ps5solutions

# ps5solutions - Problem Set 5 SOLUTIONS Due Thursday, Nov....

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Problem Set 5 SOLUTIONS Due Thursday, Nov. 12th, by 10pm 1. Suppose there are two types of consumers. Type 1 consumers’ willingness to pay for x is given by 16 x 1 / 2 . Type 2 consumers’ willingness to pay for x is given by 20 x 1 / 2 . The fraction of Type 1 consumers is given by γ . The ﬁrm producing x is a monopolist with a marginal cost of 2. (a) Suppose the ﬁrm can observe consumer types. What bundles will be oﬀered to each type of consumer for what fees? How does your answer depend on γ ? If the ﬁrm can observe types, he will oﬀer bundles to each type in which they are exactly indiﬀerent between purchasing and not purchasing. π 1 = 16 x 1 / 2 - 2 x 1 dx = (1 / 2)16 x - 1 / 2 - 2 = 0 x 1 = 16 , F 1 = 16(16) 1 / 2 = 64 π 2 = 20 x 1 / 2 - 2 x 2 dx = (1 / 2)20 x - 1 / 2 - 2 = 0 x 2 = 25 , F 2 = 20(25) 1 / 2 = 100 The solution does not depend on γ For the rest of this problem, assume that the ﬁrm cannot observe consumer types. (b)

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## This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.

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ps5solutions - Problem Set 5 SOLUTIONS Due Thursday, Nov....

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