BSdSwGg7UJsFDstmmZ6L6LmUJB-u0PhiyYw8ksht-2veveMT5dXCnl4nMaXvdzwZdd92-GyPSrtQ" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="matplotlib, seaborn Azure databricks" data-original-height="634" data-original-width="659" height="617" src="https://blogger.googleusercontent.com/img/a/AVvXsEgSs4UBreH8CiaFDMGe1Fax2jDHZCNkyEfG0tjSZXlhC2mG-N7jWT96Tp-i7W_i62jkuq3qzlXiwRZztglkcS4V1mPu61sig4buDjGHq1iB8m1a-b5BSdSwGg7UJsFDstmmZ6L6LmUJB-u0PhiyYw8ksht-2veveMT5dXCnl4nMaXvdzwZdd92-GyPSrtQ=w640-h617" title="plt.clf() # Clear the plot area # Create a bar chart ax = sns.lineplot(x="OrderYear", y="GrossRevenue", data=df_sales) plt.show()" width="640" /></a></div><br /><br /><p></p><p><br /></p><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;">Step Last. Cleanup Resources</h3><p></p><ul style="text-align: left;"><li>In the Azure Databricks portal, on the Compute page, select your cluster and select ■ Terminate to shut it down.</li><li>If you’ve finished exploring Azure Databricks, you can delete the resources you’ve created to avoid unnecessary Azure costs and free up capacity in your subscription.</li></ul><p></p><p><br /></p></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com08/10, High Grounds, Sampangi Rama Nagar, Bengaluru, Karnataka 560001, India12.9863826 77.582829511.913764320413012 76.4841966875 14.059000879586989 78.6814623125tag:blogger.com,1999:blog-830335965541290967.post-75764865650245652242024-01-30T14:07:00.003+05:302024-01-31T00:52:37.481+05:30Explore Azure Databricks - Azure Databricks Lab 1<span><a name='more'></a></span><br /><div><h1 style="text-align: center;">Explore Azure Databricks</h1><p></p><div><br /></div><div><br /></div><div><br /></div><h3 style="text-align: left;">Step 1. Setup Azure Databricks Workspace and open notebook</h3><div><br /></div><div>Steps are available: <a href="https://saurabhsinhainblogs.blogspot.com/2024/01/azure-databricks-lab-how-to-start-with.html">https://saurabhsinhainblogs.blogspot.com/2024/01/azure-databricks-lab-how-to-start-with.html</a></div><div><ul style="text-align: left;"><li>Connect to Azure Portal</li><li>Setup Azure Datbricks</li><li>Setup Cluster for Azure Databricks</li><li>Open Notebook</li></ul></div><div><br /></div><h3 style="text-align: left;">Step 2. Prepare Data to consume</h3><div><br /></div><div><ul style="text-align: left;"><li>Go to the URL: https://raw.githubusercontent.com/MicrosoftLearning/mslearn-databricks/main/data/products.csv</li><li>Download data in CSV file, I named the file product.csv</li><li>On the File menu, select Upload data to DBFS.</li><li>In the Upload Data dialog box, note the DBFS Target Directory to where the file will be uploaded. </li><li>Then select the Files area, and upload the products.csv file you downloaded to your computer. </li><li>When the file has been uploaded, select Next</li><li>In the Access files from notebooks pane, select the sample PySpark code and copy it to the clipboard. </li><li>You will use it to load the data from the file into a data frame. Then select Done.</li></ul></div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg8w-nKSGsiZ5jFpKm0tWvZAaUijOy9JoqFpC_xRmINMATaK1dzFE5hZTQ420TjOCSsBk63baNHkcPvjQPw8n108iGj1lDd0TvATNoUIXoHbWVlX4BEFU2MZlDEcRwi_S2aY9_4ppODizlJ7IM79ZBG44s1U3g-gWxTq-Cpz-fNJyzMjgVVqMMP9IvceLg" style="margin-left: 1em; margin-right: 1em;"><img alt="In the Access files from notebooks pane, select the sample PySpark code and copy it to the clipboard." data-original-height="602" data-original-width="975" height="397" src="https://blogger.googleusercontent.com/img/a/AVvXsEg8w-nKSGsiZ5jFpKm0tWvZAaUijOy9JoqFpC_xRmINMATaK1dzFE5hZTQ420TjOCSsBk63baNHkcPvjQPw8n108iGj1lDd0TvATNoUIXoHbWVlX4BEFU2MZlDEcRwi_S2aY9_4ppODizlJ7IM79ZBG44s1U3g-gWxTq-Cpz-fNJyzMjgVVqMMP9IvceLg=w640-h397" title="In the Upload Data dialog box, note the DBFS Target Directory to where the file will be uploaded." width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 3. Execute code in Notebook</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li>In the notebook, in the empty code cell, paste the code you copied; which should look similar to this:</li><li>Use the ▸ Run Cell menu option at the top-right of the cell to run it, starting and attaching the cluster if prompted.</li><li>Wait for the Spark job run by the code to complete. The code has created a data frame object named df1 from the data in the file you uploaded.</li></ul></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Code:</div><div class="separator" style="clear: both; text-align: left;"><p class="MsoNormal" style="background: #FAFAFA; line-height: 15.0pt; margin-bottom: 0in;"><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">df1 </span><span style="color: #687687; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">=</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"> spark.read.</span><span style="color: #795e26; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">format</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">(</span><span style="color: #c72e0f; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">"csv"</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">).</span><span style="color: #795e26; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">option</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">(</span><span style="color: #c72e0f; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">"header"</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">, </span><span style="color: #c72e0f; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">"true"</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">).</span><span style="color: #795e26; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">load</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">(</span><span style="color: #c72e0f; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">"dbfs:/FileStore/shared_uploads/a@b.com/products.csv"</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">)<o:p></o:p></span></p></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEivHuPz12n9mNlqLPBASm-tGkn07tk5Hd8W_D-kVOIv3XzyT1xc835S-24i4QZ8VVxlC1Rac1uONJs7Vk_CP7CmZIvjhv2TN8eIPaSebnO6AxMkMOigvbsuuEAiPBus3Cq5QHktxmluc1ZkhmiDAPkmdfpmuiB6dtB6CTqdcSlCFKn5Rk41wdab4Hr2smg" style="margin-left: 1em; margin-right: 1em;"><img alt="df1 = spark.read.format("csv").option("header", "true").load("dbfs:/FileStore/shared_uploads/saurabh.f.sinha@accenture.com/products.csv")" data-original-height="151" data-original-width="975" height="100" src="https://blogger.googleusercontent.com/img/a/AVvXsEivHuPz12n9mNlqLPBASm-tGkn07tk5Hd8W_D-kVOIv3XzyT1xc835S-24i4QZ8VVxlC1Rac1uONJs7Vk_CP7CmZIvjhv2TN8eIPaSebnO6AxMkMOigvbsuuEAiPBus3Cq5QHktxmluc1ZkhmiDAPkmdfpmuiB6dtB6CTqdcSlCFKn5Rk41wdab4Hr2smg=w640-h100" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 4. Display the contents of the data frame</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Under the existing code cell, use the + icon to add a new code cell. Then in the new cell, enter the following code:</li><li>Use the ▸ Run Cell menu option at the top-right of the new cell to run it. This code displays the contents of the data frame, which should look similar to this:</li></ul></div></div><div class="separator" style="clear: both; text-align: left;">Code:</div><div class="separator" style="clear: both; text-align: left;"><p class="MsoNormal" style="background: #FAFAFA; line-height: 15.0pt; margin-bottom: 0in;"><span style="color: #795e26; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">print</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">(df1)<o:p></o:p></span></p>
<p class="MsoNormal" style="background: #FAFAFA; line-height: 15.0pt; margin-bottom: 0in;"><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">df1.</span><span style="color: #795e26; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">collect</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">()<o:p></o:p></span></p>
<p class="MsoNormal" style="background: #FAFAFA; line-height: 15.0pt; margin-bottom: 0in;"><span style="color: #795e26; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">display</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">(df1)<o:p></o:p></span></p></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgAihcblDxOQzv_ljcQKjHBtdLgf-1vTRR4oVtImgUDx22wRYWDlO6GOZaBRsFAJiccyJ_u-zopF63xkRYRUF6AP3rRimfYGFsZ8--MZf_TQIv5BTQricbtVWdJa0Vcp1zr-Sod-DHhQzHmlaRTSoNl33j98AQPkbWQy7hA7q9CS4_k1p0je-M-Q9C7APw" style="margin-left: 1em; margin-right: 1em;"><img alt="print(df1)" data-original-height="144" data-original-width="975" height="94" src="https://blogger.googleusercontent.com/img/a/AVvXsEgAihcblDxOQzv_ljcQKjHBtdLgf-1vTRR4oVtImgUDx22wRYWDlO6GOZaBRsFAJiccyJ_u-zopF63xkRYRUF6AP3rRimfYGFsZ8--MZf_TQIv5BTQricbtVWdJa0Vcp1zr-Sod-DHhQzHmlaRTSoNl33j98AQPkbWQy7hA7q9CS4_k1p0je-M-Q9C7APw=w640-h94" title="Under the existing code cell, use the + icon to add a new code cell. Then in the new cell, enter the following code:" width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhRIjPvWcY4SvyGr_6VfJQSwhBbrn9gPBLbqTemFYuEPhYxhCgn8CiNXEjjwQM9AMkUYymwk39qcz38Z8nsin9SdfizUb6onp3HlTGyhgjnCgaJ-mbxQ6rnrIGwCJI6KFzX_EPnwQpzARJsvw8q6mHinscUSM6uAIjYu0-ufpSJXKBJJ8Wl2foNpC1vF9g" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="collect(df1)" data-original-height="198" data-original-width="975" height="130" src="https://blogger.googleusercontent.com/img/a/AVvXsEhRIjPvWcY4SvyGr_6VfJQSwhBbrn9gPBLbqTemFYuEPhYxhCgn8CiNXEjjwQM9AMkUYymwk39qcz38Z8nsin9SdfizUb6onp3HlTGyhgjnCgaJ-mbxQ6rnrIGwCJI6KFzX_EPnwQpzARJsvw8q6mHinscUSM6uAIjYu0-ufpSJXKBJJ8Wl2foNpC1vF9g=w640-h130" title="Under the existing code cell, use the + icon to add a new code cell. Then in the new cell, enter the following code:" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjuqJCna_m8e13Ozcw-XsmnwkamnFNYTM7FFedg6UFC9GFLaGbSGOFwlQdfqGunZlhZhoNa003TgtaAcrRm6OfrhNSAZpzu6oor8RY4YmhFmOQxgkaIa0dWdUdC5v6fAk2TCKRa90Hf0hqUH0cbttZa-9j7DKG-J0SAclvvj-2dxlSB5iAzUiQPEIXzODA" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="display(df1)" data-original-height="324" data-original-width="975" height="212" src="https://blogger.googleusercontent.com/img/a/AVvXsEjuqJCna_m8e13Ozcw-XsmnwkamnFNYTM7FFedg6UFC9GFLaGbSGOFwlQdfqGunZlhZhoNa003TgtaAcrRm6OfrhNSAZpzu6oor8RY4YmhFmOQxgkaIa0dWdUdC5v6fAk2TCKRa90Hf0hqUH0cbttZa-9j7DKG-J0SAclvvj-2dxlSB5iAzUiQPEIXzODA=w640-h212" title="Display the contents of the data frame" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 5. Create Data Visualization and Data Profile</h3><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Above the table of results, select + and then select Visualization to view the visualization editor, and then apply the following options:</li><li>Visualization type: Bar</li><li>X Column: Category</li><li>Y Column: Add a new column and select ProductID. Apply the Count aggregation.</li></ul></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjFYHxI7KGf91A1ckp8uQjcGC4ZOrrwlxuV8AiwzY0o9bEK4krEPNkuWduh8Z8vzj16rejgY2br4E7Si1WZeB1s9ZRPjR34Qoibkr4Vn4N1MT1nXxCrLH91YxRpFeHXqi6XT-qkKFwLpRaiSHrzfdGAQuvvHS6ySWC5dtCzdPHXvlFg7KRzFni_jZF-SvU" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: right;"><img alt="Visualization type: Bar + Data Profile" data-original-height="324" data-original-width="975" height="212" src="https://blogger.googleusercontent.com/img/a/AVvXsEjFYHxI7KGf91A1ckp8uQjcGC4ZOrrwlxuV8AiwzY0o9bEK4krEPNkuWduh8Z8vzj16rejgY2br4E7Si1WZeB1s9ZRPjR34Qoibkr4Vn4N1MT1nXxCrLH91YxRpFeHXqi6XT-qkKFwLpRaiSHrzfdGAQuvvHS6ySWC5dtCzdPHXvlFg7KRzFni_jZF-SvU=w640-h212" title="Create Data Visualization and Data Profile" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><h3 style="clear: both; text-align: left;">Step 6. Create and query a table</h3><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Save the data frame as table object </li><li>SQL code to return the name and price of products in the Touring Bikes category.</li></ul></div></div><br />Code: </div><div class="separator" style="clear: both; text-align: left;">
<p class="MsoNormal" style="background: #FAFAFA; line-height: 15.0pt; margin-bottom: 0in;"><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">df1.write.</span><span style="color: #795e26; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">saveAsTable</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">(</span><span style="color: #c72e0f; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">"products"</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">)</span></p>
<p class="MsoNormal" style="background: #FAFAFA; line-height: 15.0pt; margin-bottom: 0in;"><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">%sql</span></p>
<p class="MsoNormal" style="background: #FAFAFA; line-height: 15.0pt; margin-bottom: 0in;"><span style="color: blue; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;">SELECT</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 0pt; mso-ligatures: none;"> ProductName, ListPrice </span><span style="color: blue; font-family: Consolas; font-size: 10pt;">FROM</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10pt;"> products </span><span style="color: blue; font-family: Consolas; font-size: 10pt;">WHERE</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10pt;"> Category </span><span style="color: #687687; font-family: Consolas; font-size: 10pt;">=</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10pt;"> </span><span style="color: #c72e0f; font-family: Consolas; font-size: 10pt;">'Touring Bikes'</span><span style="color: #3b3b3b; font-family: Consolas; font-size: 10pt;">;</span></p>
<p class="MsoNormal"><o:p> </o:p></p></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgEzby4VJcb3sQUhWvEvDuRSwMcLHu2NL0XK6E7diemaNYjqBgDl_8TPnUC9vsLjztda4MBB3vQ1z3bAunBobAwZDK2DlPNBZ9WSeq3pDtqdkgCaEhh9SErhsGo52I1y5oxbKWsgw5UrKrBH2tLs2SrAUivTJ0PcHlawrdkQuDkNdmlSWP2EVGGWNLthsk" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="df1.write.saveAsTable("products")" data-original-height="246" data-original-width="605" height="260" src="https://blogger.googleusercontent.com/img/a/AVvXsEgEzby4VJcb3sQUhWvEvDuRSwMcLHu2NL0XK6E7diemaNYjqBgDl_8TPnUC9vsLjztda4MBB3vQ1z3bAunBobAwZDK2DlPNBZ9WSeq3pDtqdkgCaEhh9SErhsGo52I1y5oxbKWsgw5UrKrBH2tLs2SrAUivTJ0PcHlawrdkQuDkNdmlSWP2EVGGWNLthsk=w640-h260" title="Save the data frame as table object" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiHrvd8q0DD8IjpO270vAPNf6FzajWqZg13XtXg52CKPilPKUH6hTeanfYbxGjY-pUiynvHlDWtdW8i5AnoYlfNemmysz2ouFF7NejmMEtPIRE0CFGVXpDjwvNSbrrgbPc7FUYAJLqGryzhRtcw7MixdSvS6UjvNInpyncZLcX9Ckxxo-KnRIeka9j6gPo" style="margin-left: 1em; margin-right: 1em;"><img alt="%sql SELECT ProductName, ListPrice FROM products WHERE Category = 'Touring Bikes';" data-original-height="480" data-original-width="811" height="378" src="https://blogger.googleusercontent.com/img/a/AVvXsEiHrvd8q0DD8IjpO270vAPNf6FzajWqZg13XtXg52CKPilPKUH6hTeanfYbxGjY-pUiynvHlDWtdW8i5AnoYlfNemmysz2ouFF7NejmMEtPIRE0CFGVXpDjwvNSbrrgbPc7FUYAJLqGryzhRtcw7MixdSvS6UjvNInpyncZLcX9Ckxxo-KnRIeka9j6gPo=w640-h378" title="Retrive output from sql datafram using sql" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Now if you want, you can try a couple more options</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><h3 style="clear: both; text-align: left;"> Step Last. Cleanup Resources</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li>In the Azure Databricks portal, on the Compute page, select your cluster and select ■ Terminate to shut it down.</li><li>If you’ve finished exploring Azure Databricks, you can delete the resources you’ve created to avoid unnecessary Azure costs and free up capacity in your subscription.</li></ul></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div></div></div></div></div></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com039 S La Salle St, Chicago, IL 60603, USA41.880889400000008 -87.632131141.829740943042452 -87.700795650781245 41.932037856957564 -87.563466549218745tag:blogger.com,1999:blog-830335965541290967.post-15115844140357965732024-01-30T12:41:00.002+05:302024-01-30T12:41:36.326+05:30Azure Databricks Lab, How to Start with ?<h3><span><a name='more'></a></span></h3><p><br /></p><h1 style="text-align: center;"> My Lab Setup for Azure Databricks practice</h1><p><br /></p><h4 style="text-align: left;">Azure Databricks is a Microsoft Azure-based version of the popular open-source Databricks platform. Similarly to Azure Synapse Analytics, an Azure Databricks workspace provides a central point for managing Databricks clusters, data, and resources on Azure.</h4><p><br /></p><h3 style="text-align: left;">Step 1. Signup for Azure Free trial </h3><p>Link: <a href="https://azure.microsoft.com/en-in/free">https://azure.microsoft.com/en-in/free</a></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEihrtBMcCvzJ1LBfteqc0_xlWaU96PGGguIZYvhpqES6Kbav8BCzD4m5QTAANtowtGk14XCmqlulxR3ZV0hT_PUoVZ8oOqiEKCKZBi8uGbLXA6Iq42QpLTEKSElkxFsKY6hNRnvaFkrigmfAL8I3xdmXT_ElD2jsJxZNMno5xKtXul5F9LVq2GhqurPg70" style="margin-left: 1em; margin-right: 1em;"><img alt="https://azure.microsoft.com/en-in/free" data-original-height="619" data-original-width="1039" height="191" src="https://blogger.googleusercontent.com/img/a/AVvXsEihrtBMcCvzJ1LBfteqc0_xlWaU96PGGguIZYvhpqES6Kbav8BCzD4m5QTAANtowtGk14XCmqlulxR3ZV0hT_PUoVZ8oOqiEKCKZBi8uGbLXA6Iq42QpLTEKSElkxFsKY6hNRnvaFkrigmfAL8I3xdmXT_ElD2jsJxZNMno5xKtXul5F9LVq2GhqurPg70=w320-h191" title="https://azure.microsoft.com/en-in/free" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 2. Sign in to the Azure portal</h3><div class="separator" style="clear: both; text-align: left;">Link: <a href="https://portal.azure.com">https://portal.azure.com</a></div><div class="separator" style="clear: both; text-align: left;"><br /></div>
<div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgxkymcejTnNu8yf9Xw8-oiSAT01gPEUb3lvFYoTMHdaQbNFaCJpCgZ1IT4hwFgdkLRwgU83fu1imwUrq1nToYCYeB-yL9U12Gl6h1U-FV8lrOYdqZKs56bCUcHvV-O1eqaF4r-gfh6IBbink7buLq25mC93zhTe6HCdsaNTSE9QlNRhbhA2mahJIuWxDQ" style="margin-left: 1em; margin-right: 1em;"><img alt="https://portal.azure.com" data-original-height="278" data-original-width="1253" height="89" src="https://blogger.googleusercontent.com/img/a/AVvXsEgxkymcejTnNu8yf9Xw8-oiSAT01gPEUb3lvFYoTMHdaQbNFaCJpCgZ1IT4hwFgdkLRwgU83fu1imwUrq1nToYCYeB-yL9U12Gl6h1U-FV8lrOYdqZKs56bCUcHvV-O1eqaF4r-gfh6IBbink7buLq25mC93zhTe6HCdsaNTSE9QlNRhbhA2mahJIuWxDQ=w400-h89" title="https://portal.azure.com" width="400" /></a></div><br /><br /></div>
<div class="separator" style="clear: both; text-align: left;"><br /></div><h3 style="clear: both; text-align: left;">Step 3. Create Azure Resource Group</h3><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhfSf9e4IMduxLZXxZF1JoaYVDmf1kYnEt4HZPqLTIY66bXiOQVPKTeWAIEUR4WcQgZgguma5vmzfJIYZx_RXeNOT-4XH9Ln6JX3__FZMpbK9dYZHVLJIZmO1OZ6fmwE3ku9bvcO67GdD8OMHPS0lYHGPnnHQ0eZmdITFdDn_LRt3EsWhH6oX-GxkcgAgw" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Create Azure Resource Group" data-original-height="713" data-original-width="975" height="293" src="https://blogger.googleusercontent.com/img/a/AVvXsEhfSf9e4IMduxLZXxZF1JoaYVDmf1kYnEt4HZPqLTIY66bXiOQVPKTeWAIEUR4WcQgZgguma5vmzfJIYZx_RXeNOT-4XH9Ln6JX3__FZMpbK9dYZHVLJIZmO1OZ6fmwE3ku9bvcO67GdD8OMHPS0lYHGPnnHQ0eZmdITFdDn_LRt3EsWhH6oX-GxkcgAgw=w400-h293" title="Create Azure Resource Group" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjePwsgnpxiU_ZBljvagUzkAzqFeioLOUI2mlBEmVbcrRnZw3Wc48ZyrH57y0PyutCA1i09mbuokrAzupP-3U-ix5cBS3v096cbh6Ue6AkTbkLqPvjshoUTrfmXk5zvFhi7MlNW-pbaVqBTdJKzAQAZfAvDM8RItlwy3XUxshHindadJYBRJm7LRMDzhOg" style="margin-left: 1em; margin-right: 1em;"><img alt="Resource Group List" data-original-height="385" data-original-width="975" height="253" src="https://blogger.googleusercontent.com/img/a/AVvXsEjePwsgnpxiU_ZBljvagUzkAzqFeioLOUI2mlBEmVbcrRnZw3Wc48ZyrH57y0PyutCA1i09mbuokrAzupP-3U-ix5cBS3v096cbh6Ue6AkTbkLqPvjshoUTrfmXk5zvFhi7MlNW-pbaVqBTdJKzAQAZfAvDM8RItlwy3XUxshHindadJYBRJm7LRMDzhOg=w640-h253" title="Resource Group List" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="text-align: left;">Step 4. Open Cloud Shell in Azure Portal</h3><div style="text-align: left;"><br /></div><div style="text-align: left;">Use the [>_] button to the right of the search bar at the top of the page to create a new Cloud Shell in the Azure portal, selecting a PowerShell environment and creating storage if prompted. The cloud shell provides a command line interface in a pane at the bottom of the Azure portal, as shown here:</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgvZ8OYD2Wfn7nXhXfDFeNkEyALFsXs_Olp75uJM27xI9r8C2qMeppKFEQCsIGpZW4scG0j0orcYBiekwVUPgFxtMq2nTHbMcrIBbcyvL_DOYgj1dh5W5s1U0gG7ThjnJ0N__-37lKRLn8KdNukSmyVM1C1vjKH_BTthxIt3jhykV3v0JFS4BvYSrpDkwE" style="margin-left: 1em; margin-right: 1em;"><img alt="selecting a PowerShell environment and creating storage if prompted" data-original-height="551" data-original-width="905" height="244" src="https://blogger.googleusercontent.com/img/a/AVvXsEgvZ8OYD2Wfn7nXhXfDFeNkEyALFsXs_Olp75uJM27xI9r8C2qMeppKFEQCsIGpZW4scG0j0orcYBiekwVUPgFxtMq2nTHbMcrIBbcyvL_DOYgj1dh5W5s1U0gG7ThjnJ0N__-37lKRLn8KdNukSmyVM1C1vjKH_BTthxIt3jhykV3v0JFS4BvYSrpDkwE=w400-h244" title="Use the [>_] button to the right of the search bar at the top of the page to create a new Cloud Shell" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">We will get the option to select a subscription, create/ use a resource group, storage account, file share</div><div class="separator" style="clear: both; text-align: left;">Let us create using Cloudshell, though we can create from GUI as well without much hustle.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEijGQWPYcm5F-ar9gFYoxssfWuOQBH_h51Z3N2gLyQn442jRTGfuYckUAyORJ_EqBjUjlpRQyTZnYuy3JWVfIEje7hQRukUv1aUa1eKNhn1Bx-fgdIV5N2DCAjhPmtnETsM4hiB7pIjxGe-hpzqSkTml4uLLsqXITnLUd4lNmn5ijkRHD7vWMYzestBsn4" style="margin-left: 1em; margin-right: 1em;"><img alt="We will get the option to select a subscription, create/ use a resource group," data-original-height="287" data-original-width="975" height="188" src="https://blogger.googleusercontent.com/img/a/AVvXsEijGQWPYcm5F-ar9gFYoxssfWuOQBH_h51Z3N2gLyQn442jRTGfuYckUAyORJ_EqBjUjlpRQyTZnYuy3JWVfIEje7hQRukUv1aUa1eKNhn1Bx-fgdIV5N2DCAjhPmtnETsM4hiB7pIjxGe-hpzqSkTml4uLLsqXITnLUd4lNmn5ijkRHD7vWMYzestBsn4=w640-h188" title="select a subscription, create/ use a resource group, storage account, file share" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi_FKR7jedSv5iI8RXbrtQaInnty5kXLbtvGKZzySnZ1Ij4r8_0li3t2f6FuYpd0RRW9drM7jz4mTboW-1xJA_PtitVNwTZhwr6SQ1ByG169FHh-gqNF62pYny4Le1UH9sGFwVq0vAyxXsdy5eVk5DRXKMJrGcWQfw0NebB04-zW7FGri7rf_w8DcKG2qk" style="margin-left: 1em; margin-right: 1em;"><img alt="cloud shell provides a command line interface in a pane at the bottom of the Azure portal," data-original-height="473" data-original-width="640" height="296" src="https://blogger.googleusercontent.com/img/a/AVvXsEi_FKR7jedSv5iI8RXbrtQaInnty5kXLbtvGKZzySnZ1Ij4r8_0li3t2f6FuYpd0RRW9drM7jz4mTboW-1xJA_PtitVNwTZhwr6SQ1ByG169FHh-gqNF62pYny4Le1UH9sGFwVq0vAyxXsdy5eVk5DRXKMJrGcWQfw0NebB04-zW7FGri7rf_w8DcKG2qk=w400-h296" title="cloud shell provides a command line interface in a pane at the bottom of the Azure portal," width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 5. Clone repository from git hub</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Here we can clone the existing repository to create Databricks services or we can do manually using the Azure portal also this has some resources to be used in the future like datasets.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">In the PowerShell pane, enter the following commands to clone this repo:</div></div></div></div></div></div></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li> rm -r mslearn-databricks -f</li><li> git clone https://github.com/MicrosoftLearning/mslearn-databricks</li></ul></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhIFFY03xwuijKwy51CYgzwBprxPwhaFXH4yvXpMmzNZJqqbBnUPqf59K_OcZWxdlH3BNhyeI-DNdWbAhZmHdY7q5WkXyT6Dfx2yRoVwJhiTelOOnXPSfYX5B69us-0LzxOVLfmYJPfHbCogIqZBxOL-6kZclQyvaM9gc50VWZZPXxgHFaH4H6eQhgqWj8" style="margin-left: 1em; margin-right: 1em;"><img alt="rm -r mslearn-databricks -f" data-original-height="362" data-original-width="975" height="238" src="https://blogger.googleusercontent.com/img/a/AVvXsEhIFFY03xwuijKwy51CYgzwBprxPwhaFXH4yvXpMmzNZJqqbBnUPqf59K_OcZWxdlH3BNhyeI-DNdWbAhZmHdY7q5WkXyT6Dfx2yRoVwJhiTelOOnXPSfYX5B69us-0LzxOVLfmYJPfHbCogIqZBxOL-6kZclQyvaM9gc50VWZZPXxgHFaH4H6eQhgqWj8=w640-h238" title="git clone https://github.com/MicrosoftLearning/mslearn-databricks" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">After the repo has been cloned, enter the following command to run the setup.ps1 script, which provisions an Azure Databricks workspace in an available region:</div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li> ./mslearn-databricks/setup.ps1</li></ul></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgVpB6umcVwZOlfGmLxR48WdWJAyfkhJBaugNN8xORIw1vUfhvgto2rl7NvtmBoZIBhXGx4hdeGABBB-jOoqOFzevHJziijc9pLjJ04ujsCxBKE5gyug9GqwqCswNCh2upTRGzlONHVE51yc4X8Fd8DQfxCXy0lf2oqlvSp8jtcOqsOE5bsOloS26eUzJk" style="margin-left: 1em; margin-right: 1em;"><img alt="./mslearn-databricks/setup.ps1" data-original-height="394" data-original-width="975" height="258" src="https://blogger.googleusercontent.com/img/a/AVvXsEgVpB6umcVwZOlfGmLxR48WdWJAyfkhJBaugNN8xORIw1vUfhvgto2rl7NvtmBoZIBhXGx4hdeGABBB-jOoqOFzevHJziijc9pLjJ04ujsCxBKE5gyug9GqwqCswNCh2upTRGzlONHVE51yc4X8Fd8DQfxCXy0lf2oqlvSp8jtcOqsOE5bsOloS26eUzJk=w640-h258" title="./mslearn-databricks/setup.ps1" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">I have tried executing the setup.ps1 file in the folder "mslearn-databricks" but no luck. I got a warning Insufficient resources</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><h3 style="clear: both; text-align: left;">Step 6. Create Azure Databricks Service</h3><div class="separator" style="clear: both; text-align: left;">This step would not have been required if setup.ps1 in the previous step had been successful.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg5pbhpIsUPBwmGznLDPIS2ABEKUHRyLqoNWa2AxBHVbfjIwtjWc9P81i_nZKQvVxNLV1CCVyj1ljVogyloF6ZHWieJk31lIYGtFH4jpp7OSWldJJ-BQWlwohBAoaWmtO4XF_Xvcdlx8kSsBzrlEKrlvRJ92FoMfm403HzioyiUJ0_OfOFJ-vNN4LkmFJk" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="setup,ps1 not able to create Azure resources" data-original-height="795" data-original-width="911" height="349" src="https://blogger.googleusercontent.com/img/a/AVvXsEg5pbhpIsUPBwmGznLDPIS2ABEKUHRyLqoNWa2AxBHVbfjIwtjWc9P81i_nZKQvVxNLV1CCVyj1ljVogyloF6ZHWieJk31lIYGtFH4jpp7OSWldJJ-BQWlwohBAoaWmtO4XF_Xvcdlx8kSsBzrlEKrlvRJ92FoMfm403HzioyiUJ0_OfOFJ-vNN4LkmFJk=w400-h349" title="This step would not have been required if setup.ps1 in the previous step had been successful." width="400" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiFhYtYdV0_Rh__5lHVoGzfOD298YOfOTW6eiQ51F5ieGnDnvy6HcU-GdH_s6UagOTCpb6qLhZhsT2CJroTfM020gFRG1So7Kl6gVrMNIxv1DtPZfl4ZqqDezRES21GuxtL_Lp86rTeKHwsNmBEwbB20UOWqzHKi1Cdwno8E7C8Y5KyW8N80w5LnMdB3Fg" style="margin-left: 1em; margin-right: 1em;"><img alt="I can see Azure Dataribcks service is created along the managed resource group name required for Azure Databricks." data-original-height="348" data-original-width="975" height="229" src="https://blogger.googleusercontent.com/img/a/AVvXsEiFhYtYdV0_Rh__5lHVoGzfOD298YOfOTW6eiQ51F5ieGnDnvy6HcU-GdH_s6UagOTCpb6qLhZhsT2CJroTfM020gFRG1So7Kl6gVrMNIxv1DtPZfl4ZqqDezRES21GuxtL_Lp86rTeKHwsNmBEwbB20UOWqzHKi1Cdwno8E7C8Y5KyW8N80w5LnMdB3Fg=w640-h229" title="I can see Azure Dataribcks service is created along the managed resource group name required for Azure Databricks." width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">I can see Azure Dataribcks service is created along the managed resource group name required for Azure Databricks.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiUSmCmUowUku3uBoBSojfokpBNXMroos64FVY_bTXURMunzH1tqYzLm695bKGKTNp-XuS1UWWteY0sIckcVDY_3SBLOF4W7kWsaNKCeG2ZzfrX8FgEBS6hbqe0lYRiW9PFG3yBPSAUBFxcQ3m1sysQGW4vwuadm6d99pXuvgxfsXclaLfC3UtBUNiB5VI" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Azure myFirst resources from ms databricks" data-original-height="419" data-original-width="975" height="276" src="https://blogger.googleusercontent.com/img/a/AVvXsEiUSmCmUowUku3uBoBSojfokpBNXMroos64FVY_bTXURMunzH1tqYzLm695bKGKTNp-XuS1UWWteY0sIckcVDY_3SBLOF4W7kWsaNKCeG2ZzfrX8FgEBS6hbqe0lYRiW9PFG3yBPSAUBFxcQ3m1sysQGW4vwuadm6d99pXuvgxfsXclaLfC3UtBUNiB5VI=w640-h276" title="Azure resources" width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiDoVcTvdWq5r1TdDTD2rtgFYMdz6ZYcpU1TjUTz_5YZUl41OUW3fjS4ZmPq81zW2xc6ngHjz2VJ3DhLb72yrxfkZ1mxNaGjIkfTyue41Vxr7NToxDa2rUKla3OLFJhWImcFskFDIlnDPl8By1mltw9Cg1BxhOHCettBlqP6dFfvso4mroGHaqVVA8nTN4" style="margin-left: 1em; margin-right: 1em;"><img alt="Azure synapses lab 1" data-original-height="491" data-original-width="975" height="322" src="https://blogger.googleusercontent.com/img/a/AVvXsEiDoVcTvdWq5r1TdDTD2rtgFYMdz6ZYcpU1TjUTz_5YZUl41OUW3fjS4ZmPq81zW2xc6ngHjz2VJ3DhLb72yrxfkZ1mxNaGjIkfTyue41Vxr7NToxDa2rUKla3OLFJhWImcFskFDIlnDPl8By1mltw9Cg1BxhOHCettBlqP6dFfvso4mroGHaqVVA8nTN4=w640-h322" title="My Managed resources for Azure data bricks" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 7. Launch Azure Databricks</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We will search Azure data bricks in the resource list and click the "Launch Workspace button"</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjyCdQpm-VcSGAFNkpge_6Bvypt14lpXMrzvTLU86gZaA2yyCyivclLocuX7b7MmVz61kF8rMY2jgjsEZuMG5A2igQ2hBG7EYPXVyktw8ZZejFg3SchL6QHMcHYbeiBf2pU2mb49CLtX0LiVXYSXMcwU2UbkvHo_DhgF9fzj6kks63Caf42qNBEShzvBBk" style="margin-left: 1em; margin-right: 1em;"><img alt="You can click url also" data-original-height="371" data-original-width="975" height="245" src="https://blogger.googleusercontent.com/img/a/AVvXsEjyCdQpm-VcSGAFNkpge_6Bvypt14lpXMrzvTLU86gZaA2yyCyivclLocuX7b7MmVz61kF8rMY2jgjsEZuMG5A2igQ2hBG7EYPXVyktw8ZZejFg3SchL6QHMcHYbeiBf2pU2mb49CLtX0LiVXYSXMcwU2UbkvHo_DhgF9fzj6kks63Caf42qNBEShzvBBk=w640-h245" title="Launch Azure Databricks" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiJNbpBp_Tdmn3wajKcJGP6DcctR25M0wClaxRr_d77d2dOfwwm5BGcfrtvLaGYb6zkp3s-w-MO7X7-A671kXUgxTzrwxNBEDiXIkLcRsJu7rXDYZgykcZrhEtXgUZ-tQcaL0dZ30lYiEMj947kiRmufE5WO6dFcoli1CaUWnfBnK6xXjJjoGd5j4Y5e_0" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="Opening my Azure drabricks studio" data-original-height="708" data-original-width="908" height="250" src="https://blogger.googleusercontent.com/img/a/AVvXsEiJNbpBp_Tdmn3wajKcJGP6DcctR25M0wClaxRr_d77d2dOfwwm5BGcfrtvLaGYb6zkp3s-w-MO7X7-A671kXUgxTzrwxNBEDiXIkLcRsJu7rXDYZgykcZrhEtXgUZ-tQcaL0dZ30lYiEMj947kiRmufE5WO6dFcoli1CaUWnfBnK6xXjJjoGd5j4Y5e_0=w320-h250" title="Azure Databricks Sign in" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhjCbdEOOV8Qixetw1zPsh0GQe8qG4Lo_L0miC0ECMnDMyJr3x1IopMKsKKVHCo0JlQ82SgspG1BFYn0o82veeg7LPDdBpBrRiPeWmioeMmqweE5d1wfuAvQ4E_PZUcDgw0uQPEiSbb3rDLUosiJIhEzOFSCKWOGmj0Ld2YG2RJzJjXCYL5eqYlwAoFq0U" style="margin-left: 1em; margin-right: 1em;"><img alt="Azure Synapse workspace" data-original-height="466" data-original-width="975" height="306" src="https://blogger.googleusercontent.com/img/a/AVvXsEhjCbdEOOV8Qixetw1zPsh0GQe8qG4Lo_L0miC0ECMnDMyJr3x1IopMKsKKVHCo0JlQ82SgspG1BFYn0o82veeg7LPDdBpBrRiPeWmioeMmqweE5d1wfuAvQ4E_PZUcDgw0uQPEiSbb3rDLUosiJIhEzOFSCKWOGmj0Ld2YG2RJzJjXCYL5eqYlwAoFq0U=w640-h306" title="Azure Databricks Studio" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 8. Create Cluster in Azure DataBricks</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Azure Databricks is a distributed processing platform that uses Apache Spark clusters to process data in parallel on multiple nodes. Each cluster consists of a driver node to coordinate the work, and worker nodes to perform processing tasks. For practice, we’ll create a single-node cluster to minimize the compute resources used in the lab environment (in which resources may be constrained). In a production environment, we typically create a cluster with multiple worker nodes.