Econ 200 Problem Set 6 Solution

Econ 200 Problem Set 6 Solution - Answer Key, Problem Set 6...

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Answer Key, Problem Set 6 1. Start with stage 2. Firm 1 takes k as given and solves max q 1 (50 2 q 1 2 q 2 2+ k 4 ) . The f rst-order condition gives q 1 = 48 2 q 2 + k 4 4 . Similarly, f rm 2’s f rst-order condition gives: q 2= 48 2 q 1 4 . Together, these two equations imply q 1 =8+ k 12 and q 2 =8 k 24 .Th i sg iv e s f rm 1 pro f to f μ 8+ k 12 50 2(16 + k 24 ) 2+ k 4 ¸ k 2 18 = μ 8+ k 12 ¶μ 16 + k 6 k 2 18 . Maximizing this with respect to k gives f rm 1’s optimal investment in stage 1. From the f rst order condition we have: k ( 1 9 1 36 )=( 8 6 + 16 12 ) which has a solution of k =32 . This is a top-dog strategy: the competition in strategic substitues leads f rm 1 to be “tough” by “overinvesting” in capital. You can verify that investment makes f rm 1 tough because f rm 2’s pro f ti s decreasing in
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This note was uploaded on 07/18/2008 for the course ECON 200 taught by Professor Philiphaile during the Spring '08 term at Yale.

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Econ 200 Problem Set 6 Solution - Answer Key, Problem Set 6...

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