practice%20final%201%20solutions-1

practice%20final%201%20solutions-1 - Economics 100C Spring...

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1 Economics 100C Spring 2009 Section B00 Final Exam Solutions QUESTION 1: 16 points QUESTION 2: 46 points QUESTION 3: 22 points TOTAL: 120 points QUESTION 4: 20 points QUESTION 5: 16 points 1. Two firms (A and B) are considering bringing out competing brands of a healthy cigarette. Payoffs to the companies are as shown in the table (A’s profits are given first): Firm B Produce Don’t Produce Firm A Produce 3, 3 5, 4 Don’t produce 4, 5 2, 2 a) Briefly explain what a Nash equilibrium is. Then, find any Nash equilibria associated with the static game. A Nash equilibrium is a pair of strategies such that each player is best-responding to the other. In this one-shot simultaneous game, that means that no player can do better choosing the alternative action holding constant the other player’s action. Nash equilibria are stable, in the sense that neither player has an incentive to change his/her behavior. This game has two Nash equilibria: (1) A: Produce; B: Don't Produce (2) A: Don't Produce; B: Produce b) Show the game tree associated with the sequential version of this game where firm A moves first, and then firm B makes its move. Briefly explain what a subgame perfect Nash equilibrium is. Find any subgame perfect Nash equilibria associated with the sequential game. Does this game present a first-mover advantage for firm A? Why or why not? Produce Don’t Produce Produce Don’t Produce Produce Don’t Produce (3,3) (5,4) (4,5) (2,2) Firm A Firm B
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2 A subgame perfect Nash equilibrium (SPNE) is a pair of strategies such that each player is choosing a best response at ever possible node in the game, regardless of whether that node is reached or not during the course of play. This equilibrium concept is a refinement of the Nash equilibrium concept and rules out noncredible threats. The unique SPNE is (A: Produce; B: Don’t Produce if A produces, Produce if A doesn’t). In this game, there is a first-mover advantage. If firm A moves first, it can ensure that it receives the payoff associated with the most advantageous Nash equilibrium from the simultaneous game (a payoff of 5 rather than 4). 2. A monopolist can produce at constant average and marginal costs of AC = MC = 5. The firm faces a market demand curve given by Q = 53 – P. a) Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist’s profits. The quantity that maximizes profits equates marginal revenue and marginal cost: Q = 24, P = 29, π = (29 – 5) 24 = 576 b) Suppose a second firm enters the market and that this firm has the same costs of production. Let q 1 be the output of firm 1 and let q 2 be the output of firm 2. The total market quantity is now given by Q = q 1 + q 2 . Assume that firm 1 decides what quantity to produce first, and then firm 2 makes its production decision having observed firm 1’s output choice. What are the quantities, market price and profits associated with the resulting Stackelberg equilibrium?
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This note was uploaded on 10/21/2010 for the course ECON 1530 taught by Professor Ohly during the Spring '10 term at Dartmouth.

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practice%20final%201%20solutions-1 - Economics 100C Spring...

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