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiHL5_vvkT5SRfEwdbVkWQzLMbIlmM-d1gA-RLYP-In_4N_ibunt4bjSo5G6BWTMRlpSf3LT1jRpJrMxBIdEDMNomuh4IQwbXHeuu0SCuogIRR2nk9AIaassmonyRRjGM2qnH7dc9KX3iPfEK60zbZm_TkZPZtQNMfQ-noN1LOw9AVxbHTCcVEuM784o8E" style="margin-left: 1em; margin-right: 1em;"><img alt="Databricks runtime version: 13.3 LTS (Spark 3.4.1, Scala 2.12) or later" data-original-height="576" data-original-width="640" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiHL5_vvkT5SRfEwdbVkWQzLMbIlmM-d1gA-RLYP-In_4N_ibunt4bjSo5G6BWTMRlpSf3LT1jRpJrMxBIdEDMNomuh4IQwbXHeuu0SCuogIRR2nk9AIaassmonyRRjGM2qnH7dc9KX3iPfEK60zbZm_TkZPZtQNMfQ-noN1LOw9AVxbHTCcVEuM784o8E=w400-h360" title="we’ll create a single-node cluster to minimize the compute resources used in the lab environment" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div></div></div></div></div></div></div></div></div></div></div></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>In the sidebar on the left, select the (+) New task, and then select Cluster.</li><li>In the New Cluster page, create a new cluster with the following settings:</li><ul><li>Cluster name: User Name’s cluster (the default cluster name)</li><li>Policy: Unrestricted</li><li>Cluster mode: Single Node</li><li>Access mode: Single user (with your user account selected)</li><li>Databricks runtime version: 13.3 LTS (Spark 3.4.1, Scala 2.12) or later</li><li>Use Photon Acceleration: Selected</li><li>Node type: Standard_DS3_v2</li><li>Terminate after 20 minutes of inactivity</li></ul><li>Wait for the cluster to be created. It may take a minute or two.</li></ul></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj8J57wTvuHDwCH88HOwcr5YC4RwPUvElq8g1RFPQ4zHsbZ3fUGmjd9FkrYthnjRzLqz-_jHYgokzbm6nM5XArkv83IADlQQRbUtDyZ036XBltZhzzUS-cJNKYdr_dIPzF5UgBVtG3Dy-zsDH0B9M_OfK22e6M3mY1wAgrjpDQ69nMyZuFEXs2x8HZUxOE" style="margin-left: 1em; margin-right: 1em;"><img alt="Node type: Standard_DS3_v2" data-original-height="445" data-original-width="975" height="292" src="https://blogger.googleusercontent.com/img/a/AVvXsEj8J57wTvuHDwCH88HOwcr5YC4RwPUvElq8g1RFPQ4zHsbZ3fUGmjd9FkrYthnjRzLqz-_jHYgokzbm6nM5XArkv83IADlQQRbUtDyZ036XBltZhzzUS-cJNKYdr_dIPzF5UgBVtG3Dy-zsDH0B9M_OfK22e6M3mY1wAgrjpDQ69nMyZuFEXs2x8HZUxOE=w640-h292" title="Access mode: Single user (with your user account selected)" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Step 9. Create Pyspark Notebook</h3><div class="separator" style="clear: both; text-align: left;"><br /></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>In the sidebar, use the (+) New link to create a Notebook.</li><li>Change the default notebook name (Untitled Notebook [date]) to a new name</li><li>In the Connect drop-down list, select your cluster if it is not already selected. If the cluster is not running, it may take a minute or so to start.</li></ul></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjJxTwCXeNsaSLbaY2vItxloVVQ4KpfS7m8R8tvcQ37nJLD8IA_zXKNj_oEatAAbdFkH4K1I8SWeWgetarpEC3Ddm9Ms11i8vxPO59LfBN6iOH597upVkP6WdmQCVqdsZEcSzZa1MEy2VO1WdPG0hFOp1KbTfqr8FnATNkb3wJXJLxeBAIWqsdC8XSqFA4" style="margin-left: 1em; margin-right: 1em;"><img alt="Change the default notebook name (Untitled Notebook [date]) to a new name" data-original-height="273" data-original-width="486" height="225" src="https://blogger.googleusercontent.com/img/a/AVvXsEjJxTwCXeNsaSLbaY2vItxloVVQ4KpfS7m8R8tvcQ37nJLD8IA_zXKNj_oEatAAbdFkH4K1I8SWeWgetarpEC3Ddm9Ms11i8vxPO59LfBN6iOH597upVkP6WdmQCVqdsZEcSzZa1MEy2VO1WdPG0hFOp1KbTfqr8FnATNkb3wJXJLxeBAIWqsdC8XSqFA4=w400-h225" title="In the sidebar, use the (+) New link to create a Notebook." width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi2E5_3t0fE6Ww7sZrDPZxbtuUr_tXHeLGY6OYYX6I848pkzU_BYA_AqAGFRvn-XEWSoQEkxRw-jZuyOkrCNptjw7m78lroJaZMTpZmqMeyjS7uEt2wNjX6LCndTdIaqxcunroJXYL9QlgQAJEO5_erbXOxNhErg5xkpz8-aOlnGQDZCh8v6LMsZrKbHMo" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="MyFirst Azure Synapse Notebook" data-original-height="327" data-original-width="799" height="262" src="https://blogger.googleusercontent.com/img/a/AVvXsEi2E5_3t0fE6Ww7sZrDPZxbtuUr_tXHeLGY6OYYX6I848pkzU_BYA_AqAGFRvn-XEWSoQEkxRw-jZuyOkrCNptjw7m78lroJaZMTpZmqMeyjS7uEt2wNjX6LCndTdIaqxcunroJXYL9QlgQAJEO5_erbXOxNhErg5xkpz8-aOlnGQDZCh8v6LMsZrKbHMo=w640-h262" title="MyFirst Pyspark Notebook" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><div style="text-align: left;"><b><i>Now you can practice all the code you want and practice for your interview at least for a month</i></b></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><h3 style="text-align: left;">Step Last. Cleanup Resources</h3><div style="text-align: left;"><br /></div><div style="text-align: left;"><div><ul style="text-align: left;"><li>In the Azure Databricks portal, on the Compute page, select your cluster and select ■ Terminate to shut it down.</li><li>If you’ve finished exploring Azure Databricks, you can delete the resources you’ve created to avoid unnecessary Azure costs and free up capacity in your subscription.</li></ul></div></div></div><br /></div></div></div></div></div></div></div></div></div></div></div></div></div></div><p></p>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0Chambers St, New York, NY 10013, USA40.7131034 -74.004046640.712290177374435 -74.005119483605952 40.713916622625568 -74.002973716394038tag:blogger.com,1999:blog-830335965541290967.post-42014172035912933822024-01-29T12:55:00.003+05:302024-01-29T12:55:38.675+05:30Lab - Google's Cloud Pub\Sub - Publish message<p> <span></span></p><a name='more'></a><p></p><span><!--more--></span><p><br /></p><h1 style="text-align: center;">Google's Cloud Pub\Sub - Lab</h1><p><br /></p><h2 style="text-align: left;">Objective:</h2><p></p><ul style="text-align: left;"><li>Create some Pub/Sup topics and subscriptions</li><li>See how to publish messages and consume them.</li></ul><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhfVbRcAA0g4WFwiTAVMWHVdbQCqrwcw1BoxQq_-vMF_1mzyfMIX1mFBsgDBcKyAzSokStSaW2Ht9j4ghj-JPffI_noM-_3O82uTiO0jMj3ZZqNWvoAYF6JhcOGh3iTzOKJ2rtkJAUY-rzRtTX1MrVS4RwcV6J6MEE-b8GWwdKSK-E2odUD-9pMA-Xq" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Pub/Sup topics and subscriptions GCP" data-original-height="168" data-original-width="383" height="140" src="https://blogger.googleusercontent.com/img/a/AVvXsEhfVbRcAA0g4WFwiTAVMWHVdbQCqrwcw1BoxQq_-vMF_1mzyfMIX1mFBsgDBcKyAzSokStSaW2Ht9j4ghj-JPffI_noM-_3O82uTiO0jMj3ZZqNWvoAYF6JhcOGh3iTzOKJ2rtkJAUY-rzRtTX1MrVS4RwcV6J6MEE-b8GWwdKSK-E2odUD-9pMA-Xq=w320-h140" title="proffessional Data engineer" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div></div><h2 style="text-align: left;">Implementation tool:</h2><p></p><ul style="text-align: left;"><li>In the Cloud Console,</li><li>In the gcloud command line tool.</li></ul><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhvWH0W6ZohCaVRqBm-WIV0yATA0vPHnrtNRzpUlDGxS4pgmcqZ0DphHaIgHeDnC9k06LMpZhBK2bRy9PDn9xwOc0ltTPvu2pLGij3Ko8ERUaQoZEv7OejrmtL7-MWlZkwUsSABEr0Vffn5vxvoO3k59DKJ4VkTTzV-FS4OPK0k-pR9pywR9Whac5dG" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="pub Sub Implementation tool:" data-original-height="119" data-original-width="191" height="199" src="https://blogger.googleusercontent.com/img/a/AVvXsEhvWH0W6ZohCaVRqBm-WIV0yATA0vPHnrtNRzpUlDGxS4pgmcqZ0DphHaIgHeDnC9k06LMpZhBK2bRy9PDn9xwOc0ltTPvu2pLGij3Ko8ERUaQoZEv7OejrmtL7-MWlZkwUsSABEr0Vffn5vxvoO3k59DKJ4VkTTzV-FS4OPK0k-pR9pywR9Whac5dG=w320-h199" title="gcloud command line tool commands" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /><h2 style="text-align: left;">Steps</h2><p></p><h3 style="text-align: left;"><b>Step 1: Open your GCP project and go to GCP Cloud Console.</b></h3><p></p><ul style="text-align: left;"><li>Let's practice interacting with Pub/Sub through this interface first before we tackle the command line.</li><li>First, select Pub/Sub from the burger menu under the Big Data section.</li><li>Click Create Topic. </li><ul><li>And we can see the full path to the topic here, which includes our project name.</li><li>We'll let Google manage the encryption keys and click, Create Topic.</li></ul></ul><div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiQ8Bke1KGWRHkUJDYIhf2ag1uY6XK312pa0vUefg_kpPLPUnkmf0DMcVfJJnSDGmSQRzeIei2W8KVRTK7F1WhIXKWG-PUao6Il3Din3AOdX5X-qlN7DfzfuS5w_0ryJhXb7u0JrqHFYpVoc5VSdfOnYD6CXh9uurDK3S4qM2t2PE3w95AKsGpdlQjl" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="GCP pub sub engineering data" data-original-height="200" data-original-width="443" height="180" src="https://blogger.googleusercontent.com/img/a/AVvXsEiQ8Bke1KGWRHkUJDYIhf2ag1uY6XK312pa0vUefg_kpPLPUnkmf0DMcVfJJnSDGmSQRzeIei2W8KVRTK7F1WhIXKWG-PUao6Il3Din3AOdX5X-qlN7DfzfuS5w_0ryJhXb7u0JrqHFYpVoc5VSdfOnYD6CXh9uurDK3S4qM2t2PE3w95AKsGpdlQjl=w400-h180" title="select Pub/Sub from the burger menu under the Big Data section" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><br /><br /></div><h3></h3><h3><ul style="text-align: left;"><li>Step 2: Let's create a subscription.</li></ul></h3><ul style="text-align: left;"><ul><li>First, go back to the list of topics and click the 3 dots here to access some further options.</li><li>Then, click Create Subscription. We'll leave the delivery type as Pull and accept all the other default settings. Scroll down and click Create.</li></ul></ul><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgv8aO41aeWfPGqGXn6N_DzTGzhZXsugxT2F9Ica0zbSSteUs7kxINldZDfkPK9WnmIzfGT8_i3BYi5t57dZEUjk7P6Cev2GH6eceCgUFa0_uBUKobz-Fps4SU2oMsVGTJKI82UsVn9R_ruvZbCJMRkYglxMg_aORPzyXs124jKRMNwlQaxh00XruKt" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Let's create a subscription in pub/sub" data-original-height="128" data-original-width="416" height="122" src="https://blogger.googleusercontent.com/img/a/AVvXsEgv8aO41aeWfPGqGXn6N_DzTGzhZXsugxT2F9Ica0zbSSteUs7kxINldZDfkPK9WnmIzfGT8_i3BYi5t57dZEUjk7P6Cev2GH6eceCgUFa0_uBUKobz-Fps4SU2oMsVGTJKI82UsVn9R_ruvZbCJMRkYglxMg_aORPzyXs124jKRMNwlQaxh00XruKt=w400-h122" title="pub sub subscription creation" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><h3></h3><h3><ul style="text-align: left;"><li>Step 3: Let's create a message.</li></ul></h3><ul style="text-align: left;"><ul><li>Go back to the topics page into topic and click Publish Message.</li><li>You can type anything you want in here. Then click publish.</li><li>That message is now queued up in our Pub/Sub topic.</li></ul></ul><div><br /></div><div>Note: If you are not able to find publish message, please use command line</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhMCbf9bId1VoykxAVuInPryWVR_UFYGfr_DcHJ8T5dSDuoTNox6ExhP14BZakcuOmCkRdnwgjG632px45I04T-ZCY4N7enRWJtjGsXPZ6lIvQUdUH1bklCV84xo9BBxKEtSn6EreduXVExSNj3Z47UtlR4v1bvUakHHxHJVoBbMvM7TAr6GntRyIJk" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="That message is now queued up in our Pub/Sub topic." data-original-height="120" data-original-width="613" height="126" src="https://blogger.googleusercontent.com/img/a/AVvXsEhMCbf9bId1VoykxAVuInPryWVR_UFYGfr_DcHJ8T5dSDuoTNox6ExhP14BZakcuOmCkRdnwgjG632px45I04T-ZCY4N7enRWJtjGsXPZ6lIvQUdUH1bklCV84xo9BBxKEtSn6EreduXVExSNj3Z47UtlR4v1bvUakHHxHJVoBbMvM7TAr6GntRyIJk=w640-h126" title="That message is now queued up in our Pub/Sub topic." width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: left;"><h4><ul style="text-align: left;"><li>Set Project in Command line</li></ul></h4><ul style="text-align: left;"><ul><li>Syntax: gcloud config set project [Project-ID]</li><li>Command: gcloud config set project playground-s-11-1bcdfc2d</li></ul></ul><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgpxa6-eaJ7Q1urLxYjwLNDAZbFVb_yJmO5C2vnxM_fgAl--1ozkt-hbqeujagwh7dBAqSfMUud5mHFJUcPqcoP5Z56YAs3qcLeIAB6ljg0IhH4Cmv62mOzFbPpk90IyOjVvIrJ2bXH6eWaGjLiyMcw7dzBwmHIIARTi1JNS-ZwYesYcI-kZBUnpLHM" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="37" data-original-width="901" height="26" src="https://blogger.googleusercontent.com/img/a/AVvXsEgpxa6-eaJ7Q1urLxYjwLNDAZbFVb_yJmO5C2vnxM_fgAl--1ozkt-hbqeujagwh7dBAqSfMUud5mHFJUcPqcoP5Z56YAs3qcLeIAB6ljg0IhH4Cmv62mOzFbPpk90IyOjVvIrJ2bXH6eWaGjLiyMcw7dzBwmHIIARTi1JNS-ZwYesYcI-kZBUnpLHM=w640-h26" width="640" /></a></div><br /><br /></div><h4><ul style="text-align: left;"><li>Send message to subscription from topic</li></ul></h4><ul style="text-align: left;"><ul><li>Syntax: gcloud pubsub topics publish test1topic --message "messagae"</li><li>Command: gcloud pubsub topics publish test1topic --message "messaga1-send"</li></ul></ul></div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjNxgQ2fQSnVISXA8vC1mc3RYkQpxqI2CLudpR8S3K7UsRDLjbkgc5Mxg_gprtJ96CDSwNd5zEFwX2STooa3yJvSlwgv5ETdgnmb4dq2FUxmI7SEVrWN3toN49zqYG6cYORCkXf490oIFTnSYSR41uov_rIocTIachGvniExCQzhDalZRmcHFNSKXec" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="46" data-original-width="1014" height="30" src="https://blogger.googleusercontent.com/img/a/AVvXsEjNxgQ2fQSnVISXA8vC1mc3RYkQpxqI2CLudpR8S3K7UsRDLjbkgc5Mxg_gprtJ96CDSwNd5zEFwX2STooa3yJvSlwgv5ETdgnmb4dq2FUxmI7SEVrWN3toN49zqYG6cYORCkXf490oIFTnSYSR41uov_rIocTIachGvniExCQzhDalZRmcHFNSKXec=w640-h30" width="640" /></a></div><br /><br /><br /></div><ul style="text-align: left;"><li>We can view it by clicking View Messages, which will let us act as a subscriber, right inside the Cloud Console.</li></ul>This isn't something you'd normally do in a production environment<br /><ul style="text-align: left;"><li>First, select the subscription that we just created. Then click, And there's the message that we just published.</li><li>Notice, we didn't select this checkbox to enable ACK messages or acknowledgement messages.</li></ul><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhXQzbYdeEDLHG6qGjPqI8nWEj7GM05Oag35ywEdO0sOqNHVd9X7lKuU3eo769GIrO0nCSsIIwq1BxPnagut8dKStuQlOSs9Ca9riBwaZTfTEqrkwjHY2gnoZA_TpVO1aLSchPjnGDlzNOLiRv9KMQr4em7m-VCxeLG44Lt5D2a0S7_Bde0E71i5wjf" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="enable ACK messages or acknowledgement messages. Pub sub" data-original-height="38" data-original-width="191" height="80" src="https://blogger.googleusercontent.com/img/a/AVvXsEhXQzbYdeEDLHG6qGjPqI8nWEj7GM05Oag35ywEdO0sOqNHVd9X7lKuU3eo769GIrO0nCSsIIwq1BxPnagut8dKStuQlOSs9Ca9riBwaZTfTEqrkwjHY2gnoZA_TpVO1aLSchPjnGDlzNOLiRv9KMQr4em7m-VCxeLG44Lt5D2a0S7_Bde0E71i5wjf=w400-h80" title="enable ACK messages or acknowledgement messages." width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><ul style="text-align: left;"><li>And now, the deadline has been exceeded for us to acknowledge the receipt of the message.</li><li>This means the message stays in the queue because Pub/Sub doesn't know for sure that we definitely received it.</li><li>Now we'll retry and enable ACK messages. Now we can see our message and quickly click ACK to acknowledge it.</li><li>This is how a production Pub/Sub client would operate. The message has been received successfully, so we acknowledge that, which pops it off the top of the queue of our topic.</li></ul><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhznQjZ_kfhZMNVP064zj4A-vMTFpJUeFT2n3Ku-rXPeLjX7aprH5vs0LdU7AuLjL05w1byaO8E90EeoOC7ueHYF7Inn6ysp5UIwuanoGQb3xl8TPUDioa-xjR9GFpxeRWGhMZuoxzwTIbvB4T_uOPA0WMIKy9r9sUY7gI_Sn1NbVUfWPC59eksa0cX" style="margin-left: 1em; margin-right: 1em;"><img alt="we acknowledge that, which pops it off the top of the queue of our topic." data-original-height="71" data-original-width="737" height="62" src="https://blogger.googleusercontent.com/img/a/AVvXsEhznQjZ_kfhZMNVP064zj4A-vMTFpJUeFT2n3Ku-rXPeLjX7aprH5vs0LdU7AuLjL05w1byaO8E90EeoOC7ueHYF7Inn6ysp5UIwuanoGQb3xl8TPUDioa-xjR9GFpxeRWGhMZuoxzwTIbvB4T_uOPA0WMIKy9r9sUY7gI_Sn1NbVUfWPC59eksa0cX=w640-h62" title="we acknowledge that, which pops it off the top of the queue of our topic." width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>If we try to pull one more time, we'll see, no more messages are waiting for our subscription.</li><li>Let's try one more thing to prove the delivery wants promise. </li><li>Go back to the topics list and copy the full path of the topic by clicking this link here.</li><li>We'll go to subscriptions and create a new one. let's go back to our topic and publish another message.</li><li>Click Create Message. And type anything you like here. Click Publish Message.</li><li>Now, we'll view that message by clicking View Messages.</li><li>Select the first subscription we created. Tick Enable ACK Messages and then Pull. As soon as you see the message, click the link to acknowledge it. Now, let's click Pull again and you can see that this subscriber no longer has any messages.</li><li>For other subscriptions?</li><ul><li>Click Pull again and there's our message. And we'll quickly acknowledge it.</li><li>Each subscriber is guaranteed to get each message once.</li><li>This is an example of the one-to-many pattern.</li></ul></ul></div></div><br /><br /></div><p></p><div><h2 style="text-align: left;"><a href="https://www.algaestudy.com/2023/02/accessing-gcp-pubsub-from-command-line.html" rel="nofollow" target="_blank">Accessing Pub/Sub from the command line.</a></h2><div><br /></div></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com05F5W+93 Sage Hen, CA, USA41.1583771 -120.504765934.452287232715875 -129.2938284 47.86446696728413 -111.7157034tag:blogger.com,1999:blog-830335965541290967.post-39319684712697190422024-01-29T12:50:00.004+05:302024-01-29T12:50:39.329+05:30Google's Cloud Pub/Sub and its Use Cases<h1 style="text-align: center;"><div></div></h1><h1 style="text-align: center;"><span><a name='more'></a></span><br /></h1><h1 style="text-align: center;">Uses Cases - Google's Cloud Pub/Sub.</h1><p><br /></p><p><br /></p><div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiy4fJ5sTLDAZIO1SMQfU715sZf9JE7fkR869gQxmCyI1rNg06fHiLu-l_m_-6MyIGvmaWimmtMWwmSgItXzwwDvMT5fM-ZEduiLDkhzQr5RN__D_9WjM7EoBFMop9adOf2PoplXYthSo3H1uOor-WGdJx3IO5Ev2_vx1qxL79kJjflEdQP30Iy5RbO" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="229" data-original-width="899" height="164" src="https://blogger.googleusercontent.com/img/a/AVvXsEiy4fJ5sTLDAZIO1SMQfU715sZf9JE7fkR869gQxmCyI1rNg06fHiLu-l_m_-6MyIGvmaWimmtMWwmSgItXzwwDvMT5fM-ZEduiLDkhzQr5RN__D_9WjM7EoBFMop9adOf2PoplXYthSo3H1uOor-WGdJx3IO5Ev2_vx1qxL79kJjflEdQP30Iy5RbO=w640-h164" width="640" /></a></div><br /><br /></div><div><h3><ul style="text-align: left;"><li>Distributing workloads:</li></ul></h3><ul style="text-align: left;"><ul><li> For example, you could queue up a large number of tasks in a Pub/Sub topic and have them distribute it amongst multiple workers, such as Compute Engine instances. Each instance can grab a task in turn from its subscription. New tasks can be queued up, waiting for available capacity.</li></ul></ul><h3><ul style="text-align: left;"><li>Asynchronous workflows:</li></ul></h3><ul style="text-align: left;"><ul><li>When you need to control the order of events in a loosely coupled system.</li><li>For example, an order processing system could place an order in a topic which could then be consumed by a worker system, perhaps invoicing, before passing it into a queue for the next system to consume, perhaps packaging and posting.</li></ul></ul><h3><ul style="text-align: left;"><li>Distributing event notifications.</li></ul></h3><ul style="text-align: left;"><ul><li>For example, you have a system that sets up new users when they register with your service.</li><li>A registration could publish a message and your system could be notified to set the user up.</li></ul></ul><h3><ul style="text-align: left;"><li>Distributed logging.</li></ul></h3><ul style="text-align: left;"><ul><li>Rather than pushing logs to a single source, they could be sent to a Pub/Sub topic to be consumed by multiple subscribers, such as a monitoring system and an analytics database for later querying.</li></ul></ul><h3><ul style="text-align: left;"><li>Device data streaming.</li></ul></h3><ul style="text-align: left;"><ul><li>Hundreds, thousands, even hundreds of thousands of internet-connected devices can stream their data or telemetry into Pub/Sub topics to be consumed on-demand by your analytic streams or even transformed through Dataflow first.</li></ul></ul></div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><div><br /></div><div>Often, you'll see Pub/Sub used as the glue that adds logic and joins lots of other services together</div><div>in a topology of GCP services.</div><br /></div><div><br /></div><div><div>Depending on the workflow we need to achieve, patterns in Pub/Sub messaging</div><div><br /></div><h2 style="text-align: left;"><br /></h2><div><h3 style="text-align: left;"><span style="font-weight: 400;">Publishing messages to Pub/Sub</span></h3><div><ul style="text-align: left;"><li><span style="font-weight: 400;">You just create a message containing your data, this is going to be a JSON payload, that's base64 encoded.</span></li><li><span style="font-weight: 400;">The total size of the payload needs to be 10MB or less.</span></li><li><span style="font-weight: 400;">Then you send the payload as a request to the Pub/Sub API specifying the topic to which the message should be published.</span></li></ul></div><div><span style="font-weight: 400;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjeJGVsC2aPEYpljwRO5WrYIjzKUEcN15ytyYegUlQpNLD1IOOJG8vgVhY4n28gUhiLgUCFjCIMXpz36BfoljEl8fxUvqoLvq2X4Ku2nzIGO0I2r8vMrXsBbLaBExKVG_oTvlXC9pg-aFFCTAo1nXkW2FD3ji7ZiHxoFySFHe_jx-jzmXuUOu74DRxm" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="214" data-original-width="453" height="151" src="https://blogger.googleusercontent.com/img/a/AVvXsEjeJGVsC2aPEYpljwRO5WrYIjzKUEcN15ytyYegUlQpNLD1IOOJG8vgVhY4n28gUhiLgUCFjCIMXpz36BfoljEl8fxUvqoLvq2X4Ku2nzIGO0I2r8vMrXsBbLaBExKVG_oTvlXC9pg-aFFCTAo1nXkW2FD3ji7ZiHxoFySFHe_jx-jzmXuUOu74DRxm" width="320" /></a></div><br /><br /></span></div><h3 style="text-align: left;"><span style="font-weight: 400;">Receiving messages from Pub/Sub.</span></h3><div><ul style="text-align: left;"><li><span style="font-weight: 400;">You simply create a subscription to a topic.</span></li><li><span style="font-weight: 400;">Subscriptions are always associated with a single topic.</span></li><li><span style="font-weight: 400;">There are 2 types of delivery method for subscriptions.</span></li><li><span style="font-weight: 400;">Pull is the default method.</span></li><li><span style="font-weight: 400;">When you have created a pull subscription, you can make ad hoc pull requests to the Pub/Sub API, </span><span style="font-weight: normal;">specifying your subscription to receive messages associated to that subscription.</span></li><li><span style="font-weight: 400;">When you receive a message, note that you have to acknowledge that you've received it.</span></li><li><span style="font-weight: 400;">If you don't, that message will remain at the top of the queue associated with your subscription, </span><span style="font-weight: normal;">and you won't get the next message, or any messages after that, until you've acknowledged it.</span></li><li><span style="font-weight: 400;">Alternatively, you can configure a push subscription, which will automatically send new messages to an endpoint that you define.</span></li><li><span style="font-weight: 400;">The endpoint must use the HTTPS protocol with a valid SSL certificate. </span><span style="font-weight: normal;">And of course, something has to sit on the end of that endpoint that is capable of receiving and processing a message.</span></li></ul><div><span style="font-weight: 400;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhECyh17BEjaY-HvpLWFFD1qU9aD3NEch7C3q32fc4iGtbaLQD39dMNWqU1gAJQcskG2SySEnis7elAG0FtxSFkFTNMejxEnkSImwWZGPuw8tJpl3YG-_5hpen_wRKrx_jxAkAqesX8JLFK0iojVIKL4u4EbG0r-Nu1jg41TKdGSyl4LIMhvLSRmNea" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="220" data-original-width="473" height="149" src="https://blogger.googleusercontent.com/img/a/AVvXsEhECyh17BEjaY-HvpLWFFD1qU9aD3NEch7C3q32fc4iGtbaLQD39dMNWqU1gAJQcskG2SySEnis7elAG0FtxSFkFTNMejxEnkSImwWZGPuw8tJpl3YG-_5hpen_wRKrx_jxAkAqesX8JLFK0iojVIKL4u4EbG0r-Nu1jg41TKdGSyl4LIMhvLSRmNea" width="320" /></a></div><br /><br /></span></div><div><br /></div></div></div></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0GCCX+X3 Chernaya Kur'ya, Altai Krai, Russia52.522459299999987 81.447711339.993390836423139 63.869586299999995 65.051527763576829 99.0258363tag:blogger.com,1999:blog-830335965541290967.post-63126977340495685252024-01-28T10:56:00.001+05:302024-01-28T10:57:23.493+05:30Google's Cloud Pub/Sub Messaging Services, Let's explore<h1 style="text-align: center;"><span><a name='more'></a></span> </h1><h1 style="text-align: center;">Google's Cloud Pub/Sub.</h1><p><br /></p><p><br /></p><h3 style="text-align: left;">Pub/Sub handles messaging and event ingestion at a global level.</h3><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEho1QeINfVgN9QM-8ibyv-YVjMV5pR8M7Sw0jO6hmrFGPVmDfxtURllMK_cwoo8y4Sdjqux01rg8jm53uixmaMX4U34v22XAva7oKs6f_z0ENEC_EZcKaAS7NmZTj9dt2tL-XGzenk_T5pNj8r17BAYRWTv_dCvvLqLGZDgz2wtD8ut-OfDfzJVGs9k" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="270" data-original-width="834" height="130" src="https://blogger.googleusercontent.com/img/a/AVvXsEho1QeINfVgN9QM-8ibyv-YVjMV5pR8M7Sw0jO6hmrFGPVmDfxtURllMK_cwoo8y4Sdjqux01rg8jm53uixmaMX4U34v22XAva7oKs6f_z0ENEC_EZcKaAS7NmZTj9dt2tL-XGzenk_T5pNj8r17BAYRWTv_dCvvLqLGZDgz2wtD8ut-OfDfzJVGs9k=w400-h130" width="400" /></a></div><br /><br /><p></p><h2>Why we would use messaging middleware in the first place?</h2><p> Let's imagine a scenario where we don't use any sort of messaging middleware layer. Say, we have some users who we want to serve with our app. The communication between the 2 can be direct. The user talks directly to the app, maybe through a web browser, but it's a direct link from one to the other. Maybe in addition to our user, there's another app that needs to talk to our initial app. Maybe it's running in another cloud or in a data center, but again, it talks directly to our app. You might already be thinking of some problems with this design. All of these direct connections don't seem to have much resilience built into them.</p><p>Now let's say our app gets popular. </p><p> We're getting more users and more third-party apps connecting to us, but that's okay. We know how to auto-scale in GCP. So we add more compute to handle the load. Now let's say we have a backend app in our stack and maybe there are some mobile devices that need to send data directly to this part of the stack, but it's dependent on some data from the frontend. It can't act until it's got both pieces of information and maybe there's a further component to our stack that relies on the outcome of the second component, but it can only talk to the frontend because of its geolocation. This is all starting to look a bit tenuous. What happens if this part breaks? Well, there goes our mobile data and now the frontend can't finish what it's supposed to be processing, so it starts blocking. Eventually, this causes our original application to start crashing. We're left with a system that can barely handle its frontend requests and the response to those requests is probably just, please try again later.</p><p><br /></p><h3 style="text-align: left;">So where did it all go wrong? </h3><p></p><ul style="text-align: left;"><li>Well, the fundamental problem with this design is dependency.</li><li>Every component is dependent on some other component in order for it to function.</li><li>And often, it's relying on things to happen in a certain order that can't be guaranteed.</li><li>The second that one component has a problem, well, the whole house of cards comes tumbling down.</li></ul><p></p><div><br /></div><h3 style="text-align: left;">Solution</h3><div><ul style="text-align: left;"><li>Solution to this design problem is to introduce messaging middleware or a message bus</li><li>This is simply a layer that we introduce that handles all of the messages that used to be passed directly between each component.</li><li>There are different models of message bus, but Google pub/sub is a publish/subscribe model.</li><li>In this model, our message bus can be split into different groups of messages.</li></ul><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiHCZZlQeeYFNa6zLUZiq9Bk87w3mPg7spV3U867drOgr1pLN5YHtmBwfoGe2WCg0tDkF3YMz5LIAFTHbOUCwSG7TwLAZFT9usTRC_KUHZ4XVPoG3XluQqnbtdu8oJc2nPTqs8FHzIb3vr-kNKFOiBsYmwVROQshoM7pxvUVcTk4ZhIIaGb1CEPt3ja" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="336" data-original-width="832" height="258" src="https://blogger.googleusercontent.com/img/a/AVvXsEiHCZZlQeeYFNa6zLUZiq9Bk87w3mPg7spV3U867drOgr1pLN5YHtmBwfoGe2WCg0tDkF3YMz5LIAFTHbOUCwSG7TwLAZFT9usTRC_KUHZ4XVPoG3XluQqnbtdu8oJc2nPTqs8FHzIb3vr-kNKFOiBsYmwVROQshoM7pxvUVcTk4ZhIIaGb1CEPt3ja=w640-h258" width="640" /></a></div><br /><br /></div><h4 style="text-align: left;">In Pub/Sub, we call these Topics.</h4><ul style="text-align: left;"><li>Anything can publish a message to a topic or choose to receive a message from a topic.</li><li>So now information from our users and other apps is published to a topic which can be consumed by our application.</li><li>Our user client can also be updated to simply pull information back from a topic when it needs to.