Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the demand elastic, inelastic or neither at the indicated values? q=409-0.3p^(2)
a.) $20 b.) $36<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the elasticity of demand (E) for the given demand function (q = 409 – 0.3p^2), we can use the following formula for elasticity of demand:<\/p>\n\n\n\n [ First, we differentiate the demand function with respect to (p):<\/p>\n\n\n\n [ Now, we will evaluate the demand (q) at the indicated values of (p).<\/p>\n\n\n\n a.) (p = 20)<\/strong><\/p>\n\n\n\n [ b.) (p = 36)<\/strong><\/p>\n\n\n\n [ a.) (p = 20)<\/strong><\/p>\n\n\n\n [ b.) (p = 36)<\/strong><\/p>\n\n\n\n [ a.) At (p = 20):<\/strong> b.) At (p = 36):<\/strong> In summary, the elasticity of demand at (p = 20) is approximately -8.31, and at (p = 36) it is about -38.35. In both cases, demand is elastic, indicating that a percentage change in price will result in a larger percentage change in quantity demanded. This is essential for pricing strategies, as it suggests that lower prices could significantly increase total revenue by attracting more consumers.<\/p>\n","protected":false},"excerpt":{"rendered":" Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the demand elastic, inelastic or neither at the indicated values? q=409-0.3p^(2)a.) $20 b.) $36 The Correct Answer and Explanation is : To find the elasticity of demand (E) for the given demand function (q = 409 – […]<\/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-155708","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155708","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=155708"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155708\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=155708"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=155708"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=155708"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
E = \\left(\\frac{dq}{dp}\\right) \\cdot \\left(\\frac{p}{q}\\right)
]<\/p>\n\n\n\nStep 1: Calculate (\\frac{dq}{dp})<\/h3>\n\n\n\n
\\frac{dq}{dp} = -0.6p
]<\/p>\n\n\n\nStep 2: Evaluate (q) at the given prices<\/h3>\n\n\n\n
q = 409 – 0.3(20^2) = 409 – 0.3(400) = 409 – 120 = 289
]<\/p>\n\n\n\n
q = 409 – 0.3(36^2) = 409 – 0.3(1296) = 409 – 388.8 = 20.2
]<\/p>\n\n\n\nStep 3: Calculate Elasticity for each price<\/h3>\n\n\n\n
\\frac{dq}{dp} = -0.6(20) = -12
]
[
E = (-12) \\cdot \\left(\\frac{20}{289}\\right) \\approx -8.31
]<\/p>\n\n\n\n
\\frac{dq}{dp} = -0.6(36) = -21.6
]
[
E = (-21.6) \\cdot \\left(\\frac{36}{20.2}\\right) \\approx -38.35
]<\/p>\n\n\n\nStep 4: Determine elasticity type<\/h3>\n\n\n\n
Since (E \\approx -8.31), which is less than -1, demand is elastic. This means consumers are highly responsive to price changes at this price level.<\/p>\n\n\n\n
Since (E \\approx -38.35), which is also less than -1, demand is elastic here as well.<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n