need solution for only 1.d. Thanks a lot. Solution for 1d please. 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
I need solution for only 1.d. Thanks a lot.
Solution for 1d please.
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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.1.a Let δ be the discount factor. Find the condition on δ such that the above strategy can indeed support the collusive equilibrium.
Now suppose that Firm 2’s marginal cost is $4, but Firm 1’s marginal cost remains at zero.
1.b Find the condition on δ under which Firm 2 will not deviate from the collusive equilibrium.
1.c Find the condition on δ under which Firm 1 will not deviate from the collusive equilibrium.
1.d 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 deviating from the collusive agreement would be smaller.)
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