</li><li>Mobile data can be sent to another topic to be consumed by our backend application.</li><li>We can have a separate topic that we choose to act on only when there are messages there ready for us to receive.</li><li>In this way, we've loosely coupled our services with a message bus and in doing so, we've introduced resilience in the event of a single component failure.</li><li>Because in our case, Pub/Sub is a global fully-managed service, messages can simply queue in the topic, ready to be consumed again when a component is restored.</li><li>In this way, you can think of Pub/Sub as a kind of shock absorber for your systems.</li><li>Pub/Sub works equally well for exchanging messages and data around a distributed system, as well as simple triggers and events, acting on certain actions and triggering other actions to occur.<br /></li></ul></div><div><br /></div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhy72-5hB8zqySz8paqtkuazxqktaB8IXeetx8bwEjtor_t6d1SptSwX8VGfZNWsWu5qdVrit6m-kMswgNcPgKUvotcMGfiDAacrxy325tiy017cgQK58zIklsxT5qNLz-b_3M0gEyiRhbt_kjE_VYRs2zoBOVr3Gmqyr7fKVQwFebSo_3Ikajqf8R4" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="410" data-original-width="824" height="318" src="https://blogger.googleusercontent.com/img/a/AVvXsEhy72-5hB8zqySz8paqtkuazxqktaB8IXeetx8bwEjtor_t6d1SptSwX8VGfZNWsWu5qdVrit6m-kMswgNcPgKUvotcMGfiDAacrxy325tiy017cgQK58zIklsxT5qNLz-b_3M0gEyiRhbt_kjE_VYRs2zoBOVr3Gmqyr7fKVQwFebSo_3Ikajqf8R4=w640-h318" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div><br /></div><h3 style="text-align: left;">Cloud Pub/Sub</h3><div><ul style="text-align: left;"><li>Pub/Sub is Google's global messaging and event ingestion service.</li><li>Using the publisher/subscriber model, it can handle messages or events consistently in multiple regions as a server-less, No-Ops, fully-managed service.</li><li>There is nothing to provision. You simply consume the Pub/Sub API, which like many other GCP products,</li><li>It is a public-facing version of a tool Google has been using and developing internally for years.</li><li>Google's internal Pub/Sub handles messages and events for ads, Gmail, and search, processing up to 500 million messages per second, totaling over one terabyte per second of data.</li></ul></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhhr-jYUEMaEDbCelq-DatKfpDseJdjGADRmBfxTZ_oO9OZDLB4v-PyVGVLCqjQrnU--EEVwr1vcx1oUXN7yD2KFW_r6ICDwMD2mqw3XU5LWFVM53qRRGjHEwzRWCxd_vfikI8BmWOcYZZFEz4detuMj5ZbIf1yz-TT_Uay8kmf2ruEL4Mb4NG4iDUo" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="160" data-original-width="438" height="117" src="https://blogger.googleusercontent.com/img/a/AVvXsEhhr-jYUEMaEDbCelq-DatKfpDseJdjGADRmBfxTZ_oO9OZDLB4v-PyVGVLCqjQrnU--EEVwr1vcx1oUXN7yD2KFW_r6ICDwMD2mqw3XU5LWFVM53qRRGjHEwzRWCxd_vfikI8BmWOcYZZFEz4detuMj5ZbIf1yz-TT_Uay8kmf2ruEL4Mb4NG4iDUo" width="320" /></a></div><br /><br /></div><h3 style="text-align: left;">Cloud Pub/Sub - features:</h3><div><ul style="text-align: left;"><li>Includes multiple publisher and subscriber patterns.</li><li>There are different relationships you can set up between publishers and subscribers, such as one to many, many to one, and many to many.</li><li>Pub/Sub guarantees at-least-once delivery of every message.</li><li>In fact, due to its distributed and globally replicated nature, there's a tiny chance you might get a message more than once, although this is rare.</li><li>You can process messages in real-time or batches depending on your design pattern with exponential back off for publishing and push subscriptions.</li><li>And if you need more advanced time windowing or exactly once processing, you can integrate Pub/Sub with Cloud Dataflow.</li></ul></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiwmsn1TMpIW4QNmuvpTHn1YRNFlsf0xFg-twwZ-TNY7776RrY4nweNxvc9YnRfHIr6qanp28veZQ0easvEVLf7opxVEeW4ki8knEVyrSwHIqaVmmysI-lBPelGg7gdd39SDo8U1RkhG_ciRYrTHJe-e0zaA_y6t1n3N21jF4LOAfz0TGISl3zy7rlk" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="166" data-original-width="452" height="118" src="https://blogger.googleusercontent.com/img/a/AVvXsEiwmsn1TMpIW4QNmuvpTHn1YRNFlsf0xFg-twwZ-TNY7776RrY4nweNxvc9YnRfHIr6qanp28veZQ0easvEVLf7opxVEeW4ki8knEVyrSwHIqaVmmysI-lBPelGg7gdd39SDo8U1RkhG_ciRYrTHJe-e0zaA_y6t1n3N21jF4LOAfz0TGISl3zy7rlk" width="320" /></a></div><br /><br /></div></div><div><div><h3 style="text-align: left;"><span style="font-weight: 400;">Publishing messages to Pub/Sub</span></h3><div><ul style="text-align: left;"><li><span style="font-weight: 400;">You just create a message containing your data, this is going to be a JSON payload, that's base64 encoded.</span></li><li><span style="font-weight: 400;">The total size of the payload needs to be 10MB or less.</span></li><li><span style="font-weight: 400;">Then you send the payload as a request to the Pub/Sub API specifying the topic to which the message should be published.</span></li></ul></div><div><span style="font-weight: 400;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjeJGVsC2aPEYpljwRO5WrYIjzKUEcN15ytyYegUlQpNLD1IOOJG8vgVhY4n28gUhiLgUCFjCIMXpz36BfoljEl8fxUvqoLvq2X4Ku2nzIGO0I2r8vMrXsBbLaBExKVG_oTvlXC9pg-aFFCTAo1nXkW2FD3ji7ZiHxoFySFHe_jx-jzmXuUOu74DRxm" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="214" data-original-width="453" height="151" src="https://blogger.googleusercontent.com/img/a/AVvXsEjeJGVsC2aPEYpljwRO5WrYIjzKUEcN15ytyYegUlQpNLD1IOOJG8vgVhY4n28gUhiLgUCFjCIMXpz36BfoljEl8fxUvqoLvq2X4Ku2nzIGO0I2r8vMrXsBbLaBExKVG_oTvlXC9pg-aFFCTAo1nXkW2FD3ji7ZiHxoFySFHe_jx-jzmXuUOu74DRxm" width="320" /></a></div><br /><br /></span></div><h3 style="text-align: left;"><span style="font-weight: 400;">Receiving messages from Pub/Sub.</span></h3><div><ul style="text-align: left;"><li><span style="font-weight: 400;">You simply create a subscription to a topic.</span></li><li><span style="font-weight: 400;">Subscriptions are always associated with a single topic.</span></li><li><span style="font-weight: 400;">There are 2 types of delivery method for subscriptions.</span></li><li><span style="font-weight: 400;">Pull is the default method.</span></li><li><span style="font-weight: 400;">When you have created a pull subscription, you can make ad hoc pull requests to the Pub/Sub API, </span><span style="font-weight: normal;">specifying your subscription to receive messages associated to that subscription.</span></li><li><span style="font-weight: 400;">When you receive a message, note that you have to acknowledge that you've received it.</span></li><li><span style="font-weight: 400;">If you don't, that message will remain at the top of the queue associated with your subscription, </span><span style="font-weight: normal;">and you won't get the next message, or any messages after that, until you've acknowledged it.</span></li><li><span style="font-weight: 400;">Alternatively, you can configure a push subscription, which will automatically send new messages to an endpoint that you define.</span></li><li><span style="font-weight: 400;">The endpoint must use the HTTPS protocol with a valid SSL certificate. </span><span style="font-weight: normal;">And of course, something has to sit on the end of that endpoint that is capable of receiving and processing a message.</span></li></ul><div><span style="font-weight: 400;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhECyh17BEjaY-HvpLWFFD1qU9aD3NEch7C3q32fc4iGtbaLQD39dMNWqU1gAJQcskG2SySEnis7elAG0FtxSFkFTNMejxEnkSImwWZGPuw8tJpl3YG-_5hpen_wRKrx_jxAkAqesX8JLFK0iojVIKL4u4EbG0r-Nu1jg41TKdGSyl4LIMhvLSRmNea" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="220" data-original-width="473" height="149" src="https://blogger.googleusercontent.com/img/a/AVvXsEhECyh17BEjaY-HvpLWFFD1qU9aD3NEch7C3q32fc4iGtbaLQD39dMNWqU1gAJQcskG2SySEnis7elAG0FtxSFkFTNMejxEnkSImwWZGPuw8tJpl3YG-_5hpen_wRKrx_jxAkAqesX8JLFK0iojVIKL4u4EbG0r-Nu1jg41TKdGSyl4LIMhvLSRmNea" width="320" /></a></div><br /><br /></span></div><div><br /></div></div></div></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0FFQW+42 Bol'shaya Okunevka, Omsk Oblast, Russia55.4878531 72.49506099999999343.813488049001236 54.916935999999993 67.162218150998768 90.073185999999993tag:blogger.com,1999:blog-830335965541290967.post-40704200672092658172024-01-28T08:32:00.007+05:302024-01-28T08:33:40.381+05:30NEO4J Graph Platform - Introduction<p> <span></span></p><a name='more'></a><p></p><p></p><h1 style="text-align: center;">NEO4J Graph Platform</h1><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">The Neo4j Graph Platform is a comprehensive set of tools, services, and capabilities provided by Neo4j to build and deploy graph-based applications. It includes the Neo4j graph database, along with additional components that enhance the development and deployment experience.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgKBGi0r4wl1HoL7xihcLykU92UDb5V3iJLmramXKRP4zu9VN-rHeaUP-TNI-5d_qTpDIDhPF6R6Dshth3bXtDxGAMCgTyOJR3FrTdWf7ZQS7oeM50iVKQZKYEZPqQBwa608DDm1ekkczgnL9j2VNCRSmxD50E421tjxkljpXZX19Cg8qQd-pwaR9Ew" style="margin-left: 1em; margin-right: 1em;"><img alt="algaestudy Neo4j graph database, nosql klassroom algaeservices" data-original-height="484" data-original-width="992" height="312" src="https://blogger.googleusercontent.com/img/a/AVvXsEgKBGi0r4wl1HoL7xihcLykU92UDb5V3iJLmramXKRP4zu9VN-rHeaUP-TNI-5d_qTpDIDhPF6R6Dshth3bXtDxGAMCgTyOJR3FrTdWf7ZQS7oeM50iVKQZKYEZPqQBwa608DDm1ekkczgnL9j2VNCRSmxD50E421tjxkljpXZX19Cg8qQd-pwaR9Ew=w640-h312" title="algaestudy Neo4j graph database, nosql klassroom algaeservices" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p></p><h4 style="clear: both; text-align: left;">The key components of the Neo4j Graph Platform are:</h4><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><b>Neo4j Database: </b></li><ul><li>The core component of the platform is the Neo4j graph database, which is a high-performance, scalable, and ACID-compliant graph database management system. </li><li>It provides the foundation for storing, managing, and querying highly connected data using the power of graph data models.</li></ul><li><b>Cypher Query Language:</b> </li><ul><li>Neo4j's Cypher query language is a key part of the platform. </li><li>It is a declarative language specifically designed for querying and manipulating graph data. </li><li>Cypher provides a concise and expressive syntax to work with nodes, relationships, and graph patterns, allowing developers to easily retrieve and modify data.</li></ul><li><b>Neo4j Browser</b>: </li><ul><li>The Neo4j Browser is a web-based development tool that comes bundled with the Neo4j Graph Platform. </li><li>It provides an interactive interface for executing Cypher queries, visualizing graph data, and exploring the database. </li><li>The Browser offers a user-friendly environment for working with Neo4j and understanding the structure and content of the graph.</li></ul><li><b>Neo4j Desktop</b>: </li><ul><li>Neo4j Desktop is a desktop application that simplifies the local development and management of Neo4j databases. </li><li>It provides a graphical interface to create, manage, and deploy multiple Neo4j instances, as well as tools for designing graph models, executing queries, and monitoring database performance.</li></ul><li><b>Neo4j Aura</b>: </li><ul><li>Neo4j Aura is a fully managed graph database service offered by Neo4j. </li><li>It provides a cloud-based deployment option for running Neo4j databases without the need for infrastructure management. </li><li>With Aura, you can easily deploy and scale your graph databases in the cloud, while benefiting from automated maintenance, backups, and high availability.</li></ul><li><b>Neo4j Bloom</b>: </li><ul><li>Neo4j Bloom is a visualization and exploration tool that allows users to visually navigate and analyze graph data. </li><li>It provides an intuitive interface for non-technical users to interact with graphs, discover patterns, and gain insights. Bloom enables business users to explore graph data without writing queries or code.</li></ul><li><b>Neo4j Graph Data Science</b>: </li><ul><li>Neo4j Graph Data Science is a library and toolkit for performing advanced graph analytics and data science tasks on Neo4j databases. </li><li>It includes a collection of algorithms and functions optimized for graph data, enabling users to uncover patterns, detect anomalies, perform machine learning, and gain deeper insights from their graph data.</li></ul></ul></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">These components together form the Neo4j Graph Platform, providing a comprehensive and integrated solution for developing, managing, and analyzing graph-based applications. Whether you are building social networks, recommendation engines, fraud detection systems, or knowledge graphs, the Neo4j Graph Platform offers the necessary tools and capabilities to leverage the power of connected data.</div></div><p><br /></p><h3 style="text-align: left;">Graph Data Modelling</h3><p></p><ul style="text-align: left;"><li>Graph data modeling is the process in which a user describes an arbitrary domain as a connected graph of nodes and relationships with properties and labels. </li><li>A Neo4j graph data model is designed to answer questions in the form of Cypher queries and solve business and technical problems by organizing a data structure for the graph database.</li><li>The graph data model is often referred to as being "whiteboard-friendly". Typically, when designing a data model, people draw example data on the whiteboard and connect it to other data drawn to show how different items connect. </li><li>The whiteboard model is then re-formatted and structured to fit normalized tables for a relational model. </li><li>A similar process exists in graph data modeling, as well. However, instead of modifying the data model to fit a normalized table structure, the graph data model stays exactly as it was drawn on the whiteboard. </li><li>This is where the graph data model gets its name for being "whiteboard-friendly".</li></ul><p></p><div><br /></div><p><br /></p><h3 style="text-align: left;">REFERENCES</h3><p></p><ul style="text-align: left;"><li><a href="https://neo4j.com/developer/graph-platform/">https://neo4j.com/developer/graph-platform/</a></li><li><a href="https://graphacademy.neo4j.com/?ref=redirect">https://graphacademy.neo4j.com/?ref=redirect</a></li><li><a href="https://neo4j.com/docs/desktop-manual/current/installation/download-installation/">https://neo4j.com/docs/desktop-manual/current/installation/download-installation/</a></li><li><a href="https://neo4j.com/docs/">https://neo4j.com/docs/</a></li></ul><p></p>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com08R825WW8+FF36.1961955 140.916135520.984142716505254 123.3380105 51.40824828349475 158.4942605tag:blogger.com,1999:blog-830335965541290967.post-58163114993920938882024-01-28T08:16:00.004+05:302024-01-28T08:16:26.048+05:30Google Cloud DataProc Lab to Setup Jobs for Hadoop and Spark<p><span></span></p><a name='more'></a> <p></p><p><br /></p><h1 style="text-align: center;">Google Cloud DataProc Lab to</h1><h1 style="text-align: center;"> </h1><h1 style="text-align: center;">Setup Jobs for Hadoop and Spark</h1><div><br /></div><div><br /></div><div><br /></div><div><h2 style="text-align: left;">Working with Cloud Dataproc.</h2><div><br /></div><h4 style="text-align: left;">Lab objectives: </h4><div><ul style="text-align: left;"><li>To show you just how easy it is to create a Cloud Dataproc cluster and use it to complete a Spark job.</li><li>We'll use one of the example scripts that is bundled with Apache Spark that will estimate the value of Pi.</li></ul></div><div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhVGx9xuOivVbn1tAwokWAZc54GLzwMA7XT-axc7fNROssIwvQKlS0gtgW0zXOq_OAUIGb4CUrls1vJ7buxz2F12cljEAQvYKcDOaYNwWusxioFbljw5QHUwzg0latjJg41TpE6gOy51Yh9sgk8s-jjHbz-ZJHSjOSyiU_pWxy9CsaQnWqrJTRL-6u_" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="127" data-original-width="391" height="104" src="https://blogger.googleusercontent.com/img/a/AVvXsEhVGx9xuOivVbn1tAwokWAZc54GLzwMA7XT-axc7fNROssIwvQKlS0gtgW0zXOq_OAUIGb4CUrls1vJ7buxz2F12cljEAQvYKcDOaYNwWusxioFbljw5QHUwzg0latjJg41TpE6gOy51Yh9sgk8s-jjHbz-ZJHSjOSyiU_pWxy9CsaQnWqrJTRL-6u_" width="320" /></a></div><br /><br /><br /></div><h4 style="text-align: left;"><br /></h4><h4 style="text-align: left;"><br /></h4><h4 style="text-align: left;">Method used: </h4><div><ul style="text-align: left;"><li>Monte Carlo method.</li></ul></div><h3 style="text-align: left;"><br /></h3><h3 style="text-align: left;">Simplistic explanation of Monte Carlo method:</h3><div><ul style="text-align: left;"><li>We take a quadrant of a circle, then generate a number of uniformly distributed random plotted points.</li><li>The points can fall anywhere within the square.</li><li>So some will fall inside the curve of our circle and some won't.</li><li>If we divide the number of points within the circle by the total number of points, we should get a value that is an approximate ratio.</li><li>We know the area of the original square, so we multiply it by that ratio to get the value of Pi.</li></ul></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgbmVFobt6PeVO0pzfHk2cxwR7xP3QoNAib2yVjYkbD8X02jlFaXUVDjJpvrrb2-IWNA3HbwRkpd7FU_PNXvnUV3YFEqHkps1bnKGbEb43LNVel_W0A0LGGIPHowcHLlHbhnOqu8JcfziqX9MFaz1lKi89z_7haJpuNH4j73X5LuFtcq5zzdOosJA0h" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="500" data-original-width="500" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgbmVFobt6PeVO0pzfHk2cxwR7xP3QoNAib2yVjYkbD8X02jlFaXUVDjJpvrrb2-IWNA3HbwRkpd7FU_PNXvnUV3YFEqHkps1bnKGbEb43LNVel_W0A0LGGIPHowcHLlHbhnOqu8JcfziqX9MFaz1lKi89z_7haJpuNH4j73X5LuFtcq5zzdOosJA0h" width="240" /></a></div><br /><br /></div><div><br /></div><h2 style="text-align: left;">Steps:</h2><div><br /></div><div><ul style="text-align: left;"><li>Go to GCP project and the Cloud Console.</li><li>Go straight to the menu and locate Dataproc in the big data section.</li><li>The first time you load Dataproc, you'll be prompted to enable the Cloud Dataproc API. Just click Enable API.</li></ul><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgiDwXoJNa4pQ9sZ_oDEYFXqKk2e5CjtXUjTtZfeuo8tV5W9oq2k582wWHic2Jb48wvFJjlyEgDFGaoMWQyjuo4_wU6vZhE_Wf31VR-SDlQL3YgzB82Oytdvte9j9bwtA80AMP6Tfjb-PtQqsZ6YBG3PVaJm1Zjf71Xj7YsEZOO7csJRJgTPIOiOITs" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="180" data-original-width="344" height="167" src="https://blogger.googleusercontent.com/img/a/AVvXsEgiDwXoJNa4pQ9sZ_oDEYFXqKk2e5CjtXUjTtZfeuo8tV5W9oq2k582wWHic2Jb48wvFJjlyEgDFGaoMWQyjuo4_wU6vZhE_Wf31VR-SDlQL3YgzB82Oytdvte9j9bwtA80AMP6Tfjb-PtQqsZ6YBG3PVaJm1Zjf71Xj7YsEZOO7csJRJgTPIOiOITs" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><ul style="text-align: left;"><li>Click Create Cluster to create our first cluster.</li><li>The console will suggest a name for the cluster. You can change this if you like.</li><li>Pick a region that's near to you. I'm going to go with europe-west2.</li><li>Dataproc will then pick a zone for me.</li><li>We'll change the cluster mode to Single Node.</li><li>We'll leave the machine type as the default here, which is an n1-standard-4, including the service charge for Dataproc.</li><li>This should cost under 20 cents for 1 hour and you should finish this lab easily in that time.</li><li>Scroll down and click Create.</li></ul></div><div><br /></div><div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjF9sf5G1eV00k9mB5ronE8hIbnfutlS5M1Blg91QSAJQ7CLOVMnZ-wsRippgC-JvrZ60Z_83aBqjed2C351FHTQzvYzvE92WhJ9OiWBa9ec7vwgIgnKqEH_R1kyV1M1CInzQjbEuK6ZwsCmc_gkIDOFQcprdL5oLsigho5ORqXuZ3TKWrte8X0pkgj" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img data-original-height="302" data-original-width="544" height="223" src="https://blogger.googleusercontent.com/img/a/AVvXsEjF9sf5G1eV00k9mB5ronE8hIbnfutlS5M1Blg91QSAJQ7CLOVMnZ-wsRippgC-JvrZ60Z_83aBqjed2C351FHTQzvYzvE92WhJ9OiWBa9ec7vwgIgnKqEH_R1kyV1M1CInzQjbEuK6ZwsCmc_gkIDOFQcprdL5oLsigho5ORqXuZ3TKWrte8X0pkgj=w400-h223" width="400" /> </a></div></div><div><br /></div><div><div class="separator" style="clear: both; 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text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h4>What happens in background Now:</h4><div><ul><li>Dataproc is now provisioning a compute engine VM for us and installing and configuring Hadoop and Spark. This will take a few minutes.</li><li>The cluster is now ready to get to work without us having to do any configuration work at all.</li><li>If we select our cluster, we can see monitoring dashboards that will show us amongst other things our YARN and HDFS utilization.</li></ul></div><div><br /></div><div><h3>Let's submit our first job. </h3><h3><div style="font-size: medium; font-weight: 400;"><ul><li>Click on Jobs and Submit Job.</li><li>The first thing we need to do is change the region to match the one where we just built our cluster.</li><li>That's europe-west2 in my case. This will then automatically populate the cluster selection dropdown.</li><li>And of course, we only have one cluster, so it's already selected.</li><li>Under job type, you can see the many different types of jobs that Dataproc is configured to run.</li><li>We're going to select Spark. Spark jobs are written in Java or Scala.</li><li>So we next need to provide the name of the main class to run.</li><li>We're going to use one of the built-in examples, org.apache.spark.examples.SparkPi.</li><li>As an argument, we pass in the number 1,000. The Monte Carlo method estimates the value of Pi by plotting points on a graph.</li><li>So here we're telling Spark to plot 1,000 points. This should give us an accuracy to about three decimal places.</li><li>We also need to tell Spark where to find this main class, which is in the local file system in the examples directory.</li><li>We add this in the Jar Files section. Instead of using a local file here, we could have also specified a cloud storage location or a path in HDFS.</li><li>We don't need to provide any supplemental jar files or other properties or labels, so we can go ahead and click Submit.</li><li>We're now taken to the jobs page where we can see our job has the status of running.</li><li>If we click on our job, we can watch the console output as it runs.</li><li>We can see that a new Spark application is being created and submitted to YARN.</li><li>It will take about a minute for the job to complete,</li></ul></div></h3></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiu1lLF0e0njzc2VPgqq0IMTSErg4qCxwvSMjY023jvq12gP89w8JIOdyaP-kqmLS4zBdmFHPwDQthtksLjOrTXTvDN1HVUDKQvHySR8gDptoSGiDafq2tDdTPxgCrMi7n5iEj-c2O6_a3t2FStQ0uwIhOpGuMPlxfrMihO3N4VYFx2MpP3vHHO4nDc" style="margin-left: 1em; 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text-align: left;"><div><ul><li>It will take about a minute for the job to complete,</li><li>You may also experience an audit GCP Console bug where it looks like the job is still waiting, but if you click the page, it will refresh and you'll see it's actually already finished.</li><li>So here's our result, Pi is 3.141, and here's where it goes off track a bit, but we only used 1,000 points for our estimate.</li><li>Feel free to rerun this job with more points to see how more accurate the estimation gets.</li><li>Now that we've finished, we'll delete our cluster.</li><li>Go back to the clusters page, tick the box next to your cluster, click Delete and Confirm.</li><li>One useful thing about Dataproc in the Cloud Console here is that even after our clusters have been deleted, the logs of our jobs persist.</li><li>We can go back into the job section and revisit the output of the job we just ran, even though the cluster itself has been deleted.</li></ul><div><br /></div></div><div>Jobs can also be submitted via the G Cloud command line tool or using the Dataproc API.</div><div><br /></div><div><br /></div><h3 style="text-align: left;">Once Work is finished, make sure you delete the Cluster</h3></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj4ESwsakt-n0yybpICgqmqmiwd4iVi7gWiFxAWhhjbDR7_rls5ZuCuBRn3pIq76d2Qysnv8xZWPlOf-EY_PZkh0h589LDsxy3cjaKwN4Qiv-ofM7hPbVJlejJlPfycTTKjcLhCFuxQhwCPpbliL1JYE1e-UgM5SHEhS6378Dg26TEjWLJB9fl_5t_Y" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="309" data-original-width="716" height="277" src="https://blogger.googleusercontent.com/img/a/AVvXsEj4ESwsakt-n0yybpICgqmqmiwd4iVi7gWiFxAWhhjbDR7_rls5ZuCuBRn3pIq76d2Qysnv8xZWPlOf-EY_PZkh0h589LDsxy3cjaKwN4Qiv-ofM7hPbVJlejJlPfycTTKjcLhCFuxQhwCPpbliL1JYE1e-UgM5SHEhS6378Dg26TEjWLJB9fl_5t_Y=w640-h277" width="640" /></a></div><div class="separator" style="clear: both; text-align: right;"><br /></div><div class="separator" style="clear: both; text-align: right;"><br /></div></div></div></div></div></div></div><br /><br /></div></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0Q5CX+5H Hitté, Burkina Faso13.7703968 -1.8010417-3.0339262945231589 -19.3791667 30.57471989452316 15.7770833tag:blogger.com,1999:blog-830335965541290967.post-75661243270522487032024-01-28T08:09:00.001+05:302024-01-28T08:10:05.521+05:30Google Cloud Kubernetes Engine Cluster<span><a name='more'></a></span><p><br /></p><h1 style="text-align: center;">Clusters in GKE</h1><p><br /></p><p> </p><h2 style="text-align: left;">Anatomy of a Kubernetes cluster</h2><p><br /></p><p></p><ul style="text-align: left;"><li>The most simple way to think of Kubernetes is just like any other cluster.</li><li>It's a collection of computers joined together to perform some function.</li><li>A typical Kubernetes cluster will contain one or more masters and one or more nodes.</li><li>Nodes are just communal gang variety computers.</li><li>These can be large physical servers or even raspberry pies.</li></ul><p></p><p><br /></p><p>In the case of Google Kubernetes engine, they are virtual machines running in Google compute engine.</p><h3 style="text-align: left;">Kubernetes Master:</h3><p></p><ul style="text-align: left;"><li>Masters run several components that form what's called the control plane.</li><li>This means they're in charge of controlling the cluster.</li><li>They make decisions about the cluster.</li><li>Such as where to schedule certain workloads.</li><li>The master is responsible for the state of a cluster.</li><li>It's constantly watching everything to make sure the state is as it should be.</li></ul><div><br /></div><div><div class="separator" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjgxImYoD5wXwX7wQbVaVo9onoki6-b2vkjCFTSWH9rY1rdQLVNwKhoW_2jkEki89pbfKiZI4W9L-yRM2RSPa-XWKK30y2Gpor5-Y5aSTkhoaLgGlPhdabySJqVPa1q6eKSJV6Bf4IdoeqFFXBq3Tm09MHT3ZjvHtdxD2_wMyB_CMKYjj2lfMKbfDDc" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="311" data-original-width="474" height="210" src="https://blogger.googleusercontent.com/img/a/AVvXsEjgxImYoD5wXwX7wQbVaVo9onoki6-b2vkjCFTSWH9rY1rdQLVNwKhoW_2jkEki89pbfKiZI4W9L-yRM2RSPa-XWKK30y2Gpor5-Y5aSTkhoaLgGlPhdabySJqVPa1q6eKSJV6Bf4IdoeqFFXBq3Tm09MHT3ZjvHtdxD2_wMyB_CMKYjj2lfMKbfDDc=w320-h210" width="320" /></a></div></div><h3 style="text-align: left;">Components of a Kubernetes Master.</h3><ul style="text-align: left;"><li><b>API Server:</b></li><ul><li>The API Server is the front end of the control plane it exposes the API for all the master functions.</li><li>Every time you communicate with the master or anything else communicates with the master It would be through this API.</li><li>Most of the time you'll use google cloud counsel or command line tool but in the background it's always talking to this API.</li><li>Once a cluster is up and running your day to day interaction is just going to be with that API Server. </li><li>And with GKE there is a good reason you don't need to worry too much about this individual components.</li></ul><li><b>etcd</b></li><ul><li>etcd is Kubernetes own database.</li><li>Storing all of it's configuration in state.</li><li>We call it a database but really etcd is just a key value store.</li><li>It is very well known one that is designed for scale and higher availability.</li></ul><li><b>Scheduler</b></li><ul><li>The Scheduler is responsible for scheduling work loads.</li><li>That means is when you want to deploy a container the scheduler will pick a node to run that container on.</li><li>The node it picks can be affected by all kinds of factors such as the current load on each available node.</li><li>The requirements of your container and some other customizable constraints.</li></ul><li><b>Cloud Controller Manager</b></li><ul><li>The Cloud Controller Manager, is what allows Kubernetes to work with cloud platforms.</li><li>Kubernetes itself is an open source project with contributions from lots of large companies</li><li>not just Google So it doesn't natively contain functionality for google cloud only. </li><li>This manager is responsible for handling things like networking and load balancing as they translate to the product and services of a particular cloud platform.</li></ul><li><b>Kube Controller Manager</b></li><ul><li>Its job is to manage a handful of controllers in the cluster.</li><li>The controllers themselves look after things like nodes and a few other objects.</li></ul></ul><p><br /></p><h2 style="text-align: left;">Kubernetes Node</h2><p></p><ul style="text-align: left;"><li>Nodes run components that form the runtime environment.</li><li>There basically the workers with a container runtime.</li><li>In this node computers, provide the resources of the cluster.</li><li>All of the CPU and RAM can be used to run containers</li><li>When you deploy a container in Kubernetes the master will pick a node to run it on. </li><li>These are going to be our actual virtual machines that will run containers for us. </li><li>They're a lot more straightforward than the master.</li></ul><p></p><p><br /></p><p><br /></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEidkoJbWE3WhOAkmkGdZn-XnJK05aY9Fn41mOONjYt30zK6wqxDRuJR0cfYhI6ma75M96URbxAkMPKBp9pXvQfEAKlK33O3RuV9PKtAIQraBF1M0ZV4wKG5nvsRCw_PMvLXkqZ5OoZnuwJV0Toev6dhAutJ-p4mx73KOgHIDsEjrgZ9HVdL1vvfmYXV" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="313" data-original-width="417" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEidkoJbWE3WhOAkmkGdZn-XnJK05aY9Fn41mOONjYt30zK6wqxDRuJR0cfYhI6ma75M96URbxAkMPKBp9pXvQfEAKlK33O3RuV9PKtAIQraBF1M0ZV4wKG5nvsRCw_PMvLXkqZ5OoZnuwJV0Toev6dhAutJ-p4mx73KOgHIDsEjrgZ9HVdL1vvfmYXV=w320-h240" width="320" /></a></div><p></p><h3 style="text-align: left;">Component's of Kubernetes node </h3><ul style="text-align: left;"><li><b>Kubelet:</b></li><ul><li>It is an agent for Kubernetes.</li><li>It communicates with the control play and takes instructions such as deploying containers when it's told to.