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191hw4sol

# 191hw4sol - ECON191 Fall 2009 Outline of suggested...

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1 ECON191 Fall 2009 Outline of suggested solutions to Problem Set 4 1) Cournot Equilibirum Given the market demand function ( ) B A Q Q P + = 10 and TC = 0 for both Firm A and Firm B Firm A ( ) [ ] A B A Q Q Q Max + 10 First order condition: 0 2 10 = B A Q Q Reaction function for A: 2 5 2 2 10 B B A Q Q Q = = ……….(1) Firm B ( ) [ ] B B A Q Q Q Max + 10 First order condition: 0 2 10 = A B Q Q Reaction function for B: 2 5 2 2 10 A A B Q Q Q = = ……….(2) Solving the two reactions functions for the Cournot equilibrium, 3 10 * * = = B A Q Q , 3 10 3 10 3 10 10 = = P Profit for firm A 9 100 3 10 3 10 3 10 10 * * = + = = A Q P Profit for firm B 9 100 3 10 3 10 3 10 10 * * = + = = B Q P Cartel problem Both firms together ( ) Q Q Max 10 FOC: 0 2 10 = Q 5 * = Q 5 . 2 * * = = B A Q Q Price charged by cartel 5 10 * = = Q Profit made by each firm ( ) 2 25 2 5 5 2 * * = = = Q P 2) Pindyck, Rubinfeld and Koh, p. 522, #7.

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191hw4sol - ECON191 Fall 2009 Outline of suggested...

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