ps5 - 2. What are the two bundles oered and their...

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Problem Set 5 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 ? For the rest of this problem, assume that the firm cannot observe consumer types. (b) Write out the individual rationality constraints and incentive compatibility constraints. Which of these will hold with equality? (c) Suppose γ = 1 /
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Unformatted text preview: 2. What are the two bundles oered and their corresponding fees? (d) Using isoprot and indierence curves, graph your answers to (a) and (c). 2. Consider the two player game below where a 2 L C R T 3 , 1 a, 0 7 ,-1 1 M a, 2 , 5 7 , 1 B a-1 , 7 1 , 7 6 , 6 (a) Find all pure strategy Nash equilibria (b) Suppose a = 0. Find a mixed strategy equilibrium. Now suppose a =-1. Again nd a mixed strategy equilibrium. What is the intuition for how a changes the mixed strategy equilibrium? (c) Suppose now 1 gets to move rst. Draw the extensive form game. Find all subgame perfect Nash equilibria and one Nash equilibrium that is not subgame perfect. 1...
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