Explanation Given: Demand function value is D ( q ) = 75 e − 0.04 q , q 0 = 3 units. Calculation: Consider the following demand function D ( q ) = 75 e − 0.04 q ....... ( 1 ) At sales level q 0 = 3 , the price will be, p 0 = D ( q 0 ) = 75 e − 0.12 = 66 .51903 ⋅ ⋅ ⋅ ≈ 66 .52 Therefore, the price at which 3 units will be demanded is $ 66.52 . Use the formula for the Consumer’s surplus. “If q 0 units of a commodity are sold at a price of p 0 dollars per unit, and if p = D ( q ) is the consumer’s demand function for the commodity, then C S = ∫ 0 q 0 D ( q ) d q − p 0 q 0 " ....... ( 2 ) Substitute, the values in the above expression, D ( q ) = 75 e − 0.04 q , p 0 = 66.52 and q 0 = 3 . The consumer’s surplus at given sales level will be, C S = ∫ 0 3 75 e − 0

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.6, Problem 11PS

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To find:the corresponding consumer’s surplus sales level and sketch the consumer’s surplus.

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Chapter 6.6, Problem 10PS

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Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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the corresponding consumer’s surplus sales level and sketch the consumer’s surplus.

Solution Summary: The author calculates the consumer's surplus at a given sales level, based on the demand function value.

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To find:the corresponding consumer’s surplus sales level and sketch the consumer’s surplus.

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Chapter 6 Solutions