practice2_ak.pdf

# practice2_ak.pdf - 1 Firm 1 maximizes 1 = pq1 q1 =(10 q1 q2...

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1. Firm 1 maximizes ° 1 = pq 1 ° q 1 = (10 ° q 1 ° q 2 ) q 1 ° q 1 and °rm 2 maximizes ° 2 = pq 2 ° 4 q 2 = (10 ° q 1 ° q 2 ) q 2 ° 4 q 2 : The °rst order conditions give two reaction functions: (9 ° q 2 ) ° 2 q 1 = 0 (6 ° q 1 ) ° 2 q 2 = 0 Solving this system for q 1 and q 2 gives quantity levels in the Cournot Nash equilibrium: q 1 = 4 q 2 = 1 : Thus, ° ° 1 = 16 ° ° 2 = 1 : 2. Each °rm maximizes ° = pq i ° 2 q i so p = 2 : Since °rms are symmetric, the market clearing condition is Q ( p ) = Nq; which gives q = 98 N : Finally, the pro°t is ° = pq ° 2 q = ( p ° 2) q = 0 : In a Cournot competition, each °rm maximizes ° = p ( Q ) q i ° 2 q and the °rst order condition is ° q + 100 ° Q ° 2 = 0 : Since °rms are symmetric, we have

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• Spring '08
• Staff
• Equilibrium, lim, Economic equilibrium, lim P

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