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econ398win08hw3sol - ECON 398 HOMEWORK 3 Professor...

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ECON 398 HOMEWORK 3 Professor Ozdenoren 1. In a small town called Ham Harbour there are two shops. Wingerman’s has great cheese and Trader Moe’s has good wine. Demand for Wingerman’s cheese is given by Q W = 32 - 2P W - P M and demand for Trader Moe’s wine is given by Q M = 20 – 2P M - P W where Q W is pounds of cheese per day sold by Wingerman’s, Q M is cases of wines per day sold by Moe’s and P W and P M are prices in dollars for cheese and wine respectively. Suppose that a pound of cheese and a case of wine both cost 2 dollars to the shops. a. If both firms set their prices simultaneously, what are the equilibrium prices and profits for each shop? b. If the firms can set prices together (i.e., collude), what are the equilibrium prices and profits in this case? c. Compare this with the Donna’s and Pierce’s example solved in class. What is the main difference? Answer a) Profit function of Wingerman’s is (32 - 2 P W - P M )( P W - 2) and the profit function for Moe’s is (20 - 2P M - P W )( P M - 2). Taking the derivative of Wingerman’s profit fuction with respect to P M
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