{"id":228995,"date":"2025-06-07T19:23:43","date_gmt":"2025-06-07T19:23:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228995"},"modified":"2025-06-07T19:23:45","modified_gmt":"2025-06-07T19:23:45","slug":"three-students-have-different-demands-for-doughnuts","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/three-students-have-different-demands-for-doughnuts\/","title":{"rendered":"Three students have different demands for doughnuts."},"content":{"rendered":"\n

Three students have different demands for doughnuts. Andres’ demand is given by Q = 5P; Carlene’s demand is given by Q = 6 – 2P; Cooper’s demand is given by Q = 4 – 0.5P. a. The market demand curve for doughnuts is OQ = 15 – 3.5P b. Using the students’ demand functions and the market demand function, graph the demand curve for doughnuts. Pay special attention to any kinks in the market demand! Price 9 10 11 12 13 14 15 Doughnuts<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong><\/h3>\n\n\n\n

a. \u2705 Q = 15 \u2013 3.5P<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/h3>\n\n\n\n

To derive the market demand curve<\/strong>, we sum the individual demand curves of each student horizontally<\/strong>\u2014that is, we add up the quantities demanded by Andr\u00e9, Carlene, and Cooper at each price level.<\/p>\n\n\n\n

Step 1: Individual Demand Functions<\/strong><\/h4>\n\n\n\n
    \n
  • Andr\u00e9:<\/strong>
    QA=5\u2212PQ_A = 5 – PQA\u200b=5\u2212P
    Valid for 0\u2264P\u226450 \\leq P \\leq 50\u2264P\u22645
    He demands 0 when price hits 5 or more.<\/li>\n\n\n\n
  • Carlene:<\/strong>
    QC=6\u22122PQ_C = 6 – 2PQC\u200b=6\u22122P
    Valid for 0\u2264P\u226430 \\leq P \\leq 30\u2264P\u22643
    She demands 0 when price hits 3 or more.<\/li>\n\n\n\n
  • Cooper:<\/strong>
    QCo=4\u22120.5PQ_{Co} = 4 – 0.5PQCo\u200b=4\u22120.5P
    Valid for 0\u2264P\u226480 \\leq P \\leq 80\u2264P\u22648
    He demands 0 when price hits 8 or more.<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Step 2: Market Demand at Different Prices<\/strong><\/h4>\n\n\n\n

    Add the individual demands to get the total market demand QMQ_MQM\u200b. For prices from 0 up to 3, all three demanders are active:<\/p>\n\n\n\n

      \n
    • When P\u22643P \\leq 3P\u22643<\/strong>: QM=(5\u2212P)+(6\u22122P)+(4\u22120.5P)=15\u22123.5PQ_M = (5 – P) + (6 – 2P) + (4 – 0.5P) = 15 – 3.5PQM\u200b=(5\u2212P)+(6\u22122P)+(4\u22120.5P)=15\u22123.5P<\/li>\n\n\n\n
    • This is the correct market demand equation<\/strong> when all three are demanding<\/strong>.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Step 3: Kinks in the Demand Curve<\/strong><\/h4>\n\n\n\n

      Each consumer exits the market (i.e., demands 0) at their maximum price:<\/p>\n\n\n\n

        \n
      • Carlene stops buying at P=3P = 3P=3<\/strong><\/li>\n\n\n\n
      • Andr\u00e9 stops at P=5P = 5P=5<\/strong><\/li>\n\n\n\n
      • Cooper stops at P=8P = 8P=8<\/strong><\/li>\n<\/ul>\n\n\n\n

        These points create kinks<\/strong> in the market demand curve as the slope changes when each consumer drops out.<\/p>\n\n\n\n

        \n\n\n\n

        Step 4: Interpreting the Graph<\/strong><\/h4>\n\n\n\n

        The graph in the image appears incorrect<\/strong>, showing a vertical line<\/strong> at 15 doughnuts across multiple prices, which doesn\u2019t represent the derived demand function Q=15\u22123.5PQ = 15 – 3.5PQ=15\u22123.5P. A correct graph should show a downward-sloping, piecewise-linear curve<\/strong> with kinks<\/strong> at prices 3, 5, and 8 due to changing numbers of active consumers.<\/p>\n\n\n\n

        \n\n\n\n

        Conclusion:<\/strong><\/h3>\n\n\n\n

        The correct market demand curve is: Q=15\u22123.5P(for P\u22643)Q = 15 – 3.5P \\quad \\text{(for } P \\leq 3)Q=15\u22123.5P(for P\u22643)<\/p>\n\n\n\n

        And the overall market demand is piecewise<\/strong>, with changing slopes<\/strong> after each individual exits the market.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n","protected":false},"excerpt":{"rendered":"

        Three students have different demands for doughnuts. Andres’ demand is given by Q = 5P; Carlene’s demand is given by Q = 6 – 2P; Cooper’s demand is given by Q = 4 – 0.5P. a. The market demand curve for doughnuts is OQ = 15 – 3.5P b. Using the students’ demand functions and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-228995","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228995","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=228995"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228995\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228995"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228995"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228995"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}