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Unformatted text preview: EC 146: Industrial Organization Solutions to the Midterm Exam Department of Economics Brown University October 26, 2007 1. (a) Lets solve the problem of Firm i . I takes the output choices of the other firms as given and solves Max { q i } i = h 100 ( q i + q i ) i q i , where q i = j 6 = i q j . The first order condition is 100 2 q i q i = 0 . Hence, the best response function of Firm i is q BR i ( q 1 ,...,q i 1 ,q i +1 ,...,q n ) = 100 q i 2 . (1) Notice that the best response functions will be symmetrical, so the solution of this system of n equations and n unknowns is such that in equilibrium, each firm produces the same quantity. That is, q 1 = q 2 = ... = q n = q , which implies that q i = ( n 1) q . Equation (1) thus becomes q = 100 ( n 1) q 2 . In the CournotNash equilibrium, therefore, each firm produces q 1 = q 2 = ... = q n = 100 n + 1 . Total output and price are in equilibrium Q = 100 n n + 1 P = 100 n + 1 . The profit that each firm obtain in equilibrium is i = 100 n + 1 2 ....
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 Fall '07
 CAMPOSORTIZ
 Economics

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