Econ 325 Problem Set 3b Solutions

# Econ 325 Problem Set 3b Solutions - ECON 325 IO(Fall 2012...

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ECON 325, IO (Fall 2012) Christoph Luelfesmann, SFU Answer Key Assignment #3 Problem 1.) Answer: From the lecture, we know that the Cournot solution with N identical firms will be symmetric, and each firm i produces q C i = ( A - c ) / ( N +1) B . Inserting the numbers N = 14, A = 290, c = 50 and B = 1 / 3, this yields q C i = 240 / 5 = 48 for the present example. Market price is then P C = 290 - (14)(48) / 3 = 66 and firm profits are Π C i = (66 - 50)48 - 200 = 568 > 0 (hence, firms will enter the market despite the fixed costs). Problem 2.) Answer: (a) Consider the industry B where firms are asymmetric. In Cournot duopoly, a firm i maximizes its profits by choosing a production level, q i . Technically, the firm maximizes Π i ( q i , q j ) = [ P ( Q = q i + q j ) - c i ] q i . (1) Using P ( Q ) = 1 - q i - q j , the first-order condition reads d Π i dq i = 1 - 2 q i - q j - c i = 0 , (2) so that firm i ’s BRF is given as q * i ( q j ) = 1 - q j - c i 2 . (3) Inserting c 1 = c - d and c 2 = c + d then yields q * 1 ( q 2 ) = (1 - q 2 - c + d ) / 2 and q * 2 ( q 1 ) = (1 - q 1 - c - d ) / 2. In an Nash-equilibrium, both reaction functions 1

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intersect (WHY?) so that both first-order conditions must be satisfied at the same time. This gives us the Cournot quantities q C 1 = (1 - c + 2 d ) / 3, and q C 2 = (1 - c - 2 d ) / 3. As expected, we have q C 1 > q C 2 whenever d > 0.
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