hw2_answerkey

hw2_answerkey - Econ 440 September 2007 Peter Norman...

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Econ 440 September 2007 Peter Norman Homework 2 Answer Key 1. 2. a. Max A = (1 – y A – y B )*y A y A FOC: 1 – 2y A - y B = 0 R A (y B ) = (1 – y B ) / 2 By the same way, R B (y A ) = (1 – y A ) / 2
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By solving reaction functions simultaneously, Nash Equilibrium: y A = 1/3 y B = 1/3 b. C = (1 – 2/3)*(1/3) = 1/9 (same for both firms) c. Max (1 – y)*y y FOC: 1 – 2y = 0 y = 1/2 ( y = y A + y B ) y A + y B = 1/2
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Solution set to the problem is ( y A * y B * ) such that y A * + y B * = 1/2 (red line above) d. e. In voluntary provision of public good example, there is “underprovision”. Here, there is “overproduction”. There exists a region on the southwest of the equilibrium where both agents are strictly better off.
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3. a. Payoff functions are: I = (9 – g I – g S – c)*g I S = (9 – g I – g S – c)*g S b. max I = (9 – g I – g S - c )*g I g I FOC: 9 - 2g I – g S – c = 0 g I = (9 – g s – c)/2 By the same way, g S = (9 – g I
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This note was uploaded on 11/02/2008 for the course ECON 440 taught by Professor Peternorman during the Spring '08 term at UNC.

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hw2_answerkey - Econ 440 September 2007 Peter Norman...

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