{"id":18619,"date":"2025-06-13T07:54:34","date_gmt":"2025-06-13T07:54:34","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18619"},"modified":"2025-06-13T07:54:37","modified_gmt":"2025-06-13T07:54:37","slug":"a-demand-curve-with-constant-slope-over-all-quantity-values-can-have-a-continuously-changing-price-elasticity-of-demand","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-demand-curve-with-constant-slope-over-all-quantity-values-can-have-a-continuously-changing-price-elasticity-of-demand\/","title":{"rendered":"A demand curve with constant slope over all quantity values can have a continuously changing price elasticity of demand"},"content":{"rendered":"\n<p>True\/False: A demand curve with constant slope over all quantity values can have a continuously changing price elasticity of demand<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Answer: True<\/strong><\/p>\n\n\n\n<p>A <strong>demand curve with a constant slope<\/strong> can indeed have a <strong>continuously changing price elasticity of demand<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>The <strong>price elasticity of demand (PED)<\/strong> measures how much the <strong>quantity demanded<\/strong> of a good responds to a <strong>change in its price<\/strong>. Mathematically, it is defined as: PED=\u2223dQdP\u22c5PQ\u2223\\text{PED} = \\left| \\frac{dQ}{dP} \\cdot \\frac{P}{Q} \\right|<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>dQdP\\frac{dQ}{dP}: the derivative of quantity with respect to price (i.e., the slope of the demand curve).<\/li>\n\n\n\n<li>PP: price<\/li>\n\n\n\n<li>QQ: quantity demanded<\/li>\n<\/ul>\n\n\n\n<p>Now consider a <strong>linear demand curve<\/strong>, such as: Q=a\u2212bPQ = a &#8211; bP<\/p>\n\n\n\n<p>This equation represents a straight line with a <strong>constant slope<\/strong> of \u2212b-b (since dQ\/dP=\u2212bdQ\/dP = -b).<\/p>\n\n\n\n<p>However, the <strong>price elasticity of demand<\/strong> at any point on this demand curve is: PED=\u2223\u2212b\u22c5PQ\u2223=\u2223\u2212b\u22c5Pa\u2212bP\u2223\\text{PED} = \\left| \\frac{-b \\cdot P}{Q} \\right| = \\left| \\frac{-b \\cdot P}{a &#8211; bP} \\right|<\/p>\n\n\n\n<p>This shows that although the slope \u2212b-b is constant, the elasticity changes <strong>continuously<\/strong> as you move along the curve because <strong>both PP and QQ<\/strong> are changing.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At <strong>high prices<\/strong> (low quantities), P\/QP\/Q is large, so <strong>elasticity is high<\/strong>.<\/li>\n\n\n\n<li>At <strong>low prices<\/strong> (high quantities), P\/QP\/Q is small, so <strong>elasticity is low<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>At the <strong>midpoint<\/strong> of the linear demand curve, the price elasticity is exactly <strong>1<\/strong> (unit elastic). Above the midpoint, demand is <strong>elastic<\/strong> (PED &gt; 1), and below it, demand is <strong>inelastic<\/strong> (PED &lt; 1).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>Even though the <strong>slope of a linear demand curve is constant<\/strong>, the <strong>price elasticity of demand varies continuously<\/strong> along the curve because it depends not only on the slope but also on the <strong>ratio of price to quantity<\/strong> at each point. Therefore, the statement is <strong>True<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>True\/False: A demand curve with constant slope over all quantity values can have a continuously changing price elasticity of demand The correct answer and explanation is: Answer: True A demand curve with a constant slope can indeed have a continuously changing price elasticity of demand. Explanation (300 words): The price elasticity of demand (PED) measures [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18619","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18619","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18619"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18619\/revisions"}],"predecessor-version":[{"id":18620,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18619\/revisions\/18620"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}