191ps4sol - ECON191 Spring 2010 Outline of suggested...

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1 ECON191 Spring 2010 Outline of suggested solutions to Problem Set 4 1) Given the market demand function   B A Q Q P 10 , TC = 0 for both Firm A and Firm B Firm A Max.     A B A Q Q Q 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 Max.     B B A Q Q Q 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) Cournot equilibrium is obtained by solving (1) and (2): 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 : Max   Q Q 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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This note was uploaded on 08/26/2010 for the course ECON ECON191 taught by Professor Chan during the Spring '09 term at HKUST.

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191ps4sol - ECON191 Spring 2010 Outline of suggested...

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