Explanation Given: Demand function is D ( q ) = 14 − q 2 . Supply function is S ( q ) = 2 q 2 + 2 . Calculation: Consider the following demand function D ( q ) = 14 − q 2 ....... ( 1 ) And the following supply function, S ( q ) = 2 q 2 + 2 ....... ( 2 ) Compute the point of market equilibrium as follows, D ( q ) = S ( q ) 14 − q 2 = 2 q 2 + 2 3 q 2 = 12 q 2 = 4 Simplify further, q = ± 2 q = − 2 , 2 As q cannot be negative, the point of equilibrium will be q 0 = 2 At sales level q 0 = 2 , the price will be, p 0 = D ( q 0 ) = 14 − 2 2 = 14 − 4 = 10 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 "

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 6.6, Problem 18PS

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Chapter 6 Solutions

Calculus

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the consumer’s surplus at the point of market equilibrium.

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