Explanation Given: The price demand equation is S ( x ) = 5 ln ( x + 1 ) and p ¯ = $ 26 . Formula used: Producers’ surplus: If ( x ¯ , p ¯ ) is a point on the graph of the price supply equation p = S ( x ) , then producers’ surplus ( PS ) at a price level of p ¯ is P S = ∫ 0 x ¯ [ p ¯ − S ( x ) ] d x . Calculation: Substitute p ¯ = $ 26 in the equation p ¯ = 5 ln ( x + 1 ) to obtain the value of x ¯ as follows, p ¯ = 5 ln ( x + 1 ) 26 = 5 ln ( x ¯ + 1 ) 26 5 = ln ( x ¯ + 1 ) 5.2 = ln ( x ¯ + 1 ) Simplify further, ln ( e 5.2 ) = ln ( x ¯ + 1 ) ( x ¯ + 1 ) = e 5.2 x ¯ = e 5.2 − 1 x ¯ = 180.27 Use the above mentioned formula to calculate the producers’ surplus as follows, Substitute S ( x ) = 5 ln ( x + 1 ) , p ¯ = $ 26 and x ¯ = 180.27 in P S = ∫ 0 x ¯ [ p ¯ − S ( x ) ] d x to compute the producers’ surplus, P S = ∫ 0 x ¯ [ p ¯ − S ( x ) ] d x = ∫ 0 180

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ISBN: 9780135961407

Author: Barnett

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Chapter 6.3, Problem 84E

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