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October 11th, 2015, 08:19 AM   #1
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From: Kaunas

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Bertrand model

Hello, can any one help me to do this homework task, because I do not know how to solve it, would be really thanksfull.
1. There are 2 firms in the market, producing homogeneous goods and having such capacity constraints: and . Before the capacity is reached their cost functions are given by and . Market demand function is given by . The firms are under price competition and play a static game of complete information.
a) Solve for the best response of the 1st player to the assumed choice of the 2nd player .
b) Are the strategies in the part “a” a Nash equilibrium. Why?
c) If isn’t the best response to (suppose that the 2nd player could unilaterally boost her profit by increasing her price), then which price prevents her from boosting her profit is she sets her price equal to ?
d) Which price is the best response of the 2nd player to the assumed choice of the 1st player ?
e) Compare with the result in the part “a” . Is and a Nash equilibrium?
f) Comment on the existence of the pure strategies Nash equilibrium in this case.
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October 12th, 2015, 06:14 AM   #2
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