{"id":7533,"date":"2017-12-21T20:02:01","date_gmt":"2017-12-21T20:02:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-macroeconomics\/?post_type=chapter&#038;p=7533"},"modified":"2018-05-11T02:16:52","modified_gmt":"2018-05-11T02:16:52","slug":"the-multiplier","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/chapter\/the-multiplier\/","title":{"raw":"The Spending Multiplier in the Income-Expenditure Model","rendered":"The Spending Multiplier in the Income-Expenditure Model"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Explain and demonstrate the multiplier graphically using the income-expenditure model<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn our initial discussion of Keynesian economics in the module on Keynesian and neoclassical economics, you learned about the spending (or expenditure) multiplier.\u00a0Remember that a change in\u00a0any category of expenditure (C + I + G + X-M) can have a more than proportional impact on GDP. The idea behind the multiplier is that the change in GDP is more than the change in expenditure. In its simplest form, the calculation for this is\r\n<p style=\"text-align: center;\">[latex]\\displaystyle\\text{Spending Multiplier}=\\frac{1}{(\\text{MPS} )}[\/latex]<\/p>\r\n\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/7577\r\n\r\n<\/div>\r\n<h2>Showing the Spending Multiplier Graphically Using the Income-Expenditure Model<\/h2>\r\nWe can show the expenditure multiplier graphically using the income-expenditure model.\u00a0The original level of aggregate expenditure is shown by the AE<sub>0<\/sub>\u00a0line and yields an equilibrium level of GDP at Y<sub>0<\/sub>. Consider an increase in AE to AE<sub>1<\/sub>, which is shown by a parallel shift in the AE line. The vertical distance between the two AE lines is the increase in aggregate expenditure. The new equilibrium level of GDP occurs at Y<sub>1<\/sub>. It should be clear that the increase in GDP from Y<sub>0<\/sub>\u00a0to Y<sub>1<\/sub>\u00a0is greater than the increase in expenditure from AE<sub>0<\/sub>\u00a0to AE<sub>1<\/sub>.\r\n\r\nThe spending multiplier is defined as the ratio of the change in GDP (<strong>\u0394<\/strong>Y) to the change in autonomous expenditure (<strong>\u0394<\/strong>AE). Since the change in GDP is greater change in AE, the multiplier is greater than one. Suppose the equilibrium level of GDP\u00a0is $700 billion.\u00a0If government\u00a0spending increases by $50 billion,\u00a0GDP\u00a0 rises from is $700 billion (at Y<sub>0<\/sub>) to Y<sub>1<\/sub> $800 billion (at Y<sub>1<\/sub>). Thus, the change in GDP is $800 - $700 = $100 billion. In this example, the multiplier would be $100\/$50 = 2.\r\n\r\n[caption id=\"attachment_10856\" align=\"aligncenter\" width=\"630\"]<img class=\"wp-image-10856 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2043\/2017\/12\/09133704\/Screen-Shot-2018-04-27-at-5.20.49-AM-1.png\" alt=\"The graph shows the multiplier effect in the expenditure-output model: an increase in expenditure has a larger increase on the equilibrium output.\" width=\"630\" height=\"535\" \/> <strong>Figure 1. The Multiplier Effect\u00a0in the Expenditure-Output Model.<\/strong> The power of the multiplier effect is that an increase in expenditure has a larger increase on the equilibrium output. The increase in expenditure is the vertical increase from AE0 to AE1. However, the increase in equilibrium output, shown on the horizontal axis, is clearly larger.\u00a0Thus, the spending multiplier, \u0394Y\/\u0394AE, is greater than one.[\/caption]\r\n\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/7578\r\n\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/7540\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Explain and demonstrate the multiplier graphically using the income-expenditure model<\/li>\n<\/ul>\n<\/div>\n<p>In our initial discussion of Keynesian economics in the module on Keynesian and neoclassical economics, you learned about the spending (or expenditure) multiplier.\u00a0Remember that a change in\u00a0any category of expenditure (C + I + G + X-M) can have a more than proportional impact on GDP. The idea behind the multiplier is that the change in GDP is more than the change in expenditure. In its simplest form, the calculation for this is<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle\\text{Spending Multiplier}=\\frac{1}{(\\text{MPS} )}[\/latex]<\/p>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>\t<iframe id=\"lumen_assessment_7577\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=7577&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_7577\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n<h2>Showing the Spending Multiplier Graphically Using the Income-Expenditure Model<\/h2>\n<p>We can show the expenditure multiplier graphically using the income-expenditure model.