ps3_sol

# ps3_sol - Department of Economics University of California,...

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Fall 2007 University of California, Berkeley Prof. Farrell Problem Set 3 Solution Sketches 1. Consider an n-ﬁrm Cournot oligopoly, in which each ﬁrm (ﬁrm i ) has constant (meaning independent of output) marginal cost c i , but diﬀerent ﬁrms have diﬀerent costs. (a) Write down the Lerner equation using the ﬁrm’s market share, s i , as well as the mar- ket price p and the market demand elasticity ² . Starting from ﬁrm i ’s ﬁrst order conditions for proﬁt maximization, we have: [ P ( Q ) - c i ] + ∂P ( Q ) ∂Q q i = 0 P ( Q ) - c i = - ∂P ( Q ) ∂Q q i P ( Q ) - c i P ( Q ) = - ∂P ( Q ) ∂Q q i P ( Q ) P ( Q ) - c i P ( Q ) = - ∂P ( Q ) ∂Q Q P ( Q ) q i Q P ( Q ) - c i P ( Q ) = - s i ² . (b) Calculate the average cost of production, explaining why this in not just 1 N times the sum of c i . The average cost of production is given by: N X i =1 s i c i , which is the mean marginal cost weighted by market share. Since low cost ﬁrms produce more (Part A), this weighted average is smaller than the unweighted mean marginal cost. Solving the equation in Part A for the market share, and plugging this

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## This note was uploaded on 06/08/2008 for the course ECON 121 taught by Professor Woroch during the Fall '07 term at Berkeley.

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ps3_sol - Department of Economics University of California,...

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