Explanation Given: Supply function value is S ( q ) = 0.3 q 2 + 30 , q 0 = 4 units. Calculation: Consider the following supply function S ( q ) = 0.3 q 2 + 30 ....... ( 1 ) At sales level q 0 = 4 , the price will be, p 0 = S ( q 0 ) = 0.3 × 4 2 + 30 = 4.8 + 30 = 34.8 Therefore, the price at which 4 units will be supplied is $ 34.80 . 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 ) = 0.3 q 2 + 30 , p 0 = 34.80 and q 0 = 4

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Chapter 6.6, Problem 14PS

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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 13PS

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Chapter 6 Solutions

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 and sketched the production surplus. The price at which 4 units will be supplied is 34.80

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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