{"id":221133,"date":"2025-05-29T07:59:59","date_gmt":"2025-05-29T07:59:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=221133"},"modified":"2025-05-29T08:38:52","modified_gmt":"2025-05-29T08:38:52","slug":"market-clearing-price-and-quantity-respectively","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/29\/market-clearing-price-and-quantity-respectively\/","title":{"rendered":"Suppose The Market Demand Function For Good X Is Given By Qx = 30 &#8211; 2P"},"content":{"rendered":"\n<p>Suppose The Market Demand Function For Good X Is Given By Qx = 30 &#8211; 2P, And The Supply Function For Good X Is Given By Qx = 6 + 4P. Then, Calculate The:(2 Point)<br>A. Market Clearing Price And Quantity Respectively.<br>B. Determine Market Equilibrium<br>C. Price And Supply Elasticity Of Demand<\/p>\n\n\n\n<p><br>Suppose the market demand function for good X is given by Qx = 30 &#8211; 2P,<br>and the supply function for good X is given by Qx<br>Suppose the market demand function for good X is given by Qx = 30 &#8211; 2P, and the supply function for good X is given by Qx = 6 + 4P. Then, calculate the:(2 point) A. Market clearing price and quantity respectively. B. Determine market equilibrium C. Price and supply elasticity of demand.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Demand Function:<\/strong> Q&lt;sub>D&lt;\/sub> = 30 &#8211; 2P<\/li>\n\n\n\n<li><strong>Supply Function:<\/strong> Q&lt;sub>S&lt;\/sub> = 6 + 4P<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>A. Market Clearing Price and Quantity<\/strong><\/h3>\n\n\n\n<p>At market equilibrium (clearing point), quantity demanded = quantity supplied: 30\u22122P=6+4P30 &#8211; 2P = 6 + 4P30\u22122P=6+4P<\/p>\n\n\n\n<p>Solving for <strong>P<\/strong>: 30\u22126=2P+4P\u21d224=6P\u21d2P=430 &#8211; 6 = 2P + 4P \\Rightarrow 24 = 6P \\Rightarrow P = 430\u22126=2P+4P\u21d224=6P\u21d2P=4<\/p>\n\n\n\n<p>Now, substitute <strong>P = 4<\/strong> into either the demand or supply equation to find <strong>Q<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Q = 30 &#8211; 2(4) = 30 &#8211; 8 = <strong>22<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u2705 <strong>Answer A<\/strong>:<br><strong>Market clearing price = 4<\/strong>,<br><strong>Market clearing quantity = 22<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>B. Determine Market Equilibrium<\/strong><\/h3>\n\n\n\n<p>Market equilibrium occurs where <strong>Q&lt;sub&gt;D&lt;\/sub&gt; = Q&lt;sub&gt;S&lt;\/sub&gt;<\/strong>, which we just found:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At <strong>P = 4<\/strong>, both demand and supply equal <strong>Q = 22<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u2705 <strong>Answer B<\/strong>:<br><strong>Market equilibrium is at P = 4 and Q = 22<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>C. Price Elasticity of Demand and Supply<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Price Elasticity of Demand (E&lt;sub&gt;D&lt;\/sub&gt;):<\/strong><\/h4>\n\n\n\n<p>Formula: ED=dQDdP\u00d7PQE_D = \\frac{dQ_D}{dP} \\times \\frac{P}{Q}ED\u200b=dPdQD\u200b\u200b\u00d7QP\u200b<\/p>\n\n\n\n<p>From demand: Q&lt;sub&gt;D&lt;\/sub&gt; = 30 &#8211; 2P \u2192 dQ&lt;sub&gt;D&lt;\/sub&gt;\/dP = -2<\/p>\n\n\n\n<p>At equilibrium P = 4, Q = 22: ED=(\u22122)\u00d7422=\u2212822\u2248\u22120.36E_D = (-2) \\times \\frac{4}{22} = -\\frac{8}{22} \\approx -0.36ED\u200b=(\u22122)\u00d7224\u200b=\u2212228\u200b\u2248\u22120.36<\/p>\n\n\n\n<p>(Demand