Explanation Given Information: The likelihood that a child will attend the performance is q = 0.01 ( 0.006 x 2 + 0.38 x + 35 ) where 15 ≤ x ≤ 100 and x is the annual household income in thousand dollars. Formula used: Income Elasticity of Demand The income elasticity of demand E is defined as the percentage increase in demand of one item per percentage increase in personal income. E = d q d p ⋅ p q And the demand is elastic if E > 1 , the demand is inelastic if demand is unitary elastic if E = 1 . Calculation: The likelihood that a child will attend the performance is q = 0.01 ( 0.006 x 2 + 0.38 x + 35 ) where 15 ≤ x ≤ 100 and x is the annual household income in thousand dollars. Take derivative of q to get, d q d x = 0.01 ( 0.0012 x + 0.38 ) Price Elasticity of Demand as, E = d q d x ⋅ x q Substitute value of derivative of q as 0.01 ( 0.0012 x + 0.38 ) , value of q as 0.01 ( 0.006 x 2 + 0.38 x + 35 ) in the above formula to get, E = d q d x ⋅ x q = ( 0.01 ( 0.0012 x + 0.38 ) ) ⋅ x 0.01 ( 0

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.6, Problem 26E

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To calculate: The income elasticity of demand at an income level of $30000 where the likelihood that a child will attend the performance is q=0.01(0.006x2+0.38x+35) where 15≤x≤100.

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Chapter 12.6, Problem 25E

Chapter 12.6, Problem 27E

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Chapter 12 Solutions

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The income elasticity of demand at an income level of $ 30000 where the likelihood that a child will attend the performance is q = 0.01 ( 0.006 x 2 + 0.38 x + 35 ) where 15 ≤ x ≤ 100 .

Solution Summary: The author calculates the income elasticity of demand at an income level of 30000 where the likelihood that a child will attend the performance is Eapprox 0.27.

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To calculate: The income elasticity of demand at an income level of $30000 where the likelihood that a child will attend the performance is q=0.01(0.006x2+0.38x+35) where 15≤x≤100.

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