its capacity constraint so that the collusive equilibrium can si 1? (Hint: The idea here is that, by limiting its own output, Firm 1 have a greater market share. As a result, Firm 1's gain of from the collusive agreement would be smaller.)

Microeconomic Theory
12th Edition
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Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.4P
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1.c
Find the condition on & under which Firm 1 will not deviate
from the collusive equilibrium.
Knowing that both firms' discount factor is 0.6, how should
Firm 2 set its capacity constraint so that the collusive equilibrium can still be
supported? (Hint: The idea here is that, by limiting its own output, Firm 2
lets Firm 1 have a greater market share. As a result, Firm 1's gain of
1.d
deviating from the collusive agreement would be smaller.)
Transcribed Image Text:1.c Find the condition on & under which Firm 1 will not deviate from the collusive equilibrium. Knowing that both firms' discount factor is 0.6, how should Firm 2 set its capacity constraint so that the collusive equilibrium can still be supported? (Hint: The idea here is that, by limiting its own output, Firm 2 lets Firm 1 have a greater market share. As a result, Firm 1's gain of 1.d deviating from the collusive agreement would be smaller.)
1. Two firms compete in price in a market for infinite periods. In this market,
there are N consumers; each buys one unit per period if the price does not
exceed $10 and nothing otherwise. Consumers buy from the firm selling at
a lower price. In case both firms charge the same price, assume N/2
consumers buy from each firm. Assume zero production cost for both firms.
A possible strategy that may support the collusive equilibrium is: Announce
a price of $10 if the equilibrium price has always been $10; otherwise,
announce the price as in Nash equilibrium of the one-shot Bertrand game.
Transcribed Image Text:1. Two firms compete in price in a market for infinite periods. In this market, there are N consumers; each buys one unit per period if the price does not exceed $10 and nothing otherwise. Consumers buy from the firm selling at a lower price. In case both firms charge the same price, assume N/2 consumers buy from each firm. Assume zero production cost for both firms. A possible strategy that may support the collusive equilibrium is: Announce a price of $10 if the equilibrium price has always been $10; otherwise, announce the price as in Nash equilibrium of the one-shot Bertrand game.
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