# Consider chemical fertilizer market in an isolated village

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 â Q be the market-clearing price when the aggregate quantity on the market is Q (= q1 + q2). (More precisely, P(Q) = 30 â 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 prisonerâ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 1âd (0