\u00a0The original level of aggregate expenditure is shown by the AE<sub>0<\/sub>\u00a0line and yields an equilibrium level of GDP at Y<sub>0<\/sub>. Consider an increase in AE to AE<sub>1<\/sub>, which is shown by a parallel shift in the AE line. The vertical distance between the two AE lines is the increase in aggregate expenditure. The new equilibrium level of GDP occurs at Y<sub>1<\/sub>. It should be clear that the increase in GDP from Y<sub>0<\/sub>\u00a0to Y<sub>1<\/sub>\u00a0is greater than the increase in expenditure from AE<sub>0<\/sub>\u00a0to AE<sub>1<\/sub>.<\/p>\n<p>The spending multiplier is defined as the ratio of the change in GDP (<strong>\u0394<\/strong>Y) to the change in autonomous expenditure (<strong>\u0394<\/strong>AE). Since the change in GDP is greater change in AE, the multiplier is greater than one. Suppose the equilibrium level of GDP\u00a0is $700 billion.\u00a0If government\u00a0spending increases by $50 billion,\u00a0GDP\u00a0 rises from is $700 billion (at Y<sub>0<\/sub>) to Y<sub>1<\/sub> $800 billion (at Y<sub>1<\/sub>). Thus, the change in GDP is $800 &#8211; $700 = $100 billion. In this example, the multiplier would be $100\/$50 = 2.<\/p>\n<div id=\"attachment_10856\" style=\"width: 640px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-10856\" class=\"wp-image-10856 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2043\/2017\/12\/09133704\/Screen-Shot-2018-04-27-at-5.20.49-AM-1.png\" alt=\"The graph shows the multiplier effect in the expenditure-output model: an increase in expenditure has a larger increase on the equilibrium output.\" width=\"630\" height=\"535\" \/><\/p>\n<p id=\"caption-attachment-10856\" class=\"wp-caption-text\"><strong>Figure 1. The Multiplier Effect\u00a0in the Expenditure-Output Model.<\/strong> The power of the multiplier effect is that an increase in expenditure has a larger increase on the equilibrium output. The increase in expenditure is the vertical increase from AE0 to AE1. However, the increase in equilibrium output, shown on the horizontal axis, is clearly larger.\u00a0Thus, the spending multiplier, \u0394Y\/\u0394AE, is greater than one.<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>\t<iframe id=\"lumen_assessment_7578\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=7578&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_7578\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<p>\t<iframe id=\"lumen_assessment_7540\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=7540&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_7540\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-7533\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>The Expenditure-Output Model. <strong>Authored by<\/strong>: OpenStax College. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/cnx.org\/contents\/vEmOH-_p@4.41:2cZ9K6tp@3\/The-Expenditure-Output-Model\">https:\/\/cnx.org\/contents\/vEmOH-_p@4.41:2cZ9K6tp@3\/The-Expenditure-Output-Model<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/bc498e1f-efe9-43a0-8dea-d3569ad09a82@4.4<\/li><li><strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":29,"menu_order":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"The Expenditure-Output Model\",\"author\":\"OpenStax College\",\"organization\":\"\",\"url\":\"https:\/\/cnx.org\/contents\/vEmOH-_p@4.41:2cZ9K6tp@3\/The-Expenditure-Output-Model\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/bc498e1f-efe9-43a0-8dea-d3569ad09a82@4.4\"},{\"type\":\"cc\",\"description\":\"\",\"author\":\"\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"531c5639-2b74-49ce-9f08-9c2a5fb7bfa1, eaddbe2d-7620-4bae-85f8-4cdb4e6a81a5","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-7533","chapter","type-chapter","status-publish","hentry"],"part":10308,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/pressbooks\/v2\/chapters\/7533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/wp\/v2\/users\/29"}],"version-history":[{"count":40,"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/pressbooks\/v2\/chapters\/7533\/revisions"}],"predecessor-version":[{"id":10974,"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/pressbooks\/v2\/chapters\/7533\/revisions\/10974"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/pressbooks\/v2\/parts\/10308"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/pressbooks\/v2\/chapters\/7533\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/wp\/v2\/media?parent=7533"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/pressbooks\/v2\/chapter-type?post=7533"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/wp\/v2\/contributor?post=7533"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/oldwestbury-wm-macroeconomics\/wp-json\/wp\/v2\/license?post=7533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}