{"id":220748,"date":"2025-05-28T18:04:22","date_gmt":"2025-05-28T18:04:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220748"},"modified":"2025-05-28T18:04:24","modified_gmt":"2025-05-28T18:04:24","slug":"calculate-price-elasticity-of-demand-and-supply-for-the-following-functions-when-a-p8-and-b-q6","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/28\/calculate-price-elasticity-of-demand-and-supply-for-the-following-functions-when-a-p8-and-b-q6\/","title":{"rendered":"Calculate price elasticity of demand and supply for the following functions when (a) P=8 and (b) Q=6"},"content":{"rendered":"\n

Calculate price elasticity of demand and supply for the following functions when (a) P=8 and (b) Q=6.<\/p>\n\n\n\n

i. P= 40 \u2013 0.5Q<\/p>\n\n\n\n

ii. Q= -40 + 0.75P<\/p>\n\n\n\n

iii. Q \u2013 P + 2 = 0<\/p>\n\n\n\n

iv. 2P + 0.2Q = 40<\/p>\n\n\n\n

v. P = 20 \u2013 2Q<\/p>\n\n\n\n

vi. 4P + 4Q = 64<\/p>\n\n\n\n

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

To calculate price elasticity of demand (Ed)<\/strong> and price elasticity of supply (Es)<\/strong> at specific points, we use: Price Elasticity of Demand (Ed)=(dQdP)\u22c5(PQ)andPrice Elasticity of Supply (Es)=(dQdP)\u22c5(PQ)\\text{Price Elasticity of Demand (Ed)} = \\left(\\frac{dQ}{dP}\\right) \\cdot \\left(\\frac{P}{Q}\\right) \\quad \\text{and} \\quad \\text{Price Elasticity of Supply (Es)} = \\left(\\frac{dQ}{dP}\\right) \\cdot \\left(\\frac{P}{Q}\\right)<\/p>\n\n\n\n

\n\n\n\n

i. P=40\u22120.5QP = 40 – 0.5Q<\/h3>\n\n\n\n

Rewriting: Q=80\u22122PQ = 80 – 2P, so dQdP=\u22122\\frac{dQ}{dP} = -2<\/p>\n\n\n\n

    \n
  • At P = 8<\/strong>:
    Q=80\u22122(8)=64Q = 80 – 2(8) = 64
    Ed=\u22122\u22c5864=\u22120.25Ed = -2 \\cdot \\frac{8}{64} = -0.25<\/li>\n\n\n\n
  • At Q = 6<\/strong>:
    P=40\u22120.5(6)=37P = 40 – 0.5(6) = 37
    Ed=\u22122\u22c5376=\u221212.33Ed = -2 \\cdot \\frac{37}{6} = -12.33<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    ii. Q=\u221240+0.75PQ = -40 + 0.75P, dQdP=0.75\\frac{dQ}{dP} = 0.75<\/h3>\n\n\n\n
      \n
    • At P = 8<\/strong>:
      Q=\u221240+0.75(8)=\u221234Q = -40 + 0.75(8) = -34
      Es=0.75\u22c58\u221234=\u22120.176Es = 0.75 \\cdot \\frac{8}{-34} = -0.176<\/li>\n\n\n\n
    • At Q = 6<\/strong>:
      6=\u221240+0.75P\u21d2P=61.336 = -40 + 0.75P \\Rightarrow P = 61.33
      Es=0.75\u22c561.336=7.67Es = 0.75 \\cdot \\frac{61.33}{6} = 7.67<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      iii. Q\u2212P+2=0\u21d2Q=P\u22122Q – P + 2 = 0 \\Rightarrow Q = P – 2, dQdP=1\\frac{dQ}{dP} = 1<\/h3>\n\n\n\n
        \n
      • At P = 8<\/strong>: Q=6Q = 6, so Ed=1\u22c586=1.33Ed = 1 \\cdot \\frac{8}{6} = 1.33<\/li>\n\n\n\n
      • At Q = 6<\/strong>: P=8P = 8, so Ed=1.33Ed = 1.33<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        iv. 2P+0.2Q=40\u21d2Q=200\u221210P2P + 0.2Q = 40 \\Rightarrow Q = 200 – 10P, dQdP=\u221210\\frac{dQ}{dP} = -10<\/h3>\n\n\n\n
          \n
        • At P = 8<\/strong>: Q=200\u221210(8)=120Q = 200 – 10(8) = 120
          Ed=\u221210\u22c58120=\u22120.667Ed = -10 \\cdot \\frac{8}{120} = -0.667<\/li>\n\n\n\n
        • At Q = 6<\/strong>: P=19.4P = 19.4
          Ed=\u221210\u22c519.46=\u221232.33Ed = -10 \\cdot \\frac{19.4}{6} = -32.33<\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          v. P=20\u22122Q\u21d2Q=10\u22120.5PP = 20 – 2Q \\Rightarrow Q = 10 – 0.5P, dQdP=\u22120.5\\frac{dQ}{dP} = -0.5<\/h3>\n\n\n\n
            \n
          • At P = 8<\/strong>: Q=10\u22120.5(8)=6Q = 10 – 0.5(8) = 6
            Ed=\u22120.5\u22c586=\u22120.667Ed = -0.5 \\cdot \\frac{8}{6} = -0.667<\/li>\n\n\n\n
          • At Q = 6<\/strong>: Same result, so Ed=\u22120.667Ed = -0.667<\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            vi. 4P+4Q=64\u21d2Q=16\u2212P4P + 4Q = 64 \\Rightarrow Q = 16 – P, dQdP=\u22121\\frac{dQ}{dP} = -1<\/h3>\n\n\n\n
              \n
            • At P = 8<\/strong>: Q=8Q = 8
              Ed=\u22121\u22c588=\u22121Ed = -1 \\cdot \\frac{8}{8} = -1<\/li>\n\n\n\n
            • At Q = 6<\/strong>: P=10P = 10, so Ed=\u22121\u22c5106=\u22121.67Ed = -1 \\cdot \\frac{10}{6} = -1.67<\/li>\n<\/ul>\n\n\n\n
              \n\n\n\n