</li></ul><li><b>Kube-proxy:</b></li><ul><li>It is responsible for managing network connections in and out of the node.</li></ul><li><b>Actual Container Runtime:</b></li><ul><li>Just like when we run our first container in cloud shell the noble run docker as a container runtime to allow it to run containers.</li></ul></ul><p></p><p><br /></p><p><br /></p><h2 style="text-align: left;">How to build a Kubernetes cluster?</h2><p></p><ul style="text-align: left;"><li><b>The hard way.</b></li><ul><li>You'll need provision of virtual machines for you master and your nodes.</li><li>You'll need to install the Kubernetes software create a network overlay.</li><li>Set up certificates so that all of the components can talk to each other secularly.</li></ul><li><b>The easy way.</b></li><ul><li>Use GKE.</li><li>GKE provisions and manages the underlying cloud resources automatically.</li></ul></ul><p></p><p><br /></p><h2 style="text-align: left;">GKE is a fully managed service</h2><p></p><ul style="text-align: left;"><li>It will create masters and nodes for you to your specification using a container-optimized operating system.</li><li>You design your cluster within GKE without having to build or maintain individual masters or nodes.</li><li>It comes with built-in automatic upgrading, automatic self-repair.</li><li>It has many options for fine grain resource control and cluster scaling.</li><li>Its integrated with all of the other products and services Google cloud platform.</li><li>You don't even touch the master control plane.</li><li>It is completely managed for you.</li><li>It's made of compute engine VMs just like your nodes, but they won't even show up in your project.</li><li>Google's own CRET are looking after them for you.</li><li>Abstracting away the control plane takes away a lot of the operation overhead.</li></ul><p></p><p><br /></p><p>How do we operate and interact with GKE</p><p></p><ul style="text-align: left;"><li><b>Google Cloud Console</b>.</li><ul><li>Kubernetes functionality is exposed to us to the simple UI of the cloud console.</li></ul><li><b>Command lines for Kubernetis</b></li><li><b>Kubectl</b> for operating a running cluster</li><ul><li>Kubectl allows us to interact with Kubernetes by defining the objects we want to deploy.</li><li>These objects are just abstractions of what we want to run and how we want to run it.</li><li>Kubectl takes our instructions and passes them to the API server.</li></ul><li><b>Communicate with API Server</b></li><ul><li>Perform their own function to carry out our commands.</li></ul><li><b>Create and manage life-cycle of Kubernetes objects</b></li><ul><li>Everything in Kubernetes is an object and every object has a state.</li></ul></ul><p></p><div><br /></div><div><br /></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com05Q55F6CC+GV-26.5286491 123.222125-54.838882936178848 88.065875 1.7815847361788464 158.378375tag:blogger.com,1999:blog-830335965541290967.post-61220782904384598942024-01-28T08:04:00.004+05:302024-01-28T08:05:23.681+05:30Fire up your First Container in Google Cloud<span><a name='more'></a></span><p><br /></p><h1 style="text-align: center;"> Containers - Lab</h1><p><br /></p><h2 style="text-align: left;">Anatomy of a Container</h2><p></p><ul style="text-align: left;"><li>Containers start life as an image.</li><li>You can think of Image just like any other packaging format, like a Tarbell.</li><li>The difference is that container images, are made up of different layers, one on top of the other.</li><li>When you run a container, the image is used, and a small read-write layer is added over the top.</li><li>Every time you run a container from an image, you'll get exactly the same behavior.</li><li>When a container stops, the read-write layer goes away.</li></ul><p></p><p style="text-align: center;"><span id="docs-internal-guid-06b748f3-7fff-772b-4097-26a7918ffc84"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 301px; overflow: hidden; width: 624px;"><img alt="Containers start life as an image. You can think of Image just like any other packaging format, like a Tarbell. The difference is that container images, are made up of different layers, one on top of the other. When you run a container, the image is used, and a small read-write layer is added over the top. Every time you run a container from an image, you'll get exactly the same behavior. When a container stops, the read-write layer goes away." src="https://lh6.googleusercontent.com/bZtquKv1bJeQh6rDYrBOCj9tDNSyDvaLJ38Cz1-GVjqO-0JBO08avRVybZRyg1edkr9v7-jpC5AyM9axcOUsjKPd4tB4pYKMfHFyAWPRle77csJsqDCANz0Ajseg-1B0rHtzrM5iwBLrtkiRQGeo8A=s16000" style="margin-left: 0px; margin-top: 0px;" title="Containers start life as an image. You can think of Image just like any other packaging format, like a Tarbell. The difference is that container images, are made up of different layers, one on top of the other. When you run a container, the image is used, and a small read-write layer is added over the top. Every time you run a container from an image, you'll get exactly the same behavior. When a container stops, the read-write layer goes away." /></span></span></span></p><p><br /></p><h2 style="text-align: left;">Setting up Container in GCP</h2><div style="text-align: left;"><ul style="text-align: left;"><li>We're going to create a Python app in Docker and we'll run this app in a Docker container and learn how to interact with local containers. </li><li>We'll tag our Docker image and push it to a registry, and we'll do all this from inside the Google Cloud Console.</li></ul></div><h4 style="text-align: left;"><br /></h4><h4 style="text-align: left;">Steps:</h4><p></p><ol style="text-align: left;"><li>Open the cloud shell</li><li>create a folder myapp and create 3 files in it namely server.py, requirements.txt, Dockerfile</li><li>Copy the sample code from url: <a href="https://github.com/ACloudGuru-Resources/Course_GKE_Beginner_To_Pro/tree/master/Chapter_One/Lecture_4_Lab/myapp">https://github.com/ACloudGuru-Resources/Course_GKE_Beginner_To_Pro/tree/master/Chapter_One/Lecture_4_Lab/myapp</a></li><li>Change directory to myapp using cd myapp</li><li>Build your first container image </li><li>See all the images created using</li><li>Get the container id with below command</li><li>To see all running containers use docker ps</li><li>Test the application using curl command</li><li>Check whats there in containers using</li><li>Enable google container registry api 🡪 enable </li><li>Now we can tag the image and push in container registry gcr.io</li></ol><p></p><div><br /></div><h3 style="text-align: left;">Code For Lab: </h3><p> <a href="https://github.com/ACloudGuru-Resources/Course_GKE_Beginner_To_Pro/tree/master/Chapter_One/Lecture_4_Lab/myapp">https://github.com/ACloudGuru-Resources/Course_GKE_Beginner_To_Pro/tree/master/Chapter_One/Lecture_4_Lab/myapp</a></p><p><br /></p><h4 style="text-align: left;">Step 1 & 2: </h4><div style="text-align: left;">In Command shell create a folder myapp and create 3 files in it namely and dump the code copied from github</div><div style="text-align: left;"><ul style="text-align: left;"><li>server.py</li><li>requirements.txt</li><li>Dockerfile</li></ul></div><p><br /></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhPxRJRgCRCofDKPG8tOVWif522RMewQyhoIVUNRduHDDDdfZbuSzI-AILCNZabVkW_mAkUv-OIUppYUfLpRLBYipvRpbuX2IhduSIXzyn_URcujLn6c8ZHqO_Iw8AqoqW5W0fA7YSvBR2Fn1gIDjR7QvZiueVpLF2NshSxEdhBahzDU923L9TV72VV" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" data-original-height="119" data-original-width="334" height="114" src="https://blogger.googleusercontent.com/img/a/AVvXsEhPxRJRgCRCofDKPG8tOVWif522RMewQyhoIVUNRduHDDDdfZbuSzI-AILCNZabVkW_mAkUv-OIUppYUfLpRLBYipvRpbuX2IhduSIXzyn_URcujLn6c8ZHqO_Iw8AqoqW5W0fA7YSvBR2Fn1gIDjR7QvZiueVpLF2NshSxEdhBahzDU923L9TV72VV=w320-h114" title="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" width="320" /></a></div><div class="separator" style="clear: both; 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float: right; margin-bottom: 1em; margin-left: 1em;"><br /></a></div><br /></div><br /><br /><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhlUY-t8axNQ08NDsG68JTtwI9ZAzqiGu3NOBaJ2cwb9aolLTyDURvpADBHjpyUQ0VaEqX-u8f0lipet_DMqZpby4cjj7Zp69hMxPoWINA2HMkoUtVTpXHLkowjxIg1Mk_ykaStDjlauzsMB0268btZgJVU3OR2tBfrePXTDVCi4KLI2UzE95nNQZXA" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" data-original-height="331" data-original-width="674" height="157" src="https://blogger.googleusercontent.com/img/a/AVvXsEhlUY-t8axNQ08NDsG68JTtwI9ZAzqiGu3NOBaJ2cwb9aolLTyDURvpADBHjpyUQ0VaEqX-u8f0lipet_DMqZpby4cjj7Zp69hMxPoWINA2HMkoUtVTpXHLkowjxIg1Mk_ykaStDjlauzsMB0268btZgJVU3OR2tBfrePXTDVCi4KLI2UzE95nNQZXA=w320-h157" title="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjPOgItF0D36rY1q1rqFCE8RktPeHgxqmbVqekcghOrrNUE9PUBiVUP1QOF_4tUAKNarPZm2ZcEwT91tUSmocwrpDs6i-FJONzlmHLEPMY4rZas030ujGSUmcoCkKm8fJ8L05Rvt2ZUHkeoSZ15eqeg3qEUrd9hngAOmOb5xWdvhmQRCc6-3NrcN-hO" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" data-original-height="358" data-original-width="637" height="180" src="https://blogger.googleusercontent.com/img/a/AVvXsEjPOgItF0D36rY1q1rqFCE8RktPeHgxqmbVqekcghOrrNUE9PUBiVUP1QOF_4tUAKNarPZm2ZcEwT91tUSmocwrpDs6i-FJONzlmHLEPMY4rZas030ujGSUmcoCkKm8fJ8L05Rvt2ZUHkeoSZ15eqeg3qEUrd9hngAOmOb5xWdvhmQRCc6-3NrcN-hO=w320-h180" title="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh0iz2tUvBskcl0Rl2FRte91HO55kjS8wXtMTs22mh2IUWG-lU8mhGZiMIcZ-t6Rwk1KG7UeyTmsa2yn7yvoOxQufDh_ZKOm9uV9uYMh2ci7LF_WTIrRCg9dVE-y8yZ6z0pOhfhHATx2UpyZTlb759d5Dy3vcW3Q1YkQ2Rq5iA49TVHDk0lfFnen9j7" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" data-original-height="155" data-original-width="698" height="89" src="https://blogger.googleusercontent.com/img/a/AVvXsEh0iz2tUvBskcl0Rl2FRte91HO55kjS8wXtMTs22mh2IUWG-lU8mhGZiMIcZ-t6Rwk1KG7UeyTmsa2yn7yvoOxQufDh_ZKOm9uV9uYMh2ci7LF_WTIrRCg9dVE-y8yZ6z0pOhfhHATx2UpyZTlb759d5Dy3vcW3Q1YkQ2Rq5iA49TVHDk0lfFnen9j7=w400-h89" title="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" width="400" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhJNxLZU-0FnzYSr5ZhIlZpEC2yDUuUxVNvTr4GkZF-VeXV31txFDIGccaFQrxzQq7R75sa-Qx0wI1Pj1DyiCQ_U8ghy7NjWhrwDii0J6chapsHSKDIXGBQK-4-fWWxB003sNVWk3D3iDlqrLFrUE5bNBM6__kufG4ilxNFvfFGw2kv7wRz0UDUFJvT" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="234" data-original-width="368" height="203" src="https://blogger.googleusercontent.com/img/a/AVvXsEhJNxLZU-0FnzYSr5ZhIlZpEC2yDUuUxVNvTr4GkZF-VeXV31txFDIGccaFQrxzQq7R75sa-Qx0wI1Pj1DyiCQ_U8ghy7NjWhrwDii0J6chapsHSKDIXGBQK-4-fWWxB003sNVWk3D3iDlqrLFrUE5bNBM6__kufG4ilxNFvfFGw2kv7wRz0UDUFJvT" width="320" /></a></div><br /><br /></div></div><p></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><b>Step 3</b></span><span face="Calibri,sans-serif" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> : change directory to myapp using cd myapp</span></p><div class="separator" style="clear: both; text-align: center;"><div style="text-align: left;"><span id="docs-internal-guid-928c88fb-7fff-1d16-bc61-555969e47a18"><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 22px; overflow: hidden; width: 557px;"><img alt="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" src="https://lh5.googleusercontent.com/oDmR9qalZL3eol6kA1Xdm4m4DgHXH0mWp6mQLde5pHdhJsQTTyA_F2CiCOoSPBTbNuoX7m-uTb0PXUYPxcYUnolD0aiSfYDWQAOGHJquGPaqU4Tivb6YB5hUW3lOwopdz5_8ryTqTBeumSyzw5jGhg=s16000" style="margin-left: 0px; margin-top: 0px;" title="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" /></span></span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><b>Step 4 </b>: build your first container image with below command</span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 18px; overflow: hidden; width: 624px;"><img alt="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" src="https://lh6.googleusercontent.com/ktsSZme8BZe_Ywo5y3oPgw25TQN4MneYZ0lw1K8XeBJqXoOovV9bcyj42agK8YqcvGKYMR-wKfXKB79j9pwmsUnFMQIP_lyVYFfw6alHB6C8FPGwWN5DB4g-vnuGJ4UOzvxdKgORV-xAx_G6viNM_Q=s16000" style="margin-left: 0px; margin-top: 0px;" title="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" /></span></span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><b>Step 5</b> : see all the images created using</span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 17px; overflow: hidden; width: 624px;"><img alt="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" src="https://lh5.googleusercontent.com/MO5qHw_vRvr3XOXgIHRKSol4jHM9ubsxopfjdLA96glOfBGbgpFr4y5LPNLsLe0dhhu-vN1AZpHpt90vF7kYQKmRsqC_P32v4PeBODIG21nQIl_x5XETcuAeqdZuBdXTNHxRXV4vIpEQmdtDmf9X8g=s16000" style="margin-left: 0px; margin-top: 0px;" title="Change directory to myapp using cd myapp Build your first container image See all the images created using Get the container id with below command To see all running containers use docker ps Test the application using curl command Check whats there in containers using Enable google container registry api 🡪 enable Now we can tag the image and push in container registry gcr.io algaestudy klassroom.algaeservice algaeservices" /></span></span></p><div><br /></div></span></div></div><h2 style="text-align: left;">Docker File Explain</h2><p></p><ul style="text-align: left;"><li>We can create a container image with a Dockerfile.</li><ul><li>This is just a normal text file </li><li>It contain a set of instructions that tell Docker how to build an image.</li><li>We can inherit from an image that already exists, like a very minimal Linux distribution, then we might add some other instructions, to copy some files into the image or run other commands.</li></ul><li>We can specify in the Docker file, what commands should be executed when the container is running. </li><li>Every instruction in the Docker file creates a new layer within the image.</li><li><br /></li><li>A basic Docker File looks like.</li></ul><p></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiV1Mt_UpkA3A4iqR4euxOJ1fA7vIUInrBQzsHo7_QGGmNn2pWhd-ARyrPndoEGVl39dSS7ogf9Vg5rvopkWpLo0EAlVIHsaFEaBPms4JVlKXETglC0H8LXPLpVzTXMNT1GpurVgVMv8ZIgBeKyViQgNgm_TSf-wEdHFELTDj4lj6Ekze2gO4k07nQb" style="margin-left: 1em; margin-right: 1em;"><img alt=""FROM unbuntu: 18.04": We inherit from a public Ubuntu image (We could inherit from anything here, including our own images.) "COPY . /app": We use the copy command to copy everything in the local directory to slash app inside the Docker image. This creates a new layer within the image. "RUN make /app": The next instruction executes the make command to compile our application. "CMD python /app/app.py": The final Command states that when this container image is running a Python Application should be executed." data-original-height="200" data-original-width="319" height="201" src="https://blogger.googleusercontent.com/img/a/AVvXsEiV1Mt_UpkA3A4iqR4euxOJ1fA7vIUInrBQzsHo7_QGGmNn2pWhd-ARyrPndoEGVl39dSS7ogf9Vg5rvopkWpLo0EAlVIHsaFEaBPms4JVlKXETglC0H8LXPLpVzTXMNT1GpurVgVMv8ZIgBeKyViQgNgm_TSf-wEdHFELTDj4lj6Ekze2gO4k07nQb=w320-h201" title=""FROM unbuntu: 18.04": We inherit from a public Ubuntu image (We could inherit from anything here, including our own images.) "COPY . /app": We use the copy command to copy everything in the local directory to slash app inside the Docker image. This creates a new layer within the image. "RUN make /app": The next instruction executes the make command to compile our application. "CMD python /app/app.py": The final Command states that when this container image is running a Python Application should be executed." width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="clear: both; text-align: left;">Explain Docker File Code:</h3><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><b>"FROM unbuntu: 18.04": </b></li><ul><li>We inherit from a public Ubuntu image (We could inherit from anything here, including our own images.)</li></ul><li><b>"COPY . /app": </b></li><ul><li>We use the copy command to copy everything in the local directory to slash app inside the Docker image. This creates a new layer within the image.</li></ul><li><b>"RUN make /app": </b></li><ul><li>The next instruction executes the make command to compile our application.</li></ul><li><b>"CMD python /app/app.py": </b></li><ul><li>The final Command states that when this container image is running a Python Application should be executed.</li></ul></ul></div><div class="separator" style="clear: both;"><br /></div><h3 style="clear: both; text-align: left;">Consuming Docker File</h3><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>We saved this file with the name "Dockerfile' in our local working directory alongside our code.</li><li>To build an image with these instructions we use the Docker command line.</li><li>The keyword built tells Docker that we want to build a new image minus t lets us add a tag or name to that to refer to it later.</li><li>The dot at the end of the command refers to the directory the Docker should build the image from. So, dot means our local working directory.</li><li>If you don't specify a location, or you specify a directory that does not contain a Dockerfile, the command will fail.</li></ul></div><div><br /></div></div><div class="separator" style="clear: both;"><br /></div><h3 style="clear: both; text-align: left;">Visualization of image, once built alongside our Docker File Instructions. </h3><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>The layers are in reverse order, as it's best to imagine Docker building up adding layers from the bottom to the top.</li><li>Each layer gets its own unique ID.</li><li>The first and largest layer is our inherited Ubuntu image.</li><li>The next layer at about 195k is where we've copied in our application files.</li><li>The top most layer, represents what changed when we run the make command inside the image.</li><li>The real benefit to developers here is containers promotes smaller shared images.</li><li>If we make a change to this container, only the layer that has changed has to be updated. Built updates might only be a few kilobytes of changes.</li><li>By inheriting images, we can remain consistent in our bills, and avoid reinventing the wheel with every image we create.</li></ul></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjOtsgzO7fYPwg6F59D84a6VvuHumZqjXHXPrVP7FTDMFTsmDljDRND60HJ0LE4r-fnd3bOZQUSJTx1X9-mwsi4VxGZj5t0pRZO8KvCZVBpIacp_u1IBUCIIeQ8GlT33lMWLoFMOdDQvGmfN3QFK6D0XcDJKZJEhupwo4zfHLqa6vRHs8V_9WkjyNyO" style="margin-left: 1em; margin-right: 1em;"><img alt="The layers are in reverse order, as it's best to imagine Docker building up adding layers from the bottom to the top. Each layer gets its own unique ID. The first and largest layer is our inherited Ubuntu image. The next layer at about 195k is where we've copied in our application files. The top most layer, represents what changed when we run the make command inside the image. The real benefit to developers here is containers promotes smaller shared images. If we make a change to this container, only the layer that has changed has to be updated. Built updates might only be a few kilobytes of changes. By inheriting images, we can remain consistent in our bills, and avoid reinventing the wheel with every image we create. algaestudy" data-original-height="245" data-original-width="377" height="208" src="https://blogger.googleusercontent.com/img/a/AVvXsEjOtsgzO7fYPwg6F59D84a6VvuHumZqjXHXPrVP7FTDMFTsmDljDRND60HJ0LE4r-fnd3bOZQUSJTx1X9-mwsi4VxGZj5t0pRZO8KvCZVBpIacp_u1IBUCIIeQ8GlT33lMWLoFMOdDQvGmfN3QFK6D0XcDJKZJEhupwo4zfHLqa6vRHs8V_9WkjyNyO=w320-h208" title="The layers are in reverse order, as it's best to imagine Docker building up adding layers from the bottom to the top. Each layer gets its own unique ID. The first and largest layer is our inherited Ubuntu image. The next layer at about 195k is where we've copied in our application files. The top most layer, represents what changed when we run the make command inside the image. The real benefit to developers here is containers promotes smaller shared images. If we make a change to this container, only the layer that has changed has to be updated. Built updates might only be a few kilobytes of changes. By inheriting images, we can remain consistent in our bills, and avoid reinventing the wheel with every image we create." width="320" /></a></div><br /><br /></div><div class="separator" style="clear: both;"><br /></div></div><div class="separator" style="clear: both; text-align: left;"><span id="docs-internal-guid-13564b7e-7fff-0fbc-6b42-9f23ae63a01d"><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><b>Step 6</b> : get the container id with below command</span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 22px; overflow: hidden; width: 290px;"><img height="22" src="https://lh4.googleusercontent.com/uC3j0vW945ub-wzwluqgd--SpbKHOzPQOjCB7sfUAEzHO1KrWtnAp1iaSadrrNSthfNtEyPH-bwAJ3Vnz8gu-_pNl2pzVKZbzpGbrZXlkhgKKbrPiRPVgbDkhL1vA5Dv1yLtMw9ZB6_4w8BI9D3vhw" style="margin-left: 0px; margin-top: 0px;" width="290" /></span></span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><b>Step 7</b> : to see all running containers use docker ps</span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 26px; overflow: hidden; width: 105px;"><img height="26" src="https://lh4.googleusercontent.com/ziJ-JcN4jQNXg3vhYiXMANa-1tWS_rryhYHqMEXsNw_jlYDhawO8-2VXt_40rb3hM8sGvfuk13B3PThGE7YVGic_yxvQET_BfLhUFRspHRRSKtvp7nHmusdTbWqwT6HJrlPpTC9v11I4j2JvQvduQg" style="margin-left: 0px; margin-top: 0px;" width="105" /></span></span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><b>Step 8</b> : test the application using curl command</span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 17px; overflow: hidden; width: 238px;"><img alt="test the application using curl command" src="https://lh6.googleusercontent.com/3YeIlNEtRhrSGV7KmqaeA7WKuv1rUOAayhbFGz9BjogM8pygDK1z2VAulxxxV4TP1t_7zH2896tAIoplaRr85fdltpn5TwQpIK91VOawSn1pp8kYAQBaEo0W8Zzsm7FvEZzMM_n3odqK_xyOAOzRfg=s16000" style="margin-left: 0px; margin-top: 0px;" title="test the application using curl command" /></span></span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><br /></p><div><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEheFbtAsF-knIhSBc0DiFPNZHeT2CgPUTdJUTwCpVhdVWu3DprSzM323gr_z8u9tdFGQFA3AJyZBz363_5trMhJW8YJ-Vz9J4bxpp3dsdRR3bROlRljO7uE70TiznHcJ0ENL9D8l3b2WoFgIulO8sZeRscwHClWHmx93YpvOQsLZaGyBI047Z1TlHHr" style="margin-left: 1em; margin-right: 1em;"><img alt="We simply use Docker run with the name or tag of our image. We can add minus d which demonizes the process and puts it in the background. Other options can also be add to Docker when running containers such as mounting volumes and exposing certain ports. This layer will disappear if the container is deleted." data-original-height="174" data-original-width="960" height="117" src="https://blogger.googleusercontent.com/img/a/AVvXsEheFbtAsF-knIhSBc0DiFPNZHeT2CgPUTdJUTwCpVhdVWu3DprSzM323gr_z8u9tdFGQFA3AJyZBz363_5trMhJW8YJ-Vz9J4bxpp3dsdRR3bROlRljO7uE70TiznHcJ0ENL9D8l3b2WoFgIulO8sZeRscwHClWHmx93YpvOQsLZaGyBI047Z1TlHHr=w640-h117" title="We simply use Docker run with the name or tag of our image. We can add minus d which demonizes the process and puts it in the background. Other options can also be add to Docker when running containers such as mounting volumes and exposing certain ports. This layer will disappear if the container is deleted." width="640" /></a></div><br /><br /></span></div></span></div><div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;">How to run a simple container:</h3><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>We simply use Docker run with the name or tag of our image.</li><li>We can add minus d which demonizes the process and puts it in the background.</li><li>Other options can also be add to Docker when running containers such as mounting volumes and exposing certain ports. This layer will disappear if the container is deleted.</li></ul></div></div><span id="docs-internal-guid-3b59e979-7fff-9c3c-ace6-19a523de33f3"><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;">Step 9: check whats there in containers using</span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 29px; overflow: hidden; width: 330px;"><img height="29" src="https://lh4.googleusercontent.com/DFeFjlhtlN6M9IN-BCnDfEWR4I1MiX4NoAtZcbxxJgheLdzJeaXK6Z7CeyCFeCta8tcj7FimUiTwwk67TKIFqPw5CGjTPWxVZFD9xDOFBKOSbHka4de1_ndQz9aCaoWJQH8QCTt-YaF02XxdR3rEAw" style="margin-left: 0px; margin-top: 0px;" width="330" /></span></span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;">Step 10 : enable google container registry api 🡪 enable </span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;">Step 11 : now we can tag the image and push in container registry gcr.io</span></p><p dir="ltr" style="line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="border: none; display: inline-block; height: 60px; overflow: hidden; width: 490px;"><img height="60" src="https://lh5.googleusercontent.com/qdVYw93rMjE9fQF7aSKCPmP0-SwiJZnjJIMkh5xLkIi2Yj4F0cNKs9GNeew91HWatoJ1w6iOGbjY4tlhNyTiHwD8sTN_-UkdghPY8cgkZW7zCYBXGrG9x80YGxJ_3V4SoI4f0QdmWxvPiNa2u79LGA" style="margin-left: 0px; margin-top: 0px;" width="490" /></span></span></p><div><br /></div></span><p></p><h3 style="text-align: left;">Docker commands</h3><p>The Docker command provides all the tools we need to manage our containers locally with easy to use verbs like </p><p></p><ul style="text-align: left;"><li>$ docker ps: Shows us all the running containers.</li><li>$ docker logs container-name: Used to view a containers logs</li><li>$ docker stop container-name: Used to stop a container</li><li>$ docker rm: Used to delte container entirely</li><li>$ docker images:</li><li>$ docker tag myapp gcr.io/myapp: Tag images</li><li>$ docker Push gcr.io/myapp: push images to google registry</li><li>$ docker rmi: Remove local images</li></ul><p></p><p><br /></p><p>In Google Cloud projects, we have a built in registry called Google Container Registry, or GCR. If we have an image locally, we can simply add an additional tag to it containing the URL of our registry using Docker tag, and then use Docker push to copy it up to the registry.</p><p><br /></p>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0tag:blogger.com,1999:blog-830335965541290967.post-5726970309870427582023-12-30T10:33:00.008+05:302024-01-28T08:06:36.380+05:30Natural Language Services in Azure Cloud<p></p><p></p><span><a name='more'></a></span><h1 style="text-align: center;"><br /></h1><h1 style="text-align: center;">NLP Services in Azure</h1><p><br /></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjp7Xe68DOd1H5lcbArfAMaJyARMRhff6UI85BUx5FEURFd8dtdgQhszd-yt4ztRnfw6whWraTxhAakYkVuop0ZEHWjWa63PygalkHN9U0IPlrz3_PkxSz2z99nbeWAxU5GewqPtQVV5E6syyOYKjvj29W4j2lU_r_mA-DhOEX61_sqh0AXL7o7QW2Op-E" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="317" data-original-width="975" height="208" src="https://blogger.googleusercontent.com/img/a/AVvXsEjp7Xe68DOd1H5lcbArfAMaJyARMRhff6UI85BUx5FEURFd8dtdgQhszd-yt4ztRnfw6whWraTxhAakYkVuop0ZEHWjWa63PygalkHN9U0IPlrz3_PkxSz2z99nbeWAxU5GewqPtQVV5E6syyOYKjvj29W4j2lU_r_mA-DhOEX61_sqh0AXL7o7QW2Op-E=w640-h208" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div>Natural Language Processing (NLP) in AI involves understanding written and spoken language, as seen in voice assistants like Cortana, Siri, or Alexa. NLP includes tasks like speech-to-text, text-to-speech, sentiment analysis, and entity detection in text. It also enables translation between languages and interprets commands for actions. This cognitive aspect, known as language understanding, is crucial for applications like voice assistants.<br /><br /><p></p><p>Unlike Computer Vision, there's no service just called natural language processing. <b>Azure breaks it down into 4 main services.</b></p><h2 style="text-align: left;">Azure Services For NLP</h2><p><br /></p><p></p><h3><ul style="text-align: left;"><li>Text Analytics service: </li></ul></h3><ul style="text-align: left;"><ul><li>Here we can get back results on entities, sentiments, etc.</li><li>Text Analytics involves evaluating document or sentence content, determining language, sentiment analysis, keyphrase extraction, and entity recognition. </li><li>It helps assess text aspects, such as language dominance and sentiment (positive/negative). </li><li>The service extracts key phrases, aiding in summarization, and recognizes entities like people, dates, and locations with confidence scores. </li><li>Azure offers standalone Text Analytics or integration with Cognitive Services. </li></ul></ul><div><br /></div><h3><ul style="text-align: left;"><li>Azure Speech: </li></ul></h3><ul style="text-align: left;"><ul><li>We can use this service to recognize and synthesize speech. It will also allow us to translate spoken languages.</li><li>Azure Speech enables speech recognition, converting spoken language into text or data using the speech-to-text API. </li><li>This functionality is useful for real-time transcriptions or batch transcriptions from audio files. </li><li>On the flip side, speech synthesis transforms text into speech, applicable for voice menus, reading emails aloud, or broadcasting announcements. </li><li>The text-to-speech API facilitates this conversion, allowing the resulting computer voice to be played directly or saved as an audio file. </li><li>Azure provides a standalone Speech service for focused usage tracking or integration with the broader Cognitive Services for a unified endpoint and key.</li></ul></ul><div><br /></div><h3><ul style="text-align: left;"><li>Translator Text Service: </li></ul></h3><ul style="text-align: left;"><ul><li>It does exactly what it sounds like and will allow us to translate text between more than 60 languages.</li><li>Text translation on Azure involves translating documents or texts from one language to another, similar to Google Translate. </li><li>The service supports over 60 languages for text-to-text translation, allowing users to specify the source and target languages. </li><li>Options like the profanity filter and content tagging enhance translation accuracy. </li><li>Speech translation capabilities include direct speech-to-speech translation for presentations and translating spoken language into text files. </li><li>Azure offers the Translator text service for text translation and Azure Speech for comprehensive speech translation, both falling under the Cognitive Services umbrella. </li></ul></ul><div><br /></div><h3><ul style="text-align: left;"><li>Language Understanding Intelligence Service / or LUIS for short: </li></ul></h3><ul style="text-align: left;"><ul><li>This is where we'll be able to train a language model that can understand us and our intents.