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Problem_Set_7_Solutions

# Problem_Set_7_Solutions - ECON W3211.002 Intermediate...

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ECON W3211.002 Intermediate Microeconomics Problem Set 7 Answer Key Due Monday, November 15, 2010 1. If the inverse demand function for radios is p = a - bQ , what is the consumer surplus if price is a/ 2 ? The first step is to find quantity demanded at that price, which is Q = a 2 b . Consumer surplus is the area below the demand curve and above the price line. In this case, the area is a triangle with height a 2 and length a 2 b , so that consumer surplus is a 2 8 b . 2. If the supply function is Q = Ap η , what is the producer surplus if price is p * ? We assume η 1 so that the supply curve slopes upward. Quantity demanded at p * is A ( p * ) η . The inverse supply function is p = ( Q A ) 1 η . Producer surplus is the area under- neath the price line and above the inverse supply function, which is gotten by evaluat- ing R A ( p * ) η 0 [ p * - ( Q A ) 1 η ] dQ . Evaluating this integral and simplifying terms gives us PS = 1 η +1 A ( p * ) η +1 . 3. Suppose that the demand curve for wheat is Q = 100 - 10 p and the supply curve is Q = 10 p .
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