              Explanation<\/strong><\/h2>\n\n\n\n

              Price elasticity of demand (Ed) and supply (Es) measure how responsive quantity demanded or supplied is to changes in price. The general formula is: E=(dQdP)\u22c5(PQ)E = \\left( \\frac{dQ}{dP} \\right) \\cdot \\left( \\frac{P}{Q} \\right)<\/p>\n\n\n\n

              This combines the slope of the demand\/supply function and the price-to-quantity ratio at a specific point.<\/p>\n\n\n\n

              In linear demand curves (e.g., P=a\u2212bQP = a – bQ), demand elasticity becomes more inelastic as we move down the curve. For example, in function (i), at a high quantity (Q = 64), Ed is only \u20130.25 (inelastic), but at low quantity (Q = 6), Ed becomes highly elastic (\u201312.33).<\/p>\n\n\n\n

              Supply functions, such as in (ii), may produce unrealistic outputs (like negative quantity at low prices), highlighting the importance of evaluating economic meaning. A negative quantity supplied is not feasible, suggesting a need to limit the domain or re-specify the model.<\/p>\n\n\n\n

              Functions (iii) and (vi) are linear and symmetric: as price rises, quantity rises or falls by a constant rate. Elasticity values are relatively consistent and depend more directly on the price and quantity values used.<\/p>\n\n\n\n

              Some functions like (iv) and (v) demonstrate that elasticity can change significantly with quantity or price, even for linear relationships. In particular, (iv) shows a steep change in elasticity from \u20130.67 to \u201332.33 as quantity falls from 120 to 6, reflecting how steep curves have more volatile elasticities.<\/p>\n\n\n\n

              Understanding elasticity is crucial in real-world economics: inelastic demand means price changes won\u2019t affect quantity much (e.g., for necessities), while elastic demand means consumers are sensitive to price changes (e.g., for luxury goods).<\/p>\n\n\n\n

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

              Calculate price elasticity of demand and supply for the following functions when (a) P=8 and (b) Q=6. i. P= 40 \u2013 0.5Q ii. Q= -40 + 0.75P iii. Q \u2013 P + 2 = 0 iv. 2P + 0.2Q = 40 v. P = 20 \u2013 2Q vi. 4P + 4Q = 64 The Correct […]<\/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-220748","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220748","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=220748"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220748\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}