</li><li>Language understanding involves enabling computers to comprehend and respond to spoken phrases, as seen in home assistants like Cortana. </li><li>This process breaks down into three key elements: </li><ul><li>Utterances (spoken phrases).</li><li>Entities (items referred to in the phrases). </li><li>Intents (the purpose or goal of the phrases). </li></ul><li>For example, in the phrase "Start the coffee machine," "coffee machine" is the entity, and "start" is the intent.</li></ul></ul><p></p><p><br /></p><p>Azure provides the Language Understanding standalone service for authoring (training the model with entities, intents, and utterances) and prediction (deploying the trained model). It can be used independently or under the Cognitive Services umbrella for a unified endpoint and key. Notably, Language Understanding is specifically designed for predictions.</p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiJe9iJf0PBEoM1j81wKpG7G6MG5_ISPAoYLXYTjABhyVXxhZ0bnkfoXCRSZ5X6MsdfBtDjMQNB2uiy4ntV-Eeoz8RLPmg5YYAeW6ETXem1sZLl0MEtlMAlVW9Q8unfUrunVo3CtJQiFK7sjVnp7uJAPrl7ZbCvqXipwx-D_zO5eOp6S4H6RXqWjZodvlI" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="575" data-original-width="1196" height="309" src="https://blogger.googleusercontent.com/img/a/AVvXsEiJe9iJf0PBEoM1j81wKpG7G6MG5_ISPAoYLXYTjABhyVXxhZ0bnkfoXCRSZ5X6MsdfBtDjMQNB2uiy4ntV-Eeoz8RLPmg5YYAeW6ETXem1sZLl0MEtlMAlVW9Q8unfUrunVo3CtJQiFK7sjVnp7uJAPrl7ZbCvqXipwx-D_zO5eOp6S4H6RXqWjZodvlI=w640-h309" width="640" /></a></div><br /><br /><p></p><p><i>To succeed in using Language Understanding, one needs to grasp the distinctions between utterances, intents, and entities.</i></p><p></p><ul style="text-align: left;"><li>That utterances are spoken phrases</li><li>Intents are our goal or what we're trying to accomplish,</li><li>Entities are the items</li></ul><p></p><div><br /></div><div><br /></div><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /><p></p>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com010728 S Emerald Ave, Chicago, IL 60628, USA41.6987351 -87.64165134.769827818515765 -96.4307135 48.627642381484236 -78.8525885tag:blogger.com,1999:blog-830335965541290967.post-26378957958518329172023-12-23T12:25:00.005+05:302024-01-28T08:07:10.227+05:30Exploring Azure Cloud Automated Machine Learning<p> <span></span></p><a name='more'></a><p></p><p><br /></p><h1 style="text-align: center;">Azure Automated Machine Learning Lab</h1><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgsTJ-bz4U_0x73K0Q0mpGA60B7R-UNJPhCeU6DPaw9wfsu8kECqrw-KiBi-UhfTHCw91p4G_2jWjQfo-LmXHTKDTcuH5XmD7WamEX8bnBfcXJvbjPrMGoB-Dd4aVSAY_UHbFqXpYtbaPHKRblpMAuErhSzrhCnfLbTp8lIOvqdrcbn861ZgEXcowq6tj8" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="299" data-original-width="745" height="256" src="https://blogger.googleusercontent.com/img/a/AVvXsEgsTJ-bz4U_0x73K0Q0mpGA60B7R-UNJPhCeU6DPaw9wfsu8kECqrw-KiBi-UhfTHCw91p4G_2jWjQfo-LmXHTKDTcuH5XmD7WamEX8bnBfcXJvbjPrMGoB-Dd4aVSAY_UHbFqXpYtbaPHKRblpMAuErhSzrhCnfLbTp8lIOvqdrcbn861ZgEXcowq6tj8=w640-h256" width="640" /></a></div><br /><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><p></p><h3 style="text-align: left;">We're going to take a look at Azure automated machine learning using Studio and do the following.</h3><p></p><ul><li>We'll set up a dataset to use.</li><li>We'll build a model.</li><li>We'll train a regression model.</li><li>We'll take a look at the results.</li><li>We'll deploy the container to an Azure container instance</li><li>We can make predictions.</li></ul><p><br /></p><p></p><p style="text-align: left;">Let's hop over to the Azure portal, I already have a setup of Azure machine learning workspace to train the machine learning models and Compute Clusters. So the first thing here is the machine learning workspace. And I just created this by clicking on Create up here and creating the machine learning workspace. Which will also create all of the required resources, such as the application insights, key vault, and storage account.</p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhocQZ2CxTy7ypytPq9hQVqEOpd24Cy00JAtWCJPkFUh4bx_ONVeV-My-XA0hhdSdMjChQq94T_tkKiWeB5nyqdUFFfZ91wqVrY6_1u6A5NiwdPChoNHyUl9jvYCSTztlc2-f49Y4zhVl70QwIva-H07aE4v2k1zk7r7mG4VlOVrVX7pmPDwNA9OrZJ5VU" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="416" data-original-width="975" height="274" src="https://blogger.googleusercontent.com/img/a/AVvXsEhocQZ2CxTy7ypytPq9hQVqEOpd24Cy00JAtWCJPkFUh4bx_ONVeV-My-XA0hhdSdMjChQq94T_tkKiWeB5nyqdUFFfZ91wqVrY6_1u6A5NiwdPChoNHyUl9jvYCSTztlc2-f49Y4zhVl70QwIva-H07aE4v2k1zk7r7mG4VlOVrVX7pmPDwNA9OrZJ5VU=w640-h274" width="640" /></a></div><br /><br /></div><br />Let's click on the workspace now. And you'll see a button here to launch the Azure Machine Learning Studio. This is where you'll access all of the machine-learning features of the workspace. So let's click it now and get started. Once it launches, you'll see lots <p></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhMi18AQ1sFlT3gMXvdOYFXbakkCH5VZxKKtTqcCE7DXNvQBgyNse0p8nR2RPYX1zx5g3rbFtuUoIs75RqmbE3eorPNI8Yjd_EXwHi7xaALSPc1JICjbKcfxacWmyks6UMN4NLcdKF5nJnP46L1Rt-TLAQ3JSUk6FE4hdlc8CdnfWWRmsKDnQKC3YGnK1M" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="443" data-original-width="975" height="290" src="https://blogger.googleusercontent.com/img/a/AVvXsEhMi18AQ1sFlT3gMXvdOYFXbakkCH5VZxKKtTqcCE7DXNvQBgyNse0p8nR2RPYX1zx5g3rbFtuUoIs75RqmbE3eorPNI8Yjd_EXwHi7xaALSPc1JICjbKcfxacWmyks6UMN4NLcdKF5nJnP46L1Rt-TLAQ3JSUk6FE4hdlc8CdnfWWRmsKDnQKC3YGnK1M=w640-h290" width="640" /></a></div><br /><br /><p></p><p>We're just going to focus on automated machine learning. Let's head over to the Automated Machine Learning tab, about the only thing we can do right now is to create a new automated machine learning run. </p><p><br /><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiE9TK0g-Hyt-y_w4xskmcEi3l1J4NOPdzIL7ELtiroO8rrfym7LTHnzNUOrhEUgenPg2RElldxc5S9p45MuzSFlhlymYyc3rB2ncwfA8_NwuOeuEVkcenR-EXvcJVeskLyRgzOpgwgcTJAZBvkLPixqpvQMsMR8WPiOdQKsPI568IsYNil2QGQA2vwi00" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="425" data-original-width="975" height="278" src="https://blogger.googleusercontent.com/img/a/AVvXsEiE9TK0g-Hyt-y_w4xskmcEi3l1J4NOPdzIL7ELtiroO8rrfym7LTHnzNUOrhEUgenPg2RElldxc5S9p45MuzSFlhlymYyc3rB2ncwfA8_NwuOeuEVkcenR-EXvcJVeskLyRgzOpgwgcTJAZBvkLPixqpvQMsMR8WPiOdQKsPI568IsYNil2QGQA2vwi00=w640-h278" width="640" /></a></div><br /><br /><p></p><h4 style="text-align: left;">So let's do a regression model to predict bike rentals using a dataset from Microsoft. Let's Configure Run.</h4><p></p><ul style="text-align: left;"><li>I'm going to give this experiment a name.</li><li>Our next option is to select the type of model and we'll want to select Regression here.</li><li>Click on Create Dataset here and choose From Web Files.</li><li>I'll input the URL to the dataset in the Web URL box.</li><li>Give it a name, and hit Next.</li><li>It will detect our file format encoding and such.</li><li>Let it load</li><li>We can view the data.</li><li>validate our dataset and you can see here we've got things</li><li>Now that we have an idea of what the data looks like, </li><li>Let's click Next to the schema, In here we can remove columns and select their type if we need to</li></ul><p></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhmkcCT8yPuvRwfL72E-wEh2kSje4yQ_xROWkDGXzkBVvfWSCiJwm5mJv61rNw8F510LsqWpWcrLc3mcs9Bx_1qgyHXgsOJ-YjKEOas1q8_ghFW15sLA0wr1flMr7C11j3dJQJOJn_fOTouBM9IAVrprZLKJoWGwCS7KPvQBEsySyzlZW3hZcpU6mzZyIk" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="509" data-original-width="975" height="167" src="https://blogger.googleusercontent.com/img/a/AVvXsEhmkcCT8yPuvRwfL72E-wEh2kSje4yQ_xROWkDGXzkBVvfWSCiJwm5mJv61rNw8F510LsqWpWcrLc3mcs9Bx_1qgyHXgsOJ-YjKEOas1q8_ghFW15sLA0wr1flMr7C11j3dJQJOJn_fOTouBM9IAVrprZLKJoWGwCS7KPvQBEsySyzlZW3hZcpU6mzZyIk" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgCfXI-e_EkRkPaTfnx8eLTezg8KXL_-efjsYibiHC5a8FNh5niy3BJ6G2BPr8ekaeFzT8LNj0hKmakYgPx_wkcnaYkGJx1nGYUzYw3HZxtRJ_Dh_NGaj_4qK-lOIfNBnUZKn6FpBAhR7uqcf1L_lohzgSTihLhKVF09crbfHYGh14Ndq3-SProHyjMx9U" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="455" data-original-width="975" height="149" src="https://blogger.googleusercontent.com/img/a/AVvXsEgCfXI-e_EkRkPaTfnx8eLTezg8KXL_-efjsYibiHC5a8FNh5niy3BJ6G2BPr8ekaeFzT8LNj0hKmakYgPx_wkcnaYkGJx1nGYUzYw3HZxtRJ_Dh_NGaj_4qK-lOIfNBnUZKn6FpBAhR7uqcf1L_lohzgSTihLhKVF09crbfHYGh14Ndq3-SProHyjMx9U" width="320" /></a></div><div class="separator" style="clear: both; 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margin-right: 1em;"><img alt="" data-original-height="518" data-original-width="975" height="170" src="https://blogger.googleusercontent.com/img/a/AVvXsEgDC6WfrPPcS6Ov9JfXtD9lX-l2--bseyS2Br95nv9CPB8W9bPyOtAUMoArB-eUA1igtgxcxFdUxdTdy327QIJd1Sqi10ZJ_9RVV3Sz-8hGIB4p3fqwx18xiuFQKxnQlHI-0T-hy-soVLIYqhj8Hk0wmFclR0FvRLg2LZD3ix_6M-qzqz8HGwAvw9cHUiE" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiTlxNesL36S0s6PCxOzpp3krYJTkhiVvUm-vRAFYMtoqbcte6LqPzsV8nm1D8VdoKrj_LZ2E9ZyWtZtcu7Lw-vvXYy7JGkaCDT2Scq8xX-MwJUmQkPjZ8iNDxdAX6TC5mawMc0FJVkSBJp1NAJraf1u31tgQ8T3-sFwhjRUDuMVD2mqAMRknyu9Yjc0tA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="700" data-original-width="975" height="230" src="https://blogger.googleusercontent.com/img/a/AVvXsEiTlxNesL36S0s6PCxOzpp3krYJTkhiVvUm-vRAFYMtoqbcte6LqPzsV8nm1D8VdoKrj_LZ2E9ZyWtZtcu7Lw-vvXYy7JGkaCDT2Scq8xX-MwJUmQkPjZ8iNDxdAX6TC5mawMc0FJVkSBJp1NAJraf1u31tgQ8T3-sFwhjRUDuMVD2mqAMRknyu9Yjc0tA" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh79horTzJuPDJ3SlHbDot0DJ4oc9aq7kFGM4enx3OouIpZKljNy6Z5McyvCIUcb44BTDvUyenG-6hMldMdEmtAdvXjdrHtdtyoSl6lIHxDEIBu4XKOZufJtonM2zsbe-1wTJpRwavXin5Zyy5DL4dyFPaaOQ8UQMx1r9ookxJH0_RrDN7nK-9hruBCtys" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="446" data-original-width="975" height="146" src="https://blogger.googleusercontent.com/img/a/AVvXsEh79horTzJuPDJ3SlHbDot0DJ4oc9aq7kFGM4enx3OouIpZKljNy6Z5McyvCIUcb44BTDvUyenG-6hMldMdEmtAdvXjdrHtdtyoSl6lIHxDEIBu4XKOZufJtonM2zsbe-1wTJpRwavXin5Zyy5DL4dyFPaaOQ8UQMx1r9ookxJH0_RrDN7nK-9hruBCtys" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div></div></div></div><p></p><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><ul style="text-align: left;"><li><b>Feature engineering: </b>If we wanted to add a new column, that's the process of creating new features from raw data to increase the predictive power of the algorithm.</li></ul><div><br /></div><ul style="text-align: left;"><li><b>Feature selection:</b> where we remove unnecessary features when training the model. This can help with accuracy and making better predictions.</li></ul></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjN_sBCxw4eNlvOOQqK4WB3XXH7vvPL3MzOYVjdjsaet0suHazeGHM9-_uoehIFKQzvx_VMNbGUXb3E-u60yNIz6kJcK6A2dhMd4wwh5sjVi4dkeGOIfebt6W-DqQBaHiAnVWcjtprYoLOWC9W0aTC5S3CUW7lTOtCaOVa70qccplGZaYv0AwUwdeG_3pc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="439" data-original-width="975" height="144" src="https://blogger.googleusercontent.com/img/a/AVvXsEjN_sBCxw4eNlvOOQqK4WB3XXH7vvPL3MzOYVjdjsaet0suHazeGHM9-_uoehIFKQzvx_VMNbGUXb3E-u60yNIz6kJcK6A2dhMd4wwh5sjVi4dkeGOIfebt6W-DqQBaHiAnVWcjtprYoLOWC9W0aTC5S3CUW7lTOtCaOVa70qccplGZaYv0AwUwdeG_3pc" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi9-3oHak9PehxHTNdisAlh0s0b8aXptTFC-mZbRHYU389zOEXJQEYdkwAt-UUSMQk2wOyEgTd-Qe3DRcDxkqb0AsElPdiSL1YhJ2LH_D8O5XyZGjM9AoD5FkYh7A4GP9mY7klzNy5-byTHqiIqv8ptWCIzIYtn7aW8glyBxMKcfIyn5Y82cpDwe_jNYcc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="758" data-original-width="895" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEi9-3oHak9PehxHTNdisAlh0s0b8aXptTFC-mZbRHYU389zOEXJQEYdkwAt-UUSMQk2wOyEgTd-Qe3DRcDxkqb0AsElPdiSL1YhJ2LH_D8O5XyZGjM9AoD5FkYh7A4GP9mY7klzNy5-byTHqiIqv8ptWCIzIYtn7aW8glyBxMKcfIyn5Y82cpDwe_jNYcc" width="283" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>The Target column:</b> This is asking us which column we want to make predictions about. Of course, we want to make predictions about rentals. So let's go ahead and pick that column.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiBQalkv38R4m92eWgX32Etm5ToUtA8ES2soMr-GlpKsogNWtY7--CfS_ZEgwvOAcsG3lhGGSuZpQQuQ1449oKNFM8RATlMlponklIVdcle4gpjJv2G8lfPy_thCTMEZ2507APJF-T3yUYeD4vHmyIWjr84-nhugQvwoCcqGI0D87TkzQle36HHjMFO580" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="484" data-original-width="975" height="159" src="https://blogger.googleusercontent.com/img/a/AVvXsEiBQalkv38R4m92eWgX32Etm5ToUtA8ES2soMr-GlpKsogNWtY7--CfS_ZEgwvOAcsG3lhGGSuZpQQuQ1449oKNFM8RATlMlponklIVdcle4gpjJv2G8lfPy_thCTMEZ2507APJF-T3yUYeD4vHmyIWjr84-nhugQvwoCcqGI0D87TkzQle36HHjMFO580" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjKPoolKUBrvwjWKBsm__RYlQZJ7SiY860Pf6x1ymdSgKCVpPlw9J4rfCwZMYkX7NHMJh0j5lNqW9d_IyZwPlyqFg9iqshB_z3rkk2Vj0xapH-_oDz9tOW2XK7w4dUrvF7zzCy0nKVLjkeu2liW_R3Z7DEaZqU8hoxSSZEud7szR1SsR5TgghQONo3XcZo" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="642" data-original-width="975" height="211" src="https://blogger.googleusercontent.com/img/a/AVvXsEjKPoolKUBrvwjWKBsm__RYlQZJ7SiY860Pf6x1ymdSgKCVpPlw9J4rfCwZMYkX7NHMJh0j5lNqW9d_IyZwPlyqFg9iqshB_z3rkk2Vj0xapH-_oDz9tOW2XK7w4dUrvF7zzCy0nKVLjkeu2liW_R3Z7DEaZqU8hoxSSZEud7szR1SsR5TgghQONo3XcZo" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Now I'll select my already-built compute cluster and hit Next.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiWK43AlpdcK6PyMFdU-nyEgwrHkRPRf18k1f6BoA_LzkGrhPXFzFsf_X46WnvVqKWexEC2j9FvQqYYiXOvK2GZ6OeiV570yodhq2FMQ4kXOiXnSmKWcmM5nzE-1BKaufDQmBavA_KIzq1kkbEgI00BAjoYz4rv25sjK3FZQfwxnOXjH-digjnvp1fsGrg" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="465" data-original-width="893" height="167" src="https://blogger.googleusercontent.com/img/a/AVvXsEiWK43AlpdcK6PyMFdU-nyEgwrHkRPRf18k1f6BoA_LzkGrhPXFzFsf_X46WnvVqKWexEC2j9FvQqYYiXOvK2GZ6OeiV570yodhq2FMQ4kXOiXnSmKWcmM5nzE-1BKaufDQmBavA_KIzq1kkbEgI00BAjoYz4rv25sjK3FZQfwxnOXjH-digjnvp1fsGrg" width="320" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: left;">Let's click Save here and then Finish.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiUH_CWk37Dduw_HE5iyMdelqh1AB-OmGVYZ21Djw7W5uqGw_axaFWe9AhRh5vHm4fjKW_1lIFcjws_11fPLSzRXvQTNuqCasLnWAPENAcLdjXZAgAHKl87XZLQvC9oF0qVoeC1TGYdtXYS-k-qGEYOn2Ha84OUfj1CvWtGEitjxDm5evOYBxMTJny31j8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="492" data-original-width="975" height="161" src="https://blogger.googleusercontent.com/img/a/AVvXsEiUH_CWk37Dduw_HE5iyMdelqh1AB-OmGVYZ21Djw7W5uqGw_axaFWe9AhRh5vHm4fjKW_1lIFcjws_11fPLSzRXvQTNuqCasLnWAPENAcLdjXZAgAHKl87XZLQvC9oF0qVoeC1TGYdtXYS-k-qGEYOn2Ha84OUfj1CvWtGEitjxDm5evOYBxMTJny31j8" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">We're starting to train a machine-learning model to predict. It's really great how easy automated machine learning is to use. Well, this is going to take a little while to run (probably about 40 minutes to an hour)</div><div class="separator" style="clear: both;"><br /></div></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgAIRkj1Mlg0dveI0FONeAfuxK7rrxkdwhiIhwgAIhLfUeUN4vAkxWL2bBpaAvTRvWekuMIXP5ah2B6E7m5Q1yNYjhq0FpaYi0lRqPou6e8U1ddj4Dc8d1LR_3ylwT7SNEc_hkIeaTQi2hgX6ib0LgxVgZxXHDU9oDwCLb-4r5LRDaAl0hplBv8LA9n9bc" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="371" data-original-width="975" height="244" src="https://blogger.googleusercontent.com/img/a/AVvXsEgAIRkj1Mlg0dveI0FONeAfuxK7rrxkdwhiIhwgAIhLfUeUN4vAkxWL2bBpaAvTRvWekuMIXP5ah2B6E7m5Q1yNYjhq0FpaYi0lRqPou6e8U1ddj4Dc8d1LR_3ylwT7SNEc_hkIeaTQi2hgX6ib0LgxVgZxXHDU9oDwCLb-4r5LRDaAl0hplBv8LA9n9bc=w640-h244" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><br /></div><p style="clear: both; text-align: left;">It's all done running now. <span style="text-align: center;">So let's take a look at the results. </span><span style="text-align: center;">The first thing here is to take a look over here </span><span style="text-align: center;">under Model Summary.</span></p><div class="separator" style="clear: both; text-align: left;"><span style="text-align: center;"><br /></span></div></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhl-UE1-tF3G8JycLn11VRgBqNLeCAJcCUjgK-ZXevrKmv0tRDxcve_c9Z1waj0dMCriYky66mIeU9lc5sQchU2OJNqQOkGaevFGnu92XV8NzDjKnLv-2DX8jna-FHVOefbhU5JOJlQhV7IVQjEXfmHv4vCO3SX9FSFGhQ7p61lxq3uZbwcoX970UFlisI" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="295" data-original-width="680" height="139" src="https://blogger.googleusercontent.com/img/a/AVvXsEhl-UE1-tF3G8JycLn11VRgBqNLeCAJcCUjgK-ZXevrKmv0tRDxcve_c9Z1waj0dMCriYky66mIeU9lc5sQchU2OJNqQOkGaevFGnu92XV8NzDjKnLv-2DX8jna-FHVOefbhU5JOJlQhV7IVQjEXfmHv4vCO3SX9FSFGhQ7p61lxq3uZbwcoX970UFlisI" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">And we can see that it picked up the voting ensemble algorithm as the best option. And we have a value here, under Normalized Root Mean Squared Error. What this is telling us is the difference between the predicted and actual value and indicates the amount of error in the model.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">So a lower number is going to be a more accurate predicting model. If we click on View Other Metrics here, it's going to open up quite the list of metrics for us. Now, these are useful in determining how your model is performing.</div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg9ALbXNIMoT-_3B35eiC4MNr_sMBc2xqIOWMGxlN9FjZN8xrxT4m5EG7XAv9irQk_D2o0nhX5EavpG4fNBOh3omlfYe1BqQiK-YUv_XNm1C287GnluQnSWSZvWt58xKnmJEkJYO_WanE073qSpwLejPKitv2QiB8C9Q5ynHmD3FO8zKkX1_AS5X8nADrM" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="327" data-original-width="975" height="107" src="https://blogger.googleusercontent.com/img/a/AVvXsEg9ALbXNIMoT-_3B35eiC4MNr_sMBc2xqIOWMGxlN9FjZN8xrxT4m5EG7XAv9irQk_D2o0nhX5EavpG4fNBOh3omlfYe1BqQiK-YUv_XNm1C287GnluQnSWSZvWt58xKnmJEkJYO_WanE073qSpwLejPKitv2QiB8C9Q5ynHmD3FO8zKkX1_AS5X8nADrM" width="320" /></a></div><div class="separator" style="clear: both; text-align: right;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEge-TzafvhzRH5LBqmoud1l1nSK09gToX1og_C3criIfgAj1XXTLX6I8coCBBMyk7RmpEorV6FfjRzFTUQURyz5l1x5dLwGTaY3rt0xTPrex5tY72XbNr67wmJIl4wkKa_zYZcSgfI8K7BPUVKi8VGOrY3EKq-KxKbOXU8qDo_XNEBupz9sshvS6mnD0us" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="618" data-original-width="565" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEge-TzafvhzRH5LBqmoud1l1nSK09gToX1og_C3criIfgAj1XXTLX6I8coCBBMyk7RmpEorV6FfjRzFTUQURyz5l1x5dLwGTaY3rt0xTPrex5tY72XbNr67wmJIl4wkKa_zYZcSgfI8K7BPUVKi8VGOrY3EKq-KxKbOXU8qDo_XNEBupz9sshvS6mnD0us" width="219" /></a> <div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg6lM_-OzyNL4AdcYCZGb_xa5k1Lxd4D9UK2eelCvuIIvyf2Au3menUtCLHbkXcbQQbzk5gIBz2dpi_RvTTsevLtdgVSqfQG6uRlZ8We79vSEhi_hVuMhVQ7C_fcdZ8CrnAHFOEBNoRkeK8jFg0rnW9ysJ8yhaGKtSGwCdrNQIxrQrCQEmU6V2zBQMMcTY" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="783" data-original-width="454" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEg6lM_-OzyNL4AdcYCZGb_xa5k1Lxd4D9UK2eelCvuIIvyf2Au3menUtCLHbkXcbQQbzk5gIBz2dpi_RvTTsevLtdgVSqfQG6uRlZ8We79vSEhi_hVuMhVQ7C_fcdZ8CrnAHFOEBNoRkeK8jFg0rnW9ysJ8yhaGKtSGwCdrNQIxrQrCQEmU6V2zBQMMcTY" width="139" /></a></div><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><h4 style="clear: both; text-align: left;">To evaluate a model's performance, let's look at 2 metrics in here.</h4><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>The first one is the R squared score: This is a metric that ranges from 0 to 1 and the higher it is, the better your model is performing and predicting.</li><li>The second one is the root mean squared error: This is the measure of errors. So the larger the number is the larger the errors and the worse the model performs.</li></ul></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><h4 style="clear: both; text-align: left;">Now that we have our model, we can deploy it to an Azure container instance and then feed it values and it'll start making rental predictions for us.</h4><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>Let's head over to the Models tab, select the VotingEnsemble algorithm, and right up here, there's a Deploy button.</li><li>Change the Compute Type to Azure Container Instance, and then under Advanced, set the CPU Reserve Capacity to 1 and the Memory Capacity to 1.</li><li>Let's click Deploy, and just like that, it's going to deploy our model to an Azure container instance.</li><li>And when it gets done creating, we'll give it a spin and make sure it works. This process usually takes about 10 to 15 minutes.</li><li>Now it's finished deploying.</li><li>You can find it under the Endpoints blade and let's head to the Test tab</li><li>You can see here that we can enter data to test the real-time endpoint and our model.</li><li>To see how close our model is to the real number, we are with the first row of data entered in.</li><li>Let's press Test here and see how close our model is to the real value.</li></ul></div></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjFEHv0qef4pD9RsMuA6t9zpmJflCHYF7YbBDSJRBv82utGA6p3FTY7J6wi4RCevQjyocg3VPx0409Hqtw9n_ab9Ue72FLWnUL0FJtfSiyImP90Uk9_D3kAK8QMuSKfariAjo4CxAtMSMJ3RnCe8S8K0uR1Z4vcBfR7CncDScd41HA5tOu4VIZ1LILXBXA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="451" data-original-width="851" height="170" src="https://blogger.googleusercontent.com/img/a/AVvXsEjFEHv0qef4pD9RsMuA6t9zpmJflCHYF7YbBDSJRBv82utGA6p3FTY7J6wi4RCevQjyocg3VPx0409Hqtw9n_ab9Ue72FLWnUL0FJtfSiyImP90Uk9_D3kAK8QMuSKfariAjo4CxAtMSMJ3RnCe8S8K0uR1Z4vcBfR7CncDScd41HA5tOu4VIZ1LILXBXA" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjt04Yd8cjm8eNTiKbFR_vvNVpprwnkjwp_WT_ollkL4L508B01NiY6XFAzz8swR8vUcTnRnV4HCMmVI2ssKK6zOMGjuKYZhbyQ4-60LO1uaNazaJ1e5-waPbQodnNm5yod-YoA_L9l8Rs2doxLx4LaMuKAV_wxKkGieUWntg6SFRh5fjim9FduXlZ9TiE" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="793" data-original-width="457" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjt04Yd8cjm8eNTiKbFR_vvNVpprwnkjwp_WT_ollkL4L508B01NiY6XFAzz8swR8vUcTnRnV4HCMmVI2ssKK6zOMGjuKYZhbyQ4-60LO1uaNazaJ1e5-waPbQodnNm5yod-YoA_L9l8Rs2doxLx4LaMuKAV_wxKkGieUWntg6SFRh5fjim9FduXlZ9TiE" width="138" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjebyPUgB2SwRBVwvVjZj10MeDntY7in1uoAzUuxi1_IoUO0EcytZcNBY9ebQ4kuXTbGlKVjqCYzx6yUJ-ahGATXpl8uySNYoaNddkBAEPdpYLx2C8q3LQxr1QVcdl4eoH0QTjfBXseVMhAB4_Dh1wtva2iN2ItqnebNAu4IiEiZn0zZtvTcbaO1R1iCyA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="621" data-original-width="830" height="239" src="https://blogger.googleusercontent.com/img/a/AVvXsEjebyPUgB2SwRBVwvVjZj10MeDntY7in1uoAzUuxi1_IoUO0EcytZcNBY9ebQ4kuXTbGlKVjqCYzx6yUJ-ahGATXpl8uySNYoaNddkBAEPdpYLx2C8q3LQxr1QVcdl4eoH0QTjfBXseVMhAB4_Dh1wtva2iN2ItqnebNAu4IiEiZn0zZtvTcbaO1R1iCyA" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj0yHUwTVAOLXAsaY9PicWhW1-yDGsenhEhDcSIQS0GwS3DQmhqoO4ZNMQg1oiNnqlV4P2qNyDXyc9hsrGdFJtdCHDEG0lYp4nSOBGUD9jwFHT_jT5jRJrN5O626qJFvuFoaqSkPQdltDP8uWDa8lwWgkWrXMl1ofy4skN3k__4sAFVk-0aK71XawpUang" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="571" data-original-width="840" height="436" src="https://blogger.googleusercontent.com/img/a/AVvXsEj0yHUwTVAOLXAsaY9PicWhW1-yDGsenhEhDcSIQS0GwS3DQmhqoO4ZNMQg1oiNnqlV4P2qNyDXyc9hsrGdFJtdCHDEG0lYp4nSOBGUD9jwFHT_jT5jRJrN5O626qJFvuFoaqSkPQdltDP8uWDa8lwWgkWrXMl1ofy4skN3k__4sAFVk-0aK71XawpUang=w640-h436" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h4 style="clear: both; text-align: center;">Well, that's Azure automated machine learning from start to finish.</h4></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><p><br /></p>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com085, 23rd Cross Rd, EWS Colony, Stage 2, BTM Layout, Bengaluru, Karnataka 560076, India12.9055218 77.6119746999999912.905260354346989 77.6117064790985 12.905783245653012 77.61224292090148tag:blogger.com,1999:blog-830335965541290967.post-397798473714520242023-02-19T09:58:00.003+05:302024-01-27T09:02:55.050+05:30Demystifying Big Query in Google Cloud<p> <span></span></p><a name='more'></a><p></p><p><br /></p><h1 style="text-align: center;">Demystifying Big Query in Google Cloud</h1><span></span><div><br /></div><h3 style="text-align: left;">Big Query:</h3><p></p><ul style="text-align: left;"><li>Big Query is a really important part of the GCP Big Data suites.</li><li>Big Query is a Cloud enterprise data warehouse.</li><ul><li>Petabyte scale</li><li>Serverless</li><li>Highly-scalable</li></ul><li>It has an in-memory BI engine, creatively called Big Query BI Engine</li><ul><li>This allows you to create very fast interactive reports, and dashboards, and then you can view these in data studio.</li></ul><li>It also has machine-learning capabilities</li><ul><li>Allowing you to build machine-learning models using SQL.</li></ul><li>There is also support for geospatial, data storage and processing.</li></ul><p></p><p><br /></p><h3 style="text-align: left;">Key features of Big Query:</h3><p><br /></p><p></p><ul style="text-align: left;"><li>It is highly available.</li><li>It supports Standard SQL.</li><li>You can put your SQL skills to work directly.</li><li>Big Query also handles Federated data, which is data that is stored outside of Big Query.</li><li>There are automatic backups.</li><li>There is support for governance and security, this is critical in today's world when there is such a focus on data security and personal privacy.</li><li>There is also the separation of storage and computing.</li><li>This leads to a number of really positive things, such as acid compliance, storage operations, cost-effective scalable storage, and stateless resilient computing.</li></ul><p></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi-e_zg29KpsOBRH3BBzlY5GD09v4g4TPkc4b8JNfMnshzqfRSqJC2p95tpB4QZq3KuUPg-CP8XBEkP1ng00wzU43L2A6Q71Xiu7WVwFFxaNIcKcoQ6oQEqQ5rChbDegUoEedQpHafK3Qf7DfQhmqVhdLb69moAH_vTad4iYAht1_Q548WHdaBTiAAk" style="margin-left: 1em; margin-right: 1em;"><img alt="Key features of Big Query algaestudy.com" data-original-height="406" data-original-width="797" height="326" src="https://blogger.googleusercontent.com/img/a/AVvXsEi-e_zg29KpsOBRH3BBzlY5GD09v4g4TPkc4b8JNfMnshzqfRSqJC2p95tpB4QZq3KuUPg-CP8XBEkP1ng00wzU43L2A6Q71Xiu7WVwFFxaNIcKcoQ6oQEqQ5rChbDegUoEedQpHafK3Qf7DfQhmqVhdLb69moAH_vTad4iYAht1_Q548WHdaBTiAAk=w640-h326" title="Key features of Big Query klassroom.algaeservice.com" width="640" /></a></div><br /><br /><p></p><p><br /></p><h3 style="text-align: left;">Interact with Big Query?</h3><p></p><ul style="text-align: left;"><li>You can use the web console, which is available in your web browser.</li><li>You can use the command line tool, specifically the BQ command line tool. When you install and initialize the Cloud SDK, you will have this tool included.</li><li>BQ is a Python-based command line tool for Big Query.</li><li>There are also a number of client libraries for programmatic access to Big Query, and there are libraries for C#, Go, Java, Node.JS, PHP, Python, and Ruby.</li></ul><p></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgTeew0S-1Y_78K2dZF3L9B1JS3YjT6T9HRyHSEAn_S-PDMXk_iNiKZDzBnGhvbE0x1dDD4qNcu_n3-bojul0fAXRgRyvv_5M1-KDttO7Top8PQP9AZ8BHcQz8eNaEIous0Q7Y0dwzWewAl5bK3A7E1I08utahy87Bct4Drd3wUpOL2aaQmSWrwConu" style="margin-left: 1em; margin-right: 1em;"><img alt="Interact with Big Query algaestudy" data-original-height="215" data-original-width="702" height="122" src="https://blogger.googleusercontent.com/img/a/AVvXsEgTeew0S-1Y_78K2dZF3L9B1JS3YjT6T9HRyHSEAn_S-PDMXk_iNiKZDzBnGhvbE0x1dDD4qNcu_n3-bojul0fAXRgRyvv_5M1-KDttO7Top8PQP9AZ8BHcQz8eNaEIous0Q7Y0dwzWewAl5bK3A7E1I08utahy87Bct4Drd3wUpOL2aaQmSWrwConu=w400-h122" title="Interact with Big Query klassroom.algaeservice.com" width="400" /></a></div><br /><br /></div><br /><h3 style="text-align: left;">Big Query Data Sets</h3><p></p><ul style="text-align: left;"><li>All Big Query data assets ultimately reside in a project.</li><li>Datasets are containers for tables and views.</li><ul><li>You're able to create many datasets within a project.</li><li>You can think of a dataset as approximating a database.</li></ul><li>You create each native table, external table, or view within a specific dataset.</li><ul><li>Native tables are standard Big Query tables where the data is held within Big Query storage.</li><li>External tables are tables that are backed by storage outside of Big Query.</li></ul><li>Table schemas are defined within Big Query, but the actual data resides outside views or virtual tables that are created by an SQL Query.</li></ul><p></p><p><br /></p><h3 style="text-align: left;">Ingest data into Big Query:</h3><p></p><ul style="text-align: left;"><li>There are 2 types of data sources for Big Query:</li><li>Real-time data, and bulk data sources, such as files.</li><ul><li>Real-time events are streamed into Big Query, generally.</li><ul><li>A common pattern is to push the events to Cloud Pub/Sub, and then use a Cloud Dataflow job to process them and push them into Big Query.</li></ul></ul><li>Batch sources of bulk loaded into Big Query.</li><ul><li>A common pattern is to push the files to Cloud Storage, and then have a Cloud Dataflow job, pick that data up, process it, and push it into Big Query.</li></ul></ul><p></p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiQXC8zQX_3NV__8IeBhrKsjCU26LCT-sKcNPrTlvTh7ZiIeEy0da6Lxn-CLybNHZtulM-m-ESo1wAD67YIfpVBWcrEOrvIzyowmmsKbArDB-PblsQhyKySfLMIqArO_1-fJvgyUAB9BBMPoeExsEaRuUlh5uHWMbZqkFaIWMA4izs-ExNeFAtVL31C" style="margin-left: 1em; margin-right: 1em;"><img alt="Ingest data into Big Query algaestudy" data-original-height="487" data-original-width="786" height="248" src="https://blogger.googleusercontent.com/img/a/AVvXsEiQXC8zQX_3NV__8IeBhrKsjCU26LCT-sKcNPrTlvTh7ZiIeEy0da6Lxn-CLybNHZtulM-m-ESo1wAD67YIfpVBWcrEOrvIzyowmmsKbArDB-PblsQhyKySfLMIqArO_1-fJvgyUAB9BBMPoeExsEaRuUlh5uHWMbZqkFaIWMA4izs-ExNeFAtVL31C=w400-h248" title="Ingest data into Big Query klassroom.algaesrvice.com" width="400" /></a></div><br /><br /><p></p><p><br /></p><h3 style="text-align: left;">Analyze and visualize the data using BI tools.</h3><p></p><ul style="text-align: left;"><li>These can be external tools like </li><ul><li>Tableau</li><li>Looker</li><li>Google Data Studio etc.</li><li>Cloud Datalab</li><ul><li>You can interactively explore the data using Cloud Datalab.</li></ul><li>Google Sheets or Google Cloud Storage</li><ul><li>You can export to Google Sheets or Google Cloud Storage.</li></ul><li>Tools like Dataflow and Dataproc</li><ul><li>You can access the data from other GCP big data tools like Dataflow and Dataproc</li></ul></ul><li>You can share the data with colleagues.</li></ul>It's worth mentioning again how important Big Query is, Big Query occurs in many of the GCP reference architectures.