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PS 5 - Department of Economics University of California...

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Department of Economics University of California, Berkeley ECON 100A – Microeconomic Analysis Fall 2009 Problem Set 5 1 True or False (a) Both ABC Inc and XYZ Corp have a dominant Strategy. ABC Inc Expand West Expand South XYZ Corp Expand West 10,50 50,70 Expand South 20,90 40,80 (b) When there is Monopolistic Competition, there is no deadweight loss, because firms will enter the market until profits are equal to zero. (c) In the symmetric Cournot game with N firms, linear market demand p ( Q ) = a - bQ and constant marginal costs c , when the number of firms increases, each individual firm’s profit falls, but aggregate producer surplus rises. (d) A Stackelberg leader will necessarily make at least as much profits as if he acted as a Cournot oligopolist (e) A situation in which everyone is playing a dominant strategy must be a Nash equilibrium (f) In a Nash equilibrium, every player must be playing a dominant strategy. Answer (a) False. No firm has a dominant strategy. (b) False. The profit will be zero, but there will still be a deadweight loss. (c) False. Individual quantity is q i = a - c b ( N +1) the market price is P = a + Nc N +1 . Both fall with N (the market price falls in N since a > c ). Individual profit can then be expressed as Π i = 1 b ( a - c N +1 ) 2 and falls in N . Aggregate producer surplus is Π = N · Π i = N 1 b ( a - c N +1 ) 2 and also falls in N. Intuitively, as N rises, we move closer to the case of perfect competition, in which producer surplus is zero when marginal costs are constant. (d) True. By revealed preference, the Stackelberg leader can always choose the same point as if he played a Cournot game. If he chooses not to, it means that his profits at the Stackelberg point must be higher.
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