solutions - Problem Set 6 Suggested Solutions 1 First,...

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Unformatted text preview: Problem Set 6 Suggested Solutions 1 First, write each firms profit as a function of q 1 and q. 1 = R 1 ( q 1 ,q 2 )- C 1 ( q 1 ,q 2 ) = (10- Q ) q 1- c 1 q 1 = (10- [ q 1 + q 2 ]) q 1- c 1 q 1 = 10 q 1- q 2 1- q 1 q 2- c 1 q 1 2 = R 2 ( q 1 ,q 2 )- C 2 ( q 1 ,q 2 ) = (10- Q ) q 2- c 2 q 2 = (10- [ q 1 + q 2 ]) q 2- c 2 q 2 = 10 q 2- q 2 2- q 1 q 2- c 2 q 2 Since firm 1 will maximize profit by choosing q 1 , take the FOC of 1 wrt q 1 . 1 = 10- 2 q 1- q 2- c 1 = 0 q 1 = 10- q 2- c 1 2 Since firm 2 will maximize profit by choosing q 2 , take the FOC of 2 wrt q 2 . 2 = 10- 2 q 2- q 1- c 2 = 0 q 2 = 10- q 1- c 2 2 Combining these two equations gives q 1 = 10- 10- q 1- c 2 2- c 1 2 = 20- 10+ q 1 + c 2- 2 c 1 4 3 q 1 = 10+ c 2- 2 c 1 q * 1 = 10+ c 2- 2 c 1 3 q * 2 = 10- 10+ c 2- 2 c 1 3- c 2 2 = 30- 10- c 2 +2 c 1- 3 c 2 6 6 q 2 = 20 + 2 c 1- 4 c 2 q * 2 = 10+ c 1- 2 c 2 3 Substituting these quantities into the demand curve gives the price: P = 10- Q = 10...
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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.

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solutions - Problem Set 6 Suggested Solutions 1 First,...

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