191hw4sol

191hw4sol - 1 ECON191 Fall 2009 Outline of suggested...

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Unformatted text preview: 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: 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: 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: 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 10/11/2009 for the course ECON 191 taught by Professor Chen during the Spring '08 term at HKUST.

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191hw4sol - 1 ECON191 Fall 2009 Outline of suggested...

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