Explanation Given: Supply function value is S ( q ) = 10 + 15 e 0.03 q , q 0 = 3 units. Calculation: Consider the following supply function S ( q ) = 10 + 15 e 0.03 q ....... ( 1 ) At sales level q 0 = 3 , the price will be, p 0 = S ( q 0 ) = 10 + 15 e 0.03 × 3 = 26.4126 ⋅ ⋅ ⋅ ≈ 26.41 Therefore, the price at which 4 units will be supplied is $ 26.41 . Use the formula for the Producer’s surplus. “If q 0 units of a commodity are sold at a price of p 0 dollars per unit, and if p = S ( q ) is the producer’s supply function for the commodity, then P S = p 0 q 0 − ∫ 0 q 0 S ( q ) d q " ....... ( 2 ) Substitute, the values in the above expression, S ( q ) = 10 + 15 e 0.03 q , p 0 = 26.41 and q 0 = 3 . The producer’s surplus at given sales level will be, P S = 26.41 × 3 − ∫ 0 3 ( 10 + 15 e 0

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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Chapter 6.6, Problem 16PS

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

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Chapter 6.6, Problem 15PS

Chapter 6.6, Problem 17PS

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Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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

Solution Summary: The author calculates the corresponding producer's surplus sales level by using the formula for calculating the price at which 4 units are supplied.

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

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Chapter 6 Solutions