Problem Set 04 Solutions

# Problem Set 04 Solutions - Problem Set 4 Solutions 1 Econ...

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expected payoff in the beginning of period 3n-1 is the same as in the last period. The offers in period 3n-2 will be the same as in period 3n-1 and the same for all previous periods. Therefore, at each period t the player that is selected to make an offer will offer /2 to the other player and will keep 1 /2 for himself. In the first period the player who is selected to offer will offer /2 to the other player which will accepted. Problem Three We’ll assume C 0. Suppose k firms have entered the market. Let’s solve for the quantities the firms will choose in a subgame-perfect equilibrium. (Note that a firm will never produce a quantity greater than 1 because producing a quantity of 0, for instance, is always better.) If k 0 , we have nothing to solve for. If k 1 , the firm’s problem is max q 1 q C . The first order condition is 1 2 q 0 , so the optimal 0 q 1 quantity here is 1/2. If k 2, then we get into a situation like the Cournot game considered in class. The best response function for firm i can be obtained by solving max q i 1 q i q j C . The best response function is q i q j 1 q j /2 if 0 q i 1 j i j i j i q j 1 and q i q j 0 if q j 1. If you solve all the best response functions j i j i j i simultaneously (it’s easy to do this by just solving all the first order conditions for the best response functions simultaneously), you get that each firm produces a quantity of 1/ k 1 . The market quantity will thus be
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## This note was uploaded on 05/04/2011 for the course ECON 121 taught by Professor Woroch during the Fall '07 term at Berkeley.

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Problem Set 04 Solutions - Problem Set 4 Solutions 1 Econ...

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