<br /><p></p><div><br /></div><div><h3 style="text-align: left;">Jobs in Big Query</h3><div><br /></div><div><ul style="text-align: left;"><li>A job is an action that Big Query runs on your behalf.</li><ul><li>Jobs are run asynchronously as they can take a long time to complete. </li><li>Jobs can be polled for status to determine if they've started if they're in progress, or if they have completed.</li></ul><li>Not all actions in Big Query are executed as jobs</li><ul><li>Short-running actions are not assigned a job resource. </li></ul></ul></div></div><div><br /></div><div><br /></div><div><h3 style="text-align: left;">Four types of jobs.</h3><div><ul style="text-align: left;"><li>Load jobs. </li><ul><li>These load data into BigQuery.</li></ul><li>Export jobs. </li><ul><li>These export data from BigQuery,</li></ul><li>Query jobs: </li><ul><li>These allow you to query data within BigQuery.</li></ul><li>Copy jobs. </li><ul><li>These jobs are used to copy tables or data sets.</li></ul></ul></div></div><div><br /></div><div><br /></div><div><h4 style="text-align: left;">They are 2 priorities for jobs.</h4><div><ul style="text-align: left;"><li>There is the interactive priority and the batch priority.</li><li>The interactive priority is the default.</li><ul><li>When running interactively, the query is executed as soon as possible, interactive queries do count toward your concurrent rate limit.</li><li>That is the number of concurrent queries running at any time and towards your daily limit.</li><li>That is the total number of queries that you can run per day.</li><li>Query results for interactive queries are always saved to a table, either as a temporary table or as a permanent table, you are able to append or override data in an existing table, or you can push that information into a new table.</li></ul><li>Batch queries on the other hand are queued.</li><ul><li>The query is executed when there are, idle resources available in the BigQuery shared resource pool.</li><li>If the query has not been executed within 24 hours, the job priority is changed to interactive. In this case, it'll run as soon as possible, and the materialization of query results can be used to lower costs and simplify complex queries.</li></ul></ul></div></div><div><br /></div><div><br /></div><div><h3 style="text-align: left;">How data is stored within BigQuery.</h3><div><ul style="text-align: left;"><li>BigQuery uses the capacitor column data format.</li><li>Tables can be partitioned within BigQuery as with a relational database.</li><li>Individual records exist as rows and each record is composed of a number of columns. Table</li><li>schemas can be specified at the time of the creation of the table, or when you load data into the table.</li><li>If we have a look here it's, as you would expect from a relational database, there are records and there are columns in this table and we can have multiple partitions of the table depicted here.</li></ul></div></div><div><br /></div><div><h3 style="text-align: left;">Capacitor storage system in Big Query.</h3><div><ul style="text-align: left;"><li>The capacitor storage system is extremely efficient</li><li>It is a proprietary columnar data storage that supports semi-structured data. And by semi-structured data, we mean nested and repeated fields.</li><li>Data is converted from the input format, which could be CSV / JSON to the capacitor format when it is loaded into Big Query.</li><li>It stores data in its column the storage, which means it separates each record into column values and stores each record on a different storage volume Each column. </li><li>In addition to its value, also stores two numbers, the values repetition level, and the definition level. </li><li>This encoding allows the full or partial structure of a record to be reconstituted without reading the parent's columns. </li><li>We can think of each column being separated and stored on a separate volume</li><li>Remember each value is stored together with its repetition level and definition level.</li><li>We can show this schematically by assuming row two, column five has the value New York with repetition level three and definition level five.</li><li>How repetition level and definition level actually work.</li><ul><li>The definition and repetition level in coding is so efficient for semi-structured data that it has been used for other encodings such as the open-source Parquet encoding</li></ul></ul></div></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><h3 style="text-align: left;"><b>De-normalization in Big Query.</b></h3><div><br /></div><div><ul style="text-align: left;"><li>Big Query performance is optimized when data is denormalized appropriately. </li><li>Denormalization refers to nested and repeated columns.</li><li>Denormalization allows data to be stored in a very efficient manner, and it is also then retrieved in an efficient manner.</li><li>If you want to use nested or repeated columns, you use the record data type.</li><li>Let's look at this schematically.</li><ul><li>So here we have a table with three columns, the name, the ID, and the address column.</li><li>Suppose we want to have the address column be a nested column. We would then assign it the record data type.</li><li>And in that case, we can specify sub-columns, such as the name, the street, and the city.</li><li>We can also have repeated values for each record. </li><li>So in this example, for each name or person, we have multiple addresses stored And of course the repeated columns can also be nested.</li></ul></ul></div><div><br /></div><h4 style="text-align: left;">Let's look at this example.</h4><div><ul style="text-align: left;"><li>So here we have a schema, we have information on a person. First name, last name, date of birth.</li><li>And now we also have the addresses column, which is nested and repeated.</li><li>So it's nested because you can see the sub-values of status, address, city, state, zip code, etcetera.</li><li>And it is repeated because we can have multiple addresses for each ID.</li><li>So when we look at the JSON representation of actual information, we can see for a single ID one, we have the first address over here.</li><li>And the second address here, when importing data into Big Query, we need to keep in mind that there are a number of supported formats. </li></ul></div><div><br /></div><h3 style="text-align: left;">Formats to Upload data:</h3><div><br /></div><div><ul style="text-align: left;"><li>The first one is CSV. </li><ul><li>This is the default source format for loading data into Big Query.</li></ul><li>Next, we have JSON. </li><ul><li>It's important that each record is newline delimited.</li></ul><li>Next, we have Avro, </li><ul><li>Avro is an open-source data format where the schema is stored together with the data. </li><li>Avro is the preferred format for loading compressed data into Big Query.</li></ul><li>Then there is parquet, </li><ul><li>It is based on the dremmel storage approach.</li><li>It's a good choice because Parquet's encoding is efficient and it typically results in smaller files.</li></ul><li>Then there is ORC or optimized row columnar format. </li><ul><li>ORC is an efficient way to store hive data.</li></ul><li>Then we have cloud Datastore exports and Firestore exports.</li><ul><li>All of the data from these formats are converted to the column, the format in BigQuery.</li></ul></ul></div></div><div><br /></div><div><br /></div><div><h3 style="text-align: left;">Big Query views.</h3><div><br /></div><div><ul style="text-align: left;"><li>A view is a virtual table that is defined by an SQL query. </li><li>If we have a dataset. All views exist within a dataset, and we have an SQL query, which defines the view, that SQL query will access data from a number of tables.</li><li>We can create the view within the dataset</li><li>When you have created a view, you can access that view in the same way that you query a table. </li><li>So other SQL queries can then query that view.</li><li>A view is unmaterialized. </li><ul><li>That means that the underlying query is executed each time the view is accessed. That will have billing implications.</li></ul></ul></div><div><br /></div><h3 style="text-align: left;">Benefits of views</h3><div><ul style="text-align: left;"><li>They allow us to control access to data.</li><li>When a user queries a view, they will only have access to the tables and fields that are part of the definition of that view.</li><li>Views can be used to reduce overall query complexity.</li><li>This is done by breaking a complex query into a number of simpler queries.</li><li>Views can be used to construct logical tables.</li><li>Logical tables can be used to organize similar information from different physical tables in Big Query.</li><li>And finally, have the ability to create authorized views, authorized views allow users to have access to different subsets of rows from the view.</li></ul></div><div><br /></div><h3 style="text-align: left;">Big Query views limitations </h3><div><ul style="text-align: left;"><li>You cannot export data from a view because they are unmaterialized.</li><li>You cannot use the JSON API to retrieve data from a view, and you cannot combine standard and legacy SQL.</li><li>If you have defined a view using legacy SQL, you cannot query that view using standard SQL.</li><li>The definition of a view cannot use user-defined functions.</li><li>There can be no wild card table references in view definitions, and you're limited to 1000 authorized views per data set, a federated or external data source is a data source that you can query directly.</li></ul></div><div><br /></div><h3 style="text-align: left;">Data From External Sources</h3><div><ul style="text-align: left;"><li>Even though the data is not held within Big Query, Big Query offers support for querying data from Cloud Big table, cloud storage, and Google drive.</li><li>There are two typical use cases.</li><ul><li>First is where we want to load and clean data in one pass. </li><ul><li>In this case, we changed the data from the external source before loading it into a Big Query table.</li></ul><li>The second used case is where you have small frequently changing data joined with other tables.</li><ul><li>An example of this is when you may be querying geographical data that changes from time to time.</li><li>It is easier to change the locations within a document in Google drive than it is to change the data within the Big Query table.</li></ul></ul></ul></div><div><br /></div><h3 style="text-align: left;">Limitations that apply to external data sources. </h3><div><ul style="text-align: left;"><li>There is no guarantee of consistency.</li><li>There is a lower query performance in general,</li><li>You cannot use the Table Data List, API method.</li><li>You cannot run export jobs on external data.</li><li>You cannot reference external data in a wildcard table query.</li><li>You cannot use Parquet or ORC formats for external data.</li><li>The query results for external data sources are not caged.</li><li>You're limited to four concurrent queries where external data is involved.</li></ul></div><div><br /></div><h3 style="text-align: left;">Data sources that are useful in Big Query.</h3><div><ul style="text-align: left;"><li>There are public data sets. </li><ul><li>These are accessible to everyone within Big Query.</li></ul><li>Then there are shared data sets. </li><ul><li>These are data sets that have been shared with you.</li></ul><li>And finally, you can also view Stack driver log information within Big Query.</li><li>Big Query also allows you to bulk extract and analyze data from a number of additional data sources.</li><ul><li>Pulling bulk data into Big Query is easily facilitated using the data transfer service.</li><li>The data transfer service has a number of connectors to Google services, to GCP services like cloud storage to AWS services like S3 and Redshift.</li><li>They also connect us to other third-party systems such as Facebook, LinkedIn, and there are many others.</li><li>These bulk extractions can be one-off events or they can be scheduled to run repeatedly.</li></ul><li>The data transfer service allows for the historical restatements of data and has an uptime and delivery SLA.</li><li>You can access the Big Query data transfer service using the cloud console, the Big Query command line tool, or the Big Query data transfer service API.</li></ul></div></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com02MPJ+2W Mikope-Luabala, Democratic Republic of the Congo-4.9649722999999986 20.6823455-21.891322070408044 3.1042205000000003 11.961377470408046 38.2604705tag:blogger.com,1999:blog-830335965541290967.post-30090632694815004792023-01-25T12:22:00.005+05:302023-02-19T09:59:59.491+05:30What can quantum computers do more efficiently than regular computers?<div><br /></div><h1 style="text-align: center;">Quantum computers vs classical computers<span><a name='more'></a></span></h1><span></span><div><br /></div><div><br /></div><div>Quantum computers can perform certain types of computations much more efficiently than classical computers. The most significant advantage of quantum computers is that they can perform certain operations exponentially faster than classical computers. This is due to the unique properties of quantum mechanics. </div><div><br /></div><h4 style="text-align: left;">Unique properties of quantum mechanics</h4><div><ul style="text-align: left;"><li>quantum parallelism</li><li>quantum entanglement</li></ul></div><div><br /></div><div>One of the most important applications of quantum computers is in the field of quantum algorithms, such as Shor's algorithm and Grover's algorithm. </div><div><br /></div><div style="text-align: left;"><h4><ul style="text-align: left;"><li>Shor's algorithm:</li></ul></h4><ul style="text-align: left;"><ul><li>It can be used to factorize large numbers efficiently, which is crucial for breaking many encryption systems. </li></ul></ul><h4><ul style="text-align: left;"><li>Grover's algorithm:</li></ul></h4><ul style="text-align: left;"><ul><li>It can be used to search an unsorted database quadratically faster than any classical algorithm.</li></ul></ul></div><div><br /></div><div>Another important area where quantum computers have the potential to be much more powerful than classical computers is in simulating quantum systems. Due to the exponential scaling of the Hilbert space with the number of qubits, even a small quantum computer with only a few dozen qubits can represent an exponentially large classical system.</div><div><br /></div><h4 style="text-align: left;">Summary:</h4><div>Quantum computers can perform certain computations exponentially faster than classical computers, including factoring large integers, solving systems of linear equations, and simulating quantum systems.</div><div><br /></div><div><br /></div><h4 style="text-align: left;">Use case of factorization in quantum computing: </h4><div>The use case of factorization in quantum computing is Shor's algorithm, which is a quantum algorithm for factoring integers that were discovered by mathematician Peter Shor in 1994. </div><div><br /></div><div> It is the most efficient known classical algorithm for this task. The algorithm can be used to break RSA and other public key cryptosystems that are based on the difficulty of factoring large integers, thereby solving one of the most important problems in classical computer science and a major open problem in mathematical research. </div><div><br /></div><div>In the year 1994, Shor's algorithm was first implemented on a quantum computer with a 7-qubit NMR quantum computer. Since then, the largest factorization that has been performed using this algorithm is on a 21-qubit quantum computer, which factorized the number 15 into 3 and 5.</div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com056, Karim Block Allama Iqbal Town, Block P Gulberg 2, Lahore, Punjab, Pakistan31.5220488 74.351460831.052935152136598 73.80214439375 31.991162447863402 74.90077720625tag:blogger.com,1999:blog-830335965541290967.post-72879501872644279612022-12-11T10:59:00.001+05:302023-02-20T02:17:31.429+05:30Financial Analysis and Managerial Accounting Definitions<p> <span></span></p><a name='more'></a><p></p><p><br /></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaVk1Ay3mlCv-SCDGH9nA5WSuVurdNMB0U8ZhtorU9pEUjaMH4UMxCwcEMl0MluFyUzdLtCt0J0RbvDoMzKc2x3JJTbpVqbm7jVf9EuxntZjZRolYMEXKbuBUW-IWXuikaeu61-V76N7FsVRIhoWpD9Y41cQcvm_X_m7M5Y0rRp10SrTwyy4_ZDsZF/s500/Cost_and_Expense_balanced_algaestudy_algae.gif" style="margin-left: 1em; margin-right: 1em;"><img alt="algae study, algaeservices, algae, klassroom" border="0" data-original-height="310" data-original-width="500" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaVk1Ay3mlCv-SCDGH9nA5WSuVurdNMB0U8ZhtorU9pEUjaMH4UMxCwcEMl0MluFyUzdLtCt0J0RbvDoMzKc2x3JJTbpVqbm7jVf9EuxntZjZRolYMEXKbuBUW-IWXuikaeu61-V76N7FsVRIhoWpD9Y41cQcvm_X_m7M5Y0rRp10SrTwyy4_ZDsZF/w320-h198/Cost_and_Expense_balanced_algaestudy_algae.gif" title="cost and expense gif Managerial Accounting" width="520" /></a></div><br /><p><br /></p><p><br /></p><h1 style="text-align: left;">Introduction Financial Definitions</h1><p><br /></p>
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<h3 style="text-align: left;">Fixed Cost:</h3><p></p><ul style="text-align: left;"><li>A cost of a business expense that doesn't change even when there's an increase or decrease in the number of goods and services produced or sold.</li><li>Fixed Costs are expenses that have to be paid by a company, independent of any business activity</li><li>Fixed costs are allocated in the indirect expense section of the income statement which leads to operating profit. </li><li>Depreciation is one common fixed cost that is recorded as an indirect expense.</li></ul><p></p><p><br /></p><p></p>
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<h3 style="text-align: left;">Variable Cost:</h3><p></p><ul style="text-align: left;"><li>A variable cost is a corporate expense that changes in proportion to how much a company produces or sells. </li><li>Variable costs are usually viewed as short-term costs as they can be adjusted quickly.</li><li>The variable cost of production is a constant amount per unit produced.</li><li>Variable costs increase or decrease depending on a company's production or sales volume—they rise as production increases and fall as production decreases.</li><li>Total Variable Cost = Total Quantity of Output X Variable Cost Per Unit of Output</li></ul><p></p><p><br /></p><p><br /></p>
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<h3 style="text-align: left;">Sales Price: </h3><p>The sales price is the price at which a certain class of goods or services is typically sold</p><p><br /></p>
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<p><br /></p><h3 style="text-align: left;">Unit Margin:</h3><p></p><ul style="text-align: left;"><li>Unit margin is also called Unit Contribution Margin</li><li>Unit margin can be stated on a gross or per-unit basis</li><li>Unit Margin is the amount of the product selling price over and above the variable cost per unit</li></ul><div><br /></div>
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<p><br /></p><p><br /></p><p><br /></p><p><br /></p><h3 style="text-align: left;">Total Margin:</h3><p>Total Margin is the total amount of margin or profit made after deducting fixed costs</p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjxmBvRzE34zzmkjxnfg9asafRuYx8UCPbKUkIvFEQC_OtGkP7kHvKqPzpEZkVNzHv_X-lZnFA-_5KA7JL2QgcrVtDxYr_DO3yV3XABabLOuAQzCvf7fhu2qvseMmYXMn_a14ZX_aWFhdD2lFkwSx0N6FMg15FOjkj_-TDjdJvORpFAOBtcq_FyHPg7" style="margin-left: 1em; margin-right: 1em;"><img alt="Algae Services, Algaestudy Klassroom, algae" data-original-height="103" data-original-width="730" height="90" src="https://blogger.googleusercontent.com/img/a/AVvXsEjxmBvRzE34zzmkjxnfg9asafRuYx8UCPbKUkIvFEQC_OtGkP7kHvKqPzpEZkVNzHv_X-lZnFA-_5KA7JL2QgcrVtDxYr_DO3yV3XABabLOuAQzCvf7fhu2qvseMmYXMn_a14ZX_aWFhdD2lFkwSx0N6FMg15FOjkj_-TDjdJvORpFAOBtcq_FyHPg7=w640-h90" title="Financial Analysis and Managerial Accounting" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div>
<div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;">Ceteris Paribus</h3>
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<li>Ceteris paribus is translated into English as "all else being equal."</li>
<li>It is a Latin phrase that literally "holding other things constant," </li>
<li>ceteris paribus is often used when making arguments about cause and effect</li>
<li>It acts as a shorthand indication of the effect one economic variable has on another, provided all other variables remain the same.</li>
<li>Many economists rely on ceteris paribus to describe relative tendencies in markets and to build and test economic models.</li>
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<h3 style="text-align: left;">Unfavorable Variance</h3>
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<li>An unfavorable variance is an accounting term that describes instances where actual costs are greater than the standard or projected costs.</li>
<li>What Is Unfavorable Variance?</li>
<li>An unfavorable variance is an accounting term that describes instances where actual costs are greater than the standard or projected costs.</li>
<li>The sooner an unfavorable variance is detected, the sooner attention can be directed toward fixing any problems</li><li>The unfavorable variance could be the result of lower revenue, higher expenses, or a combination of both.</li>
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<div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;">Favorable Variances</h3>
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<li>A favorable variance is where actual income is more than budget, or actual expenditure is less than budget. </li><li>This is the same as a surplus where expenditure is less than the available income.</li><li>Favorable variances related to price are only derived from the difference between actual and expected prices paid, and so have no bearing at all on the underlying efficiency of a company's operations.</li><li>Obtaining a favorable variance does not necessarily mean much, since it is based upon a budgeted or standard amount that may not be an indicator of good performance</li>
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<div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;">Positive Correlation</h3><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>A positive correlation is a relationship between two variables that tend to move in the same direction.</li><li>A positive correlation exists when one variable tends to decrease as the other variable decreases, or one variable tends to increase when the other increases.</li><li>In finance, correlations are used to describe how individual stocks move with respect to the wider market.</li><li>Beta is a common measure of market correlation, usually using the S&P 500 index as a benchmark.</li><li>A beta of 1.0 describes a stock that is perfectly correlated with the S&P 500. Values higher than 1.0 describe stocks that are more volatile than the S&P 500, while lower values describe stocks that are less volatile.</li></ul></div><div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSexhXtUC3bbuEtv3_25IIIG4sYKYlTMW4Stk7fbRWzeGxQsc1iHmyKwW9qS8Yh9IXFoBC4ehLTYEt4XtMons05gaFBLetwzrDBPaWQui39Uq89FbydwEFNIUofpzcMuWKO44nLt1jO_t1HDAA_0Qpeq6yvaHjsx6oxFYjxEn3Uiu3YV_kwRWpyI9i/s268/Correleation-positive%20-inverse%20algaestudy%20klassroom.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="120" data-original-width="268" height="120" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSexhXtUC3bbuEtv3_25IIIG4sYKYlTMW4Stk7fbRWzeGxQsc1iHmyKwW9qS8Yh9IXFoBC4ehLTYEt4XtMons05gaFBLetwzrDBPaWQui39Uq89FbydwEFNIUofpzcMuWKO44nLt1jO_t1HDAA_0Qpeq6yvaHjsx6oxFYjxEn3Uiu3YV_kwRWpyI9i/s1600/Correleation-positive%20-inverse%20algaestudy%20klassroom.png" width="268" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h3 style="clear: both; text-align: left;">Inverse Correlation</h3><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><ul style="text-align: left;"><li>An inverse (or negative) correlation is when two variables in a data set are related such that when one is high the other is low.</li><li>Even though two variables may have a strong negative correlation, this does not necessarily imply that the behavior of one has any causal influence on the other.</li><li>The relationship between two variables can change over time and may have periods of positive correlation as well.</li></ul></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div></div><p></p>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0tag:blogger.com,1999:blog-830335965541290967.post-45275772607053161622022-11-20T01:09:00.007+05:302023-02-20T02:20:17.817+05:30All-in-one list with the Economics formulas<p><span></span></p><a name='more'></a> <p></p><p><br /></p><p><br /></p><p><br /></p><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><h2 class="has-text-align-center" style="border: 0px; box-sizing: border-box; clear: both; color: #0073b0; font-family: "Nunito Sans", sans-serif; font-size: 1.875rem; font-weight: 400; line-height: 1.3; margin: 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1. Topics in Demand and Supply Analysis</span></h2><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Price Elasticity</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Price~elasticity = \frac {\%\Delta~Quantity~demanded~(Qx)}{\%\Delta~Price~(Px)}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.363em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.936em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.427em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">%Δ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 254.521px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">%Δ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">man</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.936em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">0 > e > -1 \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68354em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">0</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.5782em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.72777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> inelastic demand<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">-1 > e > -∞ \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.72777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.5782em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.66666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">∞</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> elastic demand<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">e = -1 \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.43056em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.72777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> unit elastic demand<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">e = 0 \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.43056em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">0</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> perfectly inelastic demand<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">e = -∞ \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.43056em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.66666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">∞</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> perfectly elastic demand</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Income Elasticity</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Income~elasticity = \frac {\%\Delta~Quantity~demanded~(Qx)}{\%\Delta~Income~(Ix)}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">co</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.363em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.936em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.427em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">%Δ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">co</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 254.521px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">%Δ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">man</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.936em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">e > 0 \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.5782em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">0</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> normal goods<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">e < 0 \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.5782em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">0</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> inferior goods<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">ε{_Y}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.58056em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.15em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ε</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.328331em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Y</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span></span></span></span></span></span> = Income elasticity</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Cross-price Elasticity</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Cross-price~elasticity = \frac {\%\Delta~Quantity~demanded~(Qx)}{\%\Delta~Price~of~a~related~good~(Py)}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ross</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.363em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.936em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.427em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">%Δ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">re</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">oo</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 280.427px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">%Δ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">man</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.936em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">e > 0 \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.5782em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">0</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> the related product is a substitute<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">e < 0 \rightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.5782em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">0</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">→</span></span></span></span></span> the related product is a complement<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.625em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span></span></span></span></span> = Related product<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">ε{_{py}}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.716668em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.286108em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ε</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.151392em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mtight" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span></span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.286108em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span></span></span></span></span></span> = Cross-price elasticity</p><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><h2 class="has-text-align-center" style="border: 0px; box-sizing: border-box; clear: both; color: #0073b0; font-family: "Nunito Sans", sans-serif; font-size: 1.875rem; font-weight: 400; line-height: 1.3; margin: 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">2. The Firm and Market Structures</span></h2><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;">For all market structures, <span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Max Profit</span> <span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">\longrightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.522em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.011em;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">⟶</span></span></span></span></span> <span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">when </span><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">MC = MR</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">MC</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">MR</span></span></span></span></span></p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">MC</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">MC</span></span></span></span></span> = Marginal cost<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">MR</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">MR</span></span></span></span></span> = Marginal revenue</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Breakeven points</span>:<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">AR = ATC</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TC</span></span></span></span></span> (perfect competition)<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">TR = TC</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TR</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TC</span></span></span></span></span> (imperfect competition)</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">ATC =</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TC</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span></span></span></span></span> Average Total Cost<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">AR =</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span></span></span></span></span> Average Revenue<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">TR =</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TR</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span></span></span></span></span> Total Revenue<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">TC =</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TC</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span></span></span></span></span> Total Cost<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">AR = ATC</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TC</span></span></span></span></span> holds true in imperfect competition</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Short-run shutdown points:<br style="box-sizing: border-box;" /></span><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">AR < AVC</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.72243em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">V</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span></span></span></span></span> (perfect competition)<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">TR < TVC</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.72243em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.0391em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">TR</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">V</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span></span></span></span></span> (imperfect competition)</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Market structures:<br style="box-sizing: border-box;" /></span>Perfect Competition<br style="box-sizing: border-box;" />Monopolistic Competition<br style="box-sizing: border-box;" />Oligopoly<br style="box-sizing: border-box;" />Monopoly</p><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><h2 class="has-text-align-center" style="border: 0px; box-sizing: border-box; clear: both; color: #0073b0; font-family: "Nunito Sans", sans-serif; font-size: 1.875rem; font-weight: 400; line-height: 1.3; margin: 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">3. Aggregate Output, Prices, and Economic Growth</span></h2><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Total GDP</span> = final value of goods and services produced (market value)<br style="box-sizing: border-box;" />+ government services (at cost)<br style="box-sizing: border-box;" />+ rental value of owner-occupied housing (an estimate)</p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">GDP~Deflator = \frac{Nominal~GDP}{Real~GDP} \times 100</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">De</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">or</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.05744em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.686em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.37144em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 130.49px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">mina</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.686em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">100</span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Nominal~GDP{_t} = P{_t} \times Q{_t}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.84444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.15em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">mina</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.280556em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.83333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.15em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.280556em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.87777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.280556em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Real~GDP{_t} = P{_{b}} \times Q{_t}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.84444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.15em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.280556em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.83333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.15em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.336108em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mtight" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">b</span></span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.87777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.280556em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.61508em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span></span> = Current year<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">b</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">b</span></span></span></span></span> = Base year<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">P{_t}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.83333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.15em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.280556em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span></span></span></span></span></span> = Prices in year {_t}<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">P{_b}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.83333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.15em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.336108em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">b</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span></span></span></span></span></span> = Prices in base year<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Q{_t}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.87777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Q</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="msupsub" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.280556em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px 0.05em 0px 0px; outline: 0px; padding: 0px; position: relative; top: -2.55em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.7em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="sizing reset-size6 size3 mtight" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-size: 0.7em; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal mtight" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.15em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span></span></span></span></span></span></span> = Quantity produced in year {_t}</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Expenditure Approach</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Real~GDP = Consumption~spending~(C) + Investment~(I) + Government~spending~(G) + Net~exports~(X-M)</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pt</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">es</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">er</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">nm</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">or</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">X</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">X</span></span></span></span></span> = Exports<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">M</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span></span></span></span></span> = Imports</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Income Approach</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Real~GDP = National~income + Capital~consumption~allowance + Statistical~discrepancy</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.77777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">na</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">co</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">co</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pt</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ll</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02691em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">w</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">St</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">scre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">cy</span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Real~GDP = Consumption~spending~(C) + Savings~(S) + Taxes~(T)</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pt</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">S</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">S</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">es</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Savings~(S) = Investments~(I) + Fiscal~Balance~(G-T) + Trade~Balance~(X-M)</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">S</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">S</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">es</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">F</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">sc</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">X</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">S – I = Fiscal~Balance~(G-T) + Trade~Balance~(X-M)</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">S</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">F</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">sc</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">X</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">National Income</span> = Employees’ compensation<br style="box-sizing: border-box;" />+ Corporate and government profits before taxes<br style="box-sizing: border-box;" />+ Interest income<br style="box-sizing: border-box;" />+ Unincorporated business net income (business owners’ incomes)<br style="box-sizing: border-box;" />+ Rent<br style="box-sizing: border-box;" />+ Indirect business taxes<br style="box-sizing: border-box;" />− Subsidies</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Personal Income</span> = National income<br style="box-sizing: border-box;" />+ Transfer payments (social insurance, unemployment or disability payments)<br style="box-sizing: border-box;" />− Indirect business taxes<br style="box-sizing: border-box;" />− Corporate income taxes<br style="box-sizing: border-box;" />− Undistributed corporate profits</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Personal Disposable Income</span> = Personal income – Personal taxes</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Potential GDP</span> = Aggregate hours worked × Labor productivity<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">\longrightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.522em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.011em;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">⟶</span></span></span></span></span> <span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Aggregate hours worked</span> = Labor force × Average hours worked per week<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">\longrightarrow</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.522em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.011em;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">⟶</span></span></span></span></span> <span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Growth in Potential GDP</span> = Growth in labor force + Growth in labor productivity</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">The Production Function</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Y = A \times f (K, L)</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Y</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">K</span><span class="mpunct" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">,</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.166667em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">L</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Y</span></span></span></span></span> = Aggregate output<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span></span></span></span></span> = Total Factor Productivity (TFP)<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">K</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">K</span></span></span></span></span> = Capital<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">L</span></span></span></span></span> = Labor</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Growth in Potential GDP</span> = Growth in technology + WL × (growth in labor) + WC × (growth in capital)<br style="box-sizing: border-box;" /><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">WL </span>= Labor’s percentage share of national income<br style="box-sizing: border-box;" /><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">WC </span>= Capital’s percentage share of national income</p><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><h2 class="has-text-align-center" style="border: 0px; box-sizing: border-box; clear: both; color: #0073b0; font-family: "Nunito Sans", sans-serif; font-size: 1.875rem; font-weight: 400; line-height: 1.3; margin: 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">3. Understanding Business Cycles</span></h2><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Unemployment~Rate = \frac {Number~of~unemployed~people}{Total~labor~force}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">U</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">oy</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.25188em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.88044em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.37144em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ab</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">or</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">orce</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 263.521px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">mb</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">er</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">oye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eo</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.88044em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Participation~Rate~(Activity~Ratio) = \frac {Total~labor~force}{Total~working–age~population}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.25188em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.88044em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.37144em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02691em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">w</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">or</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">kin</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 257.771px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">T</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ab</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">or</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">orce</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.88044em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Labor~Force = Unemployed~people + Employed~people</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">L</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ab</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">or</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">F</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">orce</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">U</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">oye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eo</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">E</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">oye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eo</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Unemployed</span> = Looking for job</p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Consumer~Price~Index = \frac {Cost~of~basket~at~current–year~prices}{Cost~of~basket~at~base–year~prices} \times 100</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">er</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.25188em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.88044em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.37144em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">os</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ba</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03148em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">k</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ba</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">se</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ces</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 321.948px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">os</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ba</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03148em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">k</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">rre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ces</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.88044em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">100</span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Laspeyres’ Index = \frac {\Sigma~(Current–year~price \times Base–year~quantity)}{\Sigma~(Base–year~price \times Base–year~quantity)}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">L</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eyres</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">’</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.363em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.936em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.427em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Σ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">se</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">se</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 394.323px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Σ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">rre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">se</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.936em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Fisher’s~Index = \sqrt {(Laspeyres’~Index) \times (Paashe~Price~Index)}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">F</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">h</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">er</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">’</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1.24em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.256125em;"></span><span class="mord sqrt" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.983875em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span class="svg-align" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; text-align: left; top: -3.2em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3.2em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px 0px 0px 1em; vertical-align: baseline;"><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">L</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eyres</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">’</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">aa</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">h</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.94388em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3.2em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="hide-tail" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1.28em; margin: 0px; min-width: 1.02em; outline: 0px; overflow: hidden; padding: 0px; position: relative; vertical-align: baseline; width: 397.729px;"><svg height="1.28em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1296" width="400em"><path d="M263,681c0.7,0,18,39.7,52,119
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box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Paashe~Price~Index = \frac {\Sigma~(Current–year~price \times Current–year~quantity)}{\Sigma~(Base–year~price \times Base–year~quantity)}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">aa</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">h</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.363em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.936em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.427em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Σ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">se</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05017em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">B</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">se</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 421.708px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Σ</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">rre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">rre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">–</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ye</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">an</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.936em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><h2 class="has-text-align-center" style="border: 0px; box-sizing: border-box; clear: both; color: #0073b0; font-family: "Nunito Sans", sans-serif; font-size: 1.875rem; font-weight: 400; line-height: 1.3; margin: 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">4. Monetary and Fiscal Policy</span></h2><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Money~Multiplier = \frac {1}{Reserve~requirement}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ey</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">lt</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">er</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.20188em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.88044em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.32144em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eser</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">re</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">q</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">re</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 182.458px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.88044em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Fiscal~Multiplier = \frac {1}{1- MPC \times (1- t)}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">F</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">sc</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">lt</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">pl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">er</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.25744em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.936em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.32144em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">MPC</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 158.854px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.936em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">MPC</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">MPC</span></span></span></span></span> = Marginal propensity to consume<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.61508em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span></span> = Tax rate</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Equation of Exchange</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">MV = PY~(Money~supply \times Velocity = Price \times Real~output)</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">V</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Y</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mopen" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">(</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ey</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ppl</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.22222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">V</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">oc</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">y</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 1em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.25em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">tp</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mclose" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">)</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Fisher Effect</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Nominal~Interest~Rate = Real~interest~rate + Expected~inflation~rate</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">mina</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eres</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.77777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eres</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">E</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ec</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Neutral Interest Rate</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Neutral~interest~rate = Real~trend~rate~of~economic~growth + inflation~target</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eres</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">re</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">eco</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">mi</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ro</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">wt</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">h</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">f</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span></span></span></span></span></div><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><h2 class="has-text-align-center" style="border: 0px; box-sizing: border-box; clear: both; color: #0073b0; font-family: "Nunito Sans", sans-serif; font-size: 1.875rem; font-weight: 400; line-height: 1.3; margin: 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">5. International Trade and Capital Flows</span></h2><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">GDP</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">GDP = C + I + G + X - M</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">D</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">X</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span></span></span></span></span> = Consumption<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">I</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span></span></span></span></span> = Investments<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">G</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span></span></span></span></span> = Government Spending<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">X</span></span></span></span></span> = Export<br style="box-sizing: border-box;" /><span class="katex-eq katex-rendered" data-katex-display="false" style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">M</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span></span></span></span></span> = Import</p><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Balance of Payments</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Current~Account + Capital~Account + Financial~ Account = 0</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">rre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">cco</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07153em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">C</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">cco</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.69444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">F</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">inan</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ia</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">cco</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.64444em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">0</span></span></span></span></span></div><p style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px 0px 1.75em; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; box-sizing: border-box; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Trade Balance</em></span></p><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">X - M = Private~Savings + Government~Savings - Investments~in~domestic~capital</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.76666em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.08333em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">X</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.68333em; margin: 0px; outline: 0px; padding: 0px; vertical-align: 0em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">M</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.87777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">P</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">S</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">+</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.87777em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">G</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">er</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">nm</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">S</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">−</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">v</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">es</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">s</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">in</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">d</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">m</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">es</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span></span></span></span></span></div><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><h2 class="has-text-align-center" style="border: 0px; box-sizing: border-box; clear: both; color: #0073b0; font-family: "Nunito Sans", sans-serif; font-size: 1.875rem; font-weight: 400; line-height: 1.3; margin: 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span style="border: 0px; box-sizing: border-box; font-style: inherit; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">6. Currency Exchange Rates</span></h2><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><div aria-hidden="true" class="wp-block-spacer" style="border: 0px; box-sizing: border-box; clear: both; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 100px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></div><div class="wp-block-katex-display-block katex-eq katex-rendered" data-katex-display="true" style="border: 0px; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="katex-display" style="border: 0px; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 1em 0px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;"><span class="katex" style="border: 0px; box-sizing: border-box; display: block; font-family: KaTeX_Main, "Times New Roman", serif; font-size: 1.21em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.2; margin: 0px; outline: 0px; padding: 0px; text-rendering: auto; vertical-align: baseline; white-space: nowrap;"><span class="katex-mathml" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); font-style: inherit; font-weight: inherit; height: 1px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; position: absolute; vertical-align: baseline; width: 1px;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><annotation encoding="application/x-tex">Real~Exchange~Rate = Nominal~exchange~rate \times \frac {CPI~base~currency}{CPI~price~currency}</annotation></semantics></math></span><span aria-hidden="true" class="katex-html" style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.05764em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">E</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">han</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.00773em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">R</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mrel" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">=</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.277778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 0.88888em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.19444em;"></span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.10903em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">N</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">o</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">mina</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.01968em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">l</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">x</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">han</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">g</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">t</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">e</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span><span class="mbin" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">×</span><span class="mspace" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px 0.222222em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></span><span class="base" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline; width: min-content;"><span class="strut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 2.25188em; margin: 0px; outline: 0px; padding: 0px; vertical-align: -0.88044em;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mopen nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span><span class="mfrac" style="border: 0px currentcolor; box-sizing: border-box; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist-t vlist-t2" style="border-collapse: collapse; border: 0px currentcolor; box-sizing: border-box; display: inline-table; font-style: inherit; font-weight: inherit; margin: 0px -2px 0px 0px; outline: 0px; padding: 0px; table-layout: fixed; vertical-align: baseline;"><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 1.37144em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -2.314em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">CP</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">p</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.02778em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">r</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">i</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ce</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">rre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">cy</span></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.23em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="frac-line" style="border-bottom-style: solid; border-color: currentcolor; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: initial; border-width: 0px 0px 0.04em; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; min-height: 1px; outline: 0px; padding: 0px; vertical-align: baseline; width: 167.938px;"></span></span><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; top: -3.677em; vertical-align: baseline;"><span class="pstrut" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; height: 3em; margin: 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 0px;"></span><span class="mord" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.13889em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">CP</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.07847em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">I</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ba</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">se</span><span class="mspace nobreak" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> </span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">c</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">u</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">rre</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">n</span><span class="mord mathnormal" style="border: 0px currentcolor; box-sizing: border-box; font-family: KaTeX_Math; font-style: italic; font-weight: inherit; margin: 0px 0.03588em 0px 0px; outline: 0px; padding: 0px; vertical-align: baseline;">cy</span></span></span></span><span class="vlist-s" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-size: 1px; font-style: inherit; font-weight: inherit; margin: 0px; min-width: 2px; outline: 0px; padding: 0px; vertical-align: bottom; width: 2px;"></span></span><span class="vlist-r" style="border: 0px currentcolor; box-sizing: border-box; display: table-row; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vlist" style="border: 0px currentcolor; box-sizing: border-box; display: table-cell; font-style: inherit; font-weight: inherit; height: 0.88044em; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: bottom;"><span style="border: 0px currentcolor; box-sizing: border-box; display: block; font-style: inherit; font-weight: inherit; height: 0px; margin: 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"></span></span></span></span></span><span class="mclose nulldelimiter" style="border: 0px currentcolor; box-sizing: border-box; display: inline-block; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 0.12em;"></span></span></span></span></span></span></div><hr class="wp-block-separator" style="border-color: initial; border-image: initial; border-left-width: initial; border-right-width: initial; border-style: solid none; box-sizing: border-box; color: #272727; font-family: "Nunito Sans", sans-serif; font-size: 16px; height: 1px; margin: 0px; max-width: 100px;" /><br />Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0H4WQ+F9 Betikar Tanda, Karnataka, India17.5961355 77.13847699.2052400620844672 68.3494144 25.987030937915531 85.9275394tag:blogger.com,1999:blog-830335965541290967.post-53224146806930389702022-09-18T10:09:00.002+05:302022-09-18T10:20:40.482+05:30Vendor Relationship Management<h1 style="text-align: center;"><span style="font-family: courier;"><span><a name='more'></a></span> </span></h1><h1 style="text-align: center;"><span style="font-family: courier;">Vendor Relationship Management</span></h1><div><span style="font-family: courier;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRCcsCx_Qjv1lm8pyn3mp28AVseJ6Ar1D6UyXotCmBeSt_-2hsZO3P23HPcDmJlpLLC746MgJntB5_qU1x3MkpwqL5M_-Wmh6m4PdzrnpRazoIB-TvaMKgaJEv5j5G4HW8k-Qm_020KriBrE-0Hl-2X-Z-Pa_1rEbgenDTFIdlY7rspivr7tUtqp1J/s480/png-clipart-supplier-relationship-management-business-customer-relationship-management-supply-chain-management-business-text-hand%20algaestudy.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="270" data-original-width="480" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRCcsCx_Qjv1lm8pyn3mp28AVseJ6Ar1D6UyXotCmBeSt_-2hsZO3P23HPcDmJlpLLC746MgJntB5_qU1x3MkpwqL5M_-Wmh6m4PdzrnpRazoIB-TvaMKgaJEv5j5G4HW8k-Qm_020KriBrE-0Hl-2X-Z-Pa_1rEbgenDTFIdlY7rspivr7tUtqp1J/s320/png-clipart-supplier-relationship-management-business-customer-relationship-management-supply-chain-management-business-text-hand%20algaestudy.gif" width="320" /></a></div><br /><span style="font-family: courier;"><br /></span></div><div><span style="font-family: courier;"><br /></span></div><div><ol style="text-align: left;"><li><span style="font-family: courier;">Vendor relationship management is a process that enables your company to control costs, mitigate risks, and improve services.</span></li><li><span style="font-family: courier;">Vendor relationship management (VRM) deepens buyer-supplier relationships to achieve a mutually beneficial goal and establish trust.</span></li><li><span style="font-family: courier;">An efficient vendor relationship management process can deliver a number of key benefits from quality increments and improved total cost of ownership (TCO) to new innovations and a much smoother flow of data.</span></li></ol><div><span style="font-family: courier;"><br /><br /></span></div></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVwOv8hSuuGrlDDdE8qhbqHHlAAkaA6xrBCZyBUi0KpClT7eFwuN9zYlrNRNjTI1nH2a73OxncaAxlKjjl32I_FJkY4ZYD0KU6n3NFkE9pLp_zfG9yODWEPf_morgoofKTTMeiFzIhD_MIme0K3EfkmERJufbblUbRfM4uLbgFlohesoLsaavoitRonQ/s1040/Online-Customer-Relationship-Management.jpg" style="margin-left: 1em; margin-right: 1em;"></a></div><span style="font-family: courier;"><br /></span><div><span style="font-family: courier;"><br /></span></div><h2 style="text-align: left;"><span style="font-family: courier;">What is Vendor Governance?</span></h2><div style="text-align: left;"><span style="font-family: courier; font-weight: normal;">Sometimes referred to as vendor management, vendor
governance is a management strategy that enables organizations to get more
value from their vendors by controlling costs, increasing value, and mitigating
risk</span></div></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"></div><div><ul style="text-align: left;"><li><span style="font-family: courier;">Researching potential vendors</span></li><li><span style="font-family: courier;">Obtaining pricing quotes/ bids</span></li><li><span style="font-family: courier;">Establishing capabilities</span></li><li><span style="font-family: courier;">Identifying turnaround times</span></li><li><span style="font-family: courier;">Noting the quality of work</span></li><li><span style="font-family: courier;">Contract negotiation</span></li><li><span style="font-family: courier;">Cultivating strong business relationships</span></li><li><span style="font-family: courier;">Assigning jobs and tasks</span></li><li><span style="font-family: courier;">Evaluating performance</span></li><li><span style="font-family: courier;">Ensuring prompt payment</span></li></ul><h2 style="text-align: left;"><span style="font-family: courier;"><br /></span></h2><h2 style="text-align: left;"><span style="font-family: courier;"><br /></span><span style="font-family: courier;">Top 3 successful vendor relationship strategies</span></h2><h2 style="text-align: left;"><br /><span style="clear: right; float: right; font-family: courier; margin-bottom: 1em; margin-left: 1em;"><img alt="Vendor Relationship Management" border="0" data-original-height="563" data-original-width="1040" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVwOv8hSuuGrlDDdE8qhbqHHlAAkaA6xrBCZyBUi0KpClT7eFwuN9zYlrNRNjTI1nH2a73OxncaAxlKjjl32I_FJkY4ZYD0KU6n3NFkE9pLp_zfG9yODWEPf_morgoofKTTMeiFzIhD_MIme0K3EfkmERJufbblUbRfM4uLbgFlohesoLsaavoitRonQ/w400-h216/Online-Customer-Relationship-Management.jpg" title="Algae Services" width="400" /></span></h2></div><div><span style="font-family: courier; margin-left: 1em; margin-right: 1em;"><br /></span></div><div><span style="font-family: courier;"><br /></span></div><div><div><span style="font-family: courier;">Successful vendor relationships require quite a bit of planning and hard work. Here are three vendor relationship management strategies that can be used to maximize the value of supplier relationships</span></div><div><span style="font-family: courier;"><br /></span></div><div><span style="font-family: courier;"><br /></span></div><h4 style="text-align: left;"><span style="font-family: courier;">1. Communicate often</span></h4><div><ul style="text-align: left;"><li><span style="font-family: courier;">Poor communication is at the heart of most business failures. The inability to convey or receive important information from your suppliers can end up shaking the very foundations of your vendor management process.</span></li><li><span style="font-family: courier;">Corporate buyers need to communicate with their vendors frequently in order to transmit their requirements effectively and get a better understanding of their suppliers’ capabilities</span></li></ul></div><div><span style="font-family: courier;"><br /></span></div><h4 style="text-align: left;"><span style="font-family: courier;">2. Build partnerships</span></h4><div><ul style="text-align: left;"><li><span style="font-family: courier;">The key to efficient vendor management is moving out of a transactional relationship and into a strategic supplier-buyer relationship model</span></li><li><span style="font-family: courier;">The first step of the process is treating your suppliers as valuable partners</span></li><li><span style="font-family: courier;">Rather than just disclosing the pre-defined KPIs with your suppliers, involve them in key strategic vendor management decisions like setting clear objectives for the relationship</span></li><li><span style="font-family: courier;">This will not only allow you to tap into their expertise but also offer other benefits like increased trust, preferential treatment, and more</span></li></ul></div></div><div><span style="font-family: courier;"><br /></span></div><div><h4 style="text-align: left;"><span style="font-family: courier;">3. Create a win-win situation</span></h4><div><ul style="text-align: left;"><li><span style="font-family: courier;">Running after short-term cost savings will cost your organization more in the long run and make a substantial impact on the quality</span></li><li><span style="font-family: courier;">So, rather than squeezing your suppliers to cut down the cost, take some time to study and understand your vendor’s business</span></li><li><span style="font-family: courier;">Negotiation should be based on good faith and value rather than resorting to strong-arm tactics</span></li><li><span style="font-family: courier;">Objectives of the partnership should be structured in a way that offers equal opportunity for profitability and strengthens both businesses</span></li></ul><div><span style="font-family: courier;"><br /></span></div></div></div><div><h3 style="text-align: left;"><span style="font-family: courier;">Best practices in vendor relationship management</span></h3><div><span style="font-family: courier;">Procurement teams need to look for best practices and try implementing them to lower the total cost of ownership and improve the efficiency of their supplier management process.</span></div><div><span style="font-family: courier;"><br /></span></div><div><span style="font-family: courier;">Here are three vendor relationship management or vendor performance management best practices</span></div></div><div><span style="font-family: courier;"><br /></span></div><div><h4 style="text-align: left;"><b><span style="font-family: courier;">1. Measure performance</span></b></h4><div><span style="font-family: courier;">Organizations with the best vendor relationship process have an elaborate system to measure the performance of their vendors. Scorecards, vendor ratings, and vendor performance reviews are used to hold vendors accountable for their performance.</span></div><div><span style="font-family: courier;"><br /></span></div><h4 style="text-align: left;"><b><span style="font-family: courier;">2. Share risks</span></b></h4><div><span style="font-family: courier;">Uncertainty in the supply chain paves the way for a number of risks like price volatility, demand fluctuations, and more. Carefully designed vendor contracts reduce the amount of uncertainty, by enabling risk-sharing.</span></div><div><span style="font-family: courier;"><br /></span></div><h4 style="text-align: left;"><b><span style="font-family: courier;">3. Build trust</span></b></h4><div><span style="font-family: courier;">A truly effective vendor relationship management process is built on a foundation of trust. Buyers who ensure that their vendors are financially and emotionally invested in the relationship have a good chance of winning the trust of their vendors in a relatively short period of time</span></div></div><div><span style="font-family: courier;"><br /></span></div><div style="text-align: right;"><br /></div></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com01A Carlisle Pl, London SW1P 1NP, UK51.495721 -0.141035851.485032188709837 -0.15820193769531249 51.506409811290169 -0.12386966230468749tag:blogger.com,1999:blog-830335965541290967.post-66344813559945480602022-09-04T12:26:00.005+05:302024-01-27T09:03:59.819+05:30How to do Partitioning in Hive - Demo code<p> <span></span></p><a name='more'></a><p></p><p><br /></p><h1 style="background-color: white; color: #444444; font-family: "Source Sans Pro", "Helvetica Neue", Helvetica, Helvetica, Arial, sans-serif; font-weight: 500; margin: 0px; padding: 0px; text-align: center;"><span style="font-size: x-large; margin: 0px; padding: 0px;"> Implement Partitioning in Hive</span></h1><div><span style="font-size: x-large; margin: 0px; padding: 0px;"><br /></span></div><div><span style="font-size: x-large; margin: 0px; padding: 0px;"><br /></span></div><div><span style="font-size: x-large; margin: 0px; padding: 0px;"><br /></span></div><div><span style="margin: 0px; padding: 0px;"><span style="font-size: medium;">The partitioning in Hive means dividing the table into some parts based on the values of a particular column like date, course, city, or country.</span></span></div><div><span style="margin: 0px; padding: 0px;"><span style="font-size: medium;"><br /></span></span></div><div><span style="font-size: medium;"><span style="margin: 0px; padding: 0px;">Let's assume we have data of 10 million students studying in an institute. Now, we have to fetch the students of a particular course. If we use a traditional approach, we have to read the entire data leads to performance degradation. The better approach will be to partition the table in Hive and divide the data among the different datasets based on particular columns. </span>The advantage of partitioning is that since the data is stored in slices, the query response time becomes faster.</span></div><div><span style="margin: 0px; padding: 0px;"><p></p><div style="font-size: x-large;"><br /></div><h2 style="font-size: x-large; text-align: left;">Types of Partitioning</h2><div style="font-size: x-large;"><br /></div><div><span style="font-size: medium;">There are 2 Types of Partitioning in Hive</span></div><div style="font-size: x-large;"><br /></div><div><h3 style="text-align: left;"><span style="font-size: medium;">Static Partitioning</span></h3><div><ul style="text-align: left;"><li><span style="font-size: medium;">It is required to pass the values of partitioned columns manually while loading the data into the table.</span></li><li><span style="font-size: medium;">Insert input data files individually into each partition table is Static Partition</span></li></ul></div><div style="font-size: x-large;"><br /></div><h3 style="text-align: left;"><span style="font-size: medium;">Dynamic Partitioning</span></h3><div><ul style="text-align: left;"><li><span style="font-size: medium;">Single insert to partition table (all partitions in one go) is known as a dynamic partition.</span></li><li><span style="font-size: medium;">Usually, dynamic partition loads the data from the non-partitioned table.</span></li></ul></div></div><div style="font-size: x-large;"><br /></div><div style="font-size: x-large;"><br /></div><div style="font-size: x-large;"><br /></div><div><h2 style="text-align: center;"><span style="font-size: x-large;">Partitioning Demo -Static</span></h2><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;"><br /></span></div><h4 style="text-align: left;"><span style="font-size: large;">Step 1. Create 2 files </span></h4><div><ul style="text-align: left;"><li><span style="font-size: large;">Stud_M (for male students)</span></li><li><span style="font-size: large;">Stud_F (For female students)</span></li></ul></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgmjhjhrr7abAWtdvuJF9yhgsWd0oF0Fr0J8iVWU-8q6doO7lOoCCjuCbNxaa3JGdT2Q76PEHF7mKePLSYOjxiTzF_qb18RRFLWZicGkMvh9FmJ9fGjxqNv3LEKsOmAk3zxgyrDp9XiHHUkx8-WqkE0syFmDHgdjdUHZhyDqdvDt-rF67GJ74qEYM8f" style="margin-left: 1em; margin-right: 1em;"><img alt="bucketing algae study in hive" data-original-height="490" data-original-width="588" height="333" src="https://blogger.googleusercontent.com/img/a/AVvXsEgmjhjhrr7abAWtdvuJF9yhgsWd0oF0Fr0J8iVWU-8q6doO7lOoCCjuCbNxaa3JGdT2Q76PEHF7mKePLSYOjxiTzF_qb18RRFLWZicGkMvh9FmJ9fGjxqNv3LEKsOmAk3zxgyrDp9XiHHUkx8-WqkE0syFmDHgdjdUHZhyDqdvDt-rF67GJ74qEYM8f=w400-h333" title="hadoop partitioning algae study" width="400" /></a></div><br /><br /></span></div><div><span style="font-size: large;"><br /></span></div><h4 style="text-align: left;"><span style="font-size: large;">Step 2. Copy both files in hdfs</span></h4><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh8EInT1t7J-y2n69kSnfFZBzG2Ujh69LXXxJfn2_DtFYWav8eeF0nA7_vdVjUSfNFZb_BbeJTV2BP6n83aZtuDmzXwS6l9gXA23hZMeWhubFch_pkxocIAhcYgG2xiMmojp5FzhpOKT5ydkDTAksXHHZ0Bo77ri0D1TJkLIuQ4ED4Nv8dNgTf1FpHc" style="margin-left: 1em; margin-right: 1em;"><img alt="algae study cloudera hadoop" data-original-height="100" data-original-width="1037" height="62" src="https://blogger.googleusercontent.com/img/a/AVvXsEh8EInT1t7J-y2n69kSnfFZBzG2Ujh69LXXxJfn2_DtFYWav8eeF0nA7_vdVjUSfNFZb_BbeJTV2BP6n83aZtuDmzXwS6l9gXA23hZMeWhubFch_pkxocIAhcYgG2xiMmojp5FzhpOKT5ydkDTAksXHHZ0Bo77ri0D1TJkLIuQ4ED4Nv8dNgTf1FpHc=w640-h62" title="haortonworks sandbox algae services" width="640" /></a></div><br /></span></div><h4 style="text-align: left;"><span style="font-size: large;">Step 3. Create hive table with partition on gender</span></h4><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgr3BA9ZQCtNWELAQ3OK0_QXcDQHnm-kJNSpWzYWq9w7Y5wA7TDKq9sVnnGd-VGOxgzGw3XoYTmJQVGNHKdz3A_IJTLmarkJ2kbPAcDv8qQyTvn6mybLQd4RN_77AsSi_Wl48ZCPcTAFND5L4L0zrSolWWNgLxNjxft292bm_XLLTzHvSCSAflYWZhr" style="margin-left: 1em; margin-right: 1em;"><img alt="hdfs dfs commands algaeservices in hadoop hive big data" data-original-height="66" data-original-width="583" height="72" src="https://blogger.googleusercontent.com/img/a/AVvXsEgr3BA9ZQCtNWELAQ3OK0_QXcDQHnm-kJNSpWzYWq9w7Y5wA7TDKq9sVnnGd-VGOxgzGw3XoYTmJQVGNHKdz3A_IJTLmarkJ2kbPAcDv8qQyTvn6mybLQd4RN_77AsSi_Wl48ZCPcTAFND5L4L0zrSolWWNgLxNjxft292bm_XLLTzHvSCSAflYWZhr=w640-h72" title="hdfs dfs commands in algae hadoop hive big data" width="640" /></a></div><br /></span></div><h4 style="text-align: left;"><span style="font-size: large;">Step 4. Load stud_m with partition gender =m</span></h4><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh-O7CXh4FgHnCuqx2O95FkMF1qK1TfWyI4PNXnJZ_Kj9HP6wjmsUu325d1nw6SwBXwZ9AP2iIGrDziUg2eQHXs9IRMtrliBmYvM4y4-AYrVr-dyqOLVtplXYuuiqgMCofGnIQKE19MdHum-NNFLnhStr2AkxlESSux39V_jkS2wj8_W2ff-k-W0-IP" style="margin-left: 1em; margin-right: 1em;"><img alt="hdfs dfs commands in hadoop hive big data algaestudy" data-original-height="112" data-original-width="583" height="122" src="https://blogger.googleusercontent.com/img/a/AVvXsEh-O7CXh4FgHnCuqx2O95FkMF1qK1TfWyI4PNXnJZ_Kj9HP6wjmsUu325d1nw6SwBXwZ9AP2iIGrDziUg2eQHXs9IRMtrliBmYvM4y4-AYrVr-dyqOLVtplXYuuiqgMCofGnIQKE19MdHum-NNFLnhStr2AkxlESSux39V_jkS2wj8_W2ff-k-W0-IP=w640-h122" title="algae services hive big data" width="640" /></a></div><br /></span></div><h4 style="text-align: left;"><span style="font-size: large;">Step 5. Load stud_f with partiton gender = f</span></h4></div><div style="font-size: x-large;"><br /></div><div style="font-size: x-large;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjmkYAhRghdEltizsL5OGPJpi6S9QcR3Z2qmqq49V3mZVoX7sdWqdXJCmpNjYE4F6QaovlRVcsFTY_YM7sb0sBF0ZVkXGtuUFyNAl-aGaEbWvKoHF45wLoPMqgwmbw5OvtBsRDW5naY8Tq4RQg98SRPLC78AZImrA1xtnF9IcvKvGPcfetVEPIEHoRj" style="margin-left: 1em; margin-right: 1em;"><img alt="algaeservices.co.in hadoop big data" data-original-height="234" data-original-width="1229" height="122" src="https://blogger.googleusercontent.com/img/a/AVvXsEjmkYAhRghdEltizsL5OGPJpi6S9QcR3Z2qmqq49V3mZVoX7sdWqdXJCmpNjYE4F6QaovlRVcsFTY_YM7sb0sBF0ZVkXGtuUFyNAl-aGaEbWvKoHF45wLoPMqgwmbw5OvtBsRDW5naY8Tq4RQg98SRPLC78AZImrA1xtnF9IcvKvGPcfetVEPIEHoRj=w640-h122" title="hdfs dfs commands in hadoop hive big data" width="640" /></a></div><br /></div><h4 style="font-size: x-large; text-align: left;">Step 6. Validate the physical location of the file</h4><div style="font-size: x-large;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg09x76oYzeeBewqgC5Bh4ffvFg10Mj6i7s-jOU3q-juh740i6FCMV50HEfEsA_a5J9jlWNARqsP7JkitFkI5dgkrwbWoenTOeSEDDJ-bDXnuopsDwa6_VzqBNi2Bt34IzgugP7kKAp_bCUh9XjUNjfvatWFuoRFflrykKjxtxL4aBld15PH6hGnJW9" style="margin-left: 1em; margin-right: 1em;"><img alt="hdfs dfs commands in hadoop hive big data" data-original-height="201" data-original-width="1230" height="104" src="https://blogger.googleusercontent.com/img/a/AVvXsEg09x76oYzeeBewqgC5Bh4ffvFg10Mj6i7s-jOU3q-juh740i6FCMV50HEfEsA_a5J9jlWNARqsP7JkitFkI5dgkrwbWoenTOeSEDDJ-bDXnuopsDwa6_VzqBNi2Bt34IzgugP7kKAp_bCUh9XjUNjfvatWFuoRFflrykKjxtxL4aBld15PH6hGnJW9=w640-h104" title="algaestudy.com" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h4 style="clear: both; text-align: left;">Step 7. Validate the data</h4><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiOS0wrTC884x6CO7lfgfhSzTb4MiggpeDfhxyeCOQldXxtluEcKOKjbRLjfG5M7H0jgrdlifpYPxIONR8G5GLo6GVc2OiaBdSvZlBzsVGIqy_LfQPhSa2A-_qwoR2IC0JFcRQiok3yBDrOYurqilkOXvEtYcHRsLHzw8QlC1NvMi8cGOvDIUjImEVF" style="margin-left: 1em; margin-right: 1em;"><img alt="algaestudy.com" data-original-height="371" data-original-width="661" height="225" src="https://blogger.googleusercontent.com/img/a/AVvXsEiOS0wrTC884x6CO7lfgfhSzTb4MiggpeDfhxyeCOQldXxtluEcKOKjbRLjfG5M7H0jgrdlifpYPxIONR8G5GLo6GVc2OiaBdSvZlBzsVGIqy_LfQPhSa2A-_qwoR2IC0JFcRQiok3yBDrOYurqilkOXvEtYcHRsLHzw8QlC1NvMi8cGOvDIUjImEVF=w400-h225" title="Hive query big data Hadoop" width="400" /></a></div><br /><br /></div><br /></div></span></div>Saurabh Sinhahttp://www.blogger.com/profile/11120038651556545818noreply@blogger.com0Alameda Julio Muller-res Noise Cur, 900 - Pte. Nova, Várzea Grande - MT, 78115-200, Brazil-15.6232807 -56.098251299999987-15.755534532717741 -56.235580401562487 -15.49102686728226 -55.960922198437487