To determine the marginal revenue function from the given demand function D(q)=40q\u22122D(q) = 40q – 2D(q)=40q\u22122, we need to follow a step-by-step process that involves first determining the revenue function and then differentiating it to find the marginal revenue.<\/p>\n\n\n\n
Step 1: Express Revenue as a Function of Quantity<\/h3>\n\n\n\n
Revenue is given by the product of the quantity sold qqq and the price P(q)P(q)P(q) at that quantity. In this case, the price function P(q)P(q)P(q) is equivalent to the demand function D(q)D(q)D(q), so we can express the revenue function R(q)R(q)R(q) as:R(q)=P(q)\u00d7qR(q) = P(q) \\times qR(q)=P(q)\u00d7q<\/p>\n\n\n\n
Substitute the demand function D(q)=40q\u22122D(q) = 40q – 2D(q)=40q\u22122 into this equation:R(q)=(40q\u22122)\u00d7qR(q) = (40q – 2) \\times qR(q)=(40q\u22122)\u00d7q<\/p>\n\n\n\n
Now, expand the expression:R(q)=40q2\u22122qR(q) = 40q^2 – 2qR(q)=40q2\u22122q<\/p>\n\n\n\n
Step 2: Find the Marginal Revenue Function<\/h3>\n\n\n\n
Marginal revenue is the derivative of the revenue function with respect to quantity qqq. Differentiate the revenue function R(q)=40q2\u22122qR(q) = 40q^2 – 2qR(q)=40q2\u22122q with respect to qqq:MR(q)=ddq(40q2\u22122q)MR(q) = \\frac{d}{dq} (40q^2 – 2q)MR(q)=dqd\u200b(40q2\u22122q)<\/p>\n\n\n\n
Applying the power rule of differentiation:MR(q)=80q\u22122MR(q) = 80q – 2MR(q)=80q\u22122<\/p>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n
Thus, the marginal revenue function is:MR(q)=80q\u22122MR(q) = 80q – 2MR(q)=80q\u22122<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The marginal revenue function represents the additional revenue gained from selling one more unit of the good. In this case, for each unit increase in qqq, the revenue increases by 80q\u2212280q – 280q\u22122. The relationship MR(q)=80q\u22122MR(q) = 80q – 2MR(q)=80q\u22122 shows that the marginal revenue increases as the quantity sold increases. However, the rate of increase diminishes due to the negative linear term (-2). This reflects typical behavior in price-demand functions, where the first few units sold often have higher marginal revenues, but as more units are sold, the additional revenue from each unit tends to decrease.<\/p>\n\n\n\n Determine the marginal revenue function in terms of q, given the demand function D(q) = 40q – 2. The Correct Answer and Explanation is:1 To determine the marginal revenue function from the given demand function D(q)=40q\u22122D(q) = 40q – 2D(q)=40q\u22122, we need to follow a step-by-step process that involves first determining the revenue function 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-250694","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250694","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=250694"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250694\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=250694"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=250694"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=250694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-144.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"