Question

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 $10 if the equilibrium price has always been $10; otherwise, announce the price as in the one-shot Bertrand game.

1.a. (3 points) Let x be the discount factor. Find the condition on x 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 zero.

1.b. (3 points) Find the condition on x under which Firm 2 will not deviate from the collusive equilibrium.

1.c. (3 points) Find the condition on x under which Firm 1 will not deviate from the collusive equilibrium.

1.d. (4 points) 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 is smaller.)

2. In 1986, the U.S. Congress enacted a regulation (PL99-509) requiring railroads to disclose contractual terms with grain shippers. Following the passing of the regulation, rates increased on corridors with no direct competition from barge traffic, while rates decreased on corridors with substantial direct competition. How do you interpret these events?

Answer 1

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