is <strong>inelastic<\/strong> in absolute value since |E&lt;sub&gt;D&lt;\/sub&gt;| &lt; 1)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Price Elasticity of Supply (E&lt;sub&gt;S&lt;\/sub&gt;):<\/strong><\/h4>\n\n\n\n<p>From supply: Q&lt;sub&gt;S&lt;\/sub&gt; = 6 + 4P \u2192 dQ&lt;sub&gt;S&lt;\/sub&gt;\/dP = 4 ES=4\u00d7422=1622\u22480.73E_S = 4 \\times \\frac{4}{22} = \\frac{16}{22} \\approx 0.73ES\u200b=4\u00d7224\u200b=2216\u200b\u22480.73<\/p>\n\n\n\n<p>(Supply is <strong>inelastic<\/strong> as well)<\/p>\n\n\n\n<p>\u2705 <strong>Answer C<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Price Elasticity of Demand \u2248 -0.36<\/strong><\/li>\n\n\n\n<li><strong>Price Elasticity of Supply \u2248 0.73<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 Words)<\/strong><\/h3>\n\n\n\n<p>To find the market equilibrium for good X, we equate the market demand and supply functions. The demand function, QD=30\u22122PQ_D = 30 &#8211; 2PQD\u200b=30\u22122P, shows that as price increases, quantity demanded decreases. The supply function, QS=6+4PQ_S = 6 + 4PQS\u200b=6+4P, indicates that quantity supplied increases with price. Setting QD=QSQ_D = Q_SQD\u200b=QS\u200b allows us to determine the market-clearing price, which balances the interest of consumers and producers.<\/p>\n\n\n\n<p>Solving the equation 30\u22122P=6+4P30 &#8211; 2P = 6 + 4P30\u22122P=6+4P, we find the equilibrium price P=4P = 4P=4. Substituting back into either function gives an equilibrium quantity Q=22Q = 22Q=22. This equilibrium reflects a stable point in the market where there is neither excess demand nor excess supply.<\/p>\n\n\n\n<p>We further analyze how sensitive demand and supply are to price changes using elasticity. The price elasticity of demand measures how much quantity demanded responds to a change in price. Using the formula ED=(dQD\/dP)\u00d7(P\/Q)E_D = (dQ_D\/dP) \\times (P\/Q)ED\u200b=(dQD\u200b\/dP)\u00d7(P\/Q), we calculate ED=\u22120.36E_D = -0.36ED\u200b=\u22120.36, indicating that demand is inelastic\u2014consumers do not significantly reduce quantity demanded when price rises.<\/p>\n\n\n\n<p>Similarly, we calculate the price elasticity of supply as ES=(dQS\/dP)\u00d7(P\/Q)=0.73E_S = (dQ_S\/dP) \\times (P\/Q) = 0.73ES\u200b=(dQS\u200b\/dP)\u00d7(P\/Q)=0.73, also inelastic. This suggests that producers do not rapidly increase output when price rises. Inelastic elasticities are common in the short run due to fixed consumer habits and production limitations.<\/p>\n\n\n\n<p>Understanding these values is crucial for policymakers and businesses when forecasting market behavior or implementing pricing strategies.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/learnexams-banner4-97.jpeg\" alt=\"\" class=\"wp-image-221135\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Suppose The Market Demand Function For Good X Is Given By Qx = 30 &#8211; 2P, And The Supply Function For Good X Is Given By Qx = 6 + 4P. Then, Calculate The:(2 Point)A. Market Clearing Price And Quantity Respectively.B. Determine Market EquilibriumC. Price And Supply Elasticity Of Demand Suppose the market demand function [&hellip;]<\/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-221133","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221133","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=221133"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221133\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}