Ec146_soln_hw_2

Ec146_soln_hw_2 - EC 146: Industrial Organization Solutions...

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Unformatted text preview: EC 146: Industrial Organization Solutions to Homework 2 Department of Economics Brown University October 15, 2007 1. If firm 1 sets the price such that c 1 < p ≤ c 2 , it appropriates the entire market, and accrues a positive profit. Firm 1 can keep firm 2 out of business and behave as a monopolist as long as the profit-maximizing price is such that p M < c 2 . On the other hand, if the monopoly price is such that p M ≥ c 2 , then the optimal strategy would be to set p = c 2 , in which case firm 1 continues serving the entire market, keeping any competition out of business. 2. We can solve this problem in a few steps. First, let’s start by computing the Cournot-Nash equilibrium. Firm i takes q j as given and solves Max { q i } π i = h 1- ( q i + q j ) i q i- c i q i . The first order condition is 1- 2 q i- q j- c i = 0 , which determines the best response function q BR i ( q j ) = 1- c i- q j 2 . That is, q BR 1 ( q 2 ) = 1- c 1- q 2 2 and q BR 2 ( q 1 ) = 1- c 2- q 1 2 . Solving this system yields the equilibrium choices of both firms, namely q C 1 = 1- 2 c 1 + c 2 3 (1) and q C 2 = 1- 2 c 2 + c 1 3 . (2) If c 1 = c 2 = c , equations (1) and (2) imply that the equilibrium is such that q C 1 = q C 2 = 1- c 3 . Thus, total output is Q C = 2(1- c ) 3 , 1 EC 146 HW 2 while the equilibrium price is p C = 1 + 2 c 3 ....
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This note was uploaded on 07/06/2009 for the course ECON 146 taught by Professor Campos-ortiz during the Fall '07 term at Brown.

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Ec146_soln_hw_2 - EC 146: Industrial Organization Solutions...

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