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THE GEORGE WASHINGTON UNIVERSITY Department of Economics A. Yezer Answers to Problem Set #7 in Economics 11 Fall 2007 1.Assume that Mydump Mufflers and GotNoKey Muffler Shops are the only two firms providing automobile muffler repair services. Further assume that if both firms charge \$40 per muffler, they will each earn \$100 million per year and that if both charge \$60 per muffler, they will each earn \$200 million per year. However, if one charges \$40 while the other charges \$60, the one with a \$40 price will earn \$50 million while the one charging \$60 will sell so few mufflers that earnings will fall to \$0. Set up a simple payoff matrix for these two firms and discuss the likely nature of pricing behavior of the two firms. Consider cooperative, dominant strategy, and Nash equilibrium solution concepts. This is an opportunity to apply the oligopoly pricing game. Each player can choose a price of \$60 or \$40 (high or low price) The payoff matrix is shown below: Mydump Mufflers \$60 \$40 \$60 \$200 /\$200 \$0 /\$50 GotNoKey Muffler \$40 \$50 /\$0 \$100 /\$100 Now the equilibrium in this oligopoly depends on which notion of equilibrium you apply. The cooperative equilibrium is \$60-\$60 because it allows both oligopolists to earn a joint profit of \$400, which is \$200 larger than total payoff under any other strategy combination. There is no dominant strategy equilibrium because pricing at \$60 is best if the competitor also prices at \$60 but pricing at \$40 is best if your competitor prices at \$40. Both \$200/\$200 and \$100/\$100 are Nash equilibria in this case (2 Nas h Equilibria) because neither oligopolist has an incentive to move from a strategy pair in which they both are charging the same price. As in the Pepsi-Coke case in class, there is a temptation for these oligopolists to collude and both charge \$60. 2. Consider the controversy between Microsoft and Netscape. Microsoft was requiring firms selling computers with Windows 2000 to include its browser (at no additional cost). Assume Netscape won the case and that Microsoft could not control pricing. Then each firm would have the alternative of charging \$30 for its browser or giving it away for free. The payoff matrix is reproduced below Netscape Actions \$30 free Microsoft \$30 3.0/ 3.0 -1.0/ 4.0 Microsoft free 4.0/ -1.0 2/ 2 Find and discuss the cooperative and (one-shot) Nash equilibria likely to characterize the relation between these two firms. Note if there is a dominant strategy for either firm. Solution concepts: 1) Cooperative equilibrium - both play cooperate and each gets 3.0, consumers lose

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2) Dominant strategy equilibrium - free-free, for Netscape, 3.0 < 4.0 and -1.0 < 2.0. 3) Nash equilibrium in pure strategies- even if you start in cooperate, in a single play, each has an incentive to defect from cooperate and play free. free-free is a dominant strategy and hence a Nash equilibrium of a one-shot game. Given the nature of the rivalry between these firms, it appears to be the equilibrium even under repeated plays. If the firms were not so hostile, one could imagine that, over
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