6. SYMMETRIC FIRMS AND MULTIMARKET CONTACT Firm NY's main headquarters and production plant are in New York City and Firm SD's main headquarter and production plants are in San Diego. Both firms produce exactly the same good, which is purchased only by consumers in the New York and San Diego markets. The marginal cost of producing one more unit of the good are equal to c = 2. In other words, firms are identical. Transporting a unit of the good from one city to the other costs t = 1. Firms compete in prices and the demand for the good is equal to qsd = 9-P in San Diego (sd), and to qny = 9 -p in New York (ny). Firms interact repeatedly in both markets. The time horizon is infinite, in the sense that in any period firms assume that they will keep on interacting for the foreseeable future. (1) Suppose that Firm NY and Firm SD meet and discuss a collusive deal. The pro- posal is that each firm operates only in their own market. That is, Firm NY would operate exclusively in New York and Firm SD would operate exclusively in San Diego. Determine the per-period profit that a firm would make if they used this arrangement. 3 (2) Assume that the proposal for a collusive deal changes. In the alternative arrange- ment both firms would operate in both markets and split the markets in half. Determine the per-period profit that a Firm would make if they used this arrange- ment. Is this arrangement preferable to the one proposed previously? Does your answer change if t = 0? (3) Assume from now on that t = 0. Find the value of deviating from the collusive agreement described in (1) in case firms use a grim-trigger strategy. (4) A dollar next period is valued at o in the current period. Assuming firms use the collusive arrangement described in (1), find the lowest value of & such that firms will not want to deviate from collusion