Consider chemical fertilizer market in an isolated village where suppliers are limited to two at most. Let q1 and q2 denote the quantities of homogeneous fertilizer produced by firms 1 and 2 respectively. Let P(Q) = 30 – Q be the market-clearing price when the aggregate quantity on the market is Q (= q1 + q2). (More precisely, P(Q) = 30 – Q for Q < 30, and P(Q) = 0 for Q ? 30.) Assume that the total cost for firm i (i = 1 and 2) of producing qi is Ci (qi) = 6qi. That is, there are no fixed costs for both firms and the constant marginal cost is common to two firms at 6.
Consider the interaction between firm 1 and firm 2 in the long-run in this market by appropriately constructing infinite repeated prisoner’s dilemma game. At each stage, both firms independently and strategically set their own production quantities to maximize their own expected profits in the long run. The transactions can potentially continue forever, however, there is a probability of 1–d (0<d<1) that the government lifts import restriction for chemical fertilizer, which leads to entries of foreign firms. Those foreign firms have much lower marginal costs with better production technology, and thus will absorb all the demand thereafter in every stage (Two domestic producers will then be closed down). Specify the range of d?which makes cartel self-enforceable. In answering this, clearly state the payoff matrix and make explicit the “strategy” of the firms. You may
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