3 Uollusion Consider two identical ï¬rms with constant marginal costs, 0, and no capacity conâ€” straints who both discount future payoffs with discount factor 6. They interact repeatâ€” edly in the same market, using Cournot competition. Demand is given by P(Q) = 1 â€” 2Q, where Q = q1 + (12. (a) (b) (d) Suppose the two ï¬rms successfully sustain a collusive game where each sets quanâ€” tity so that price is at the monopoly level in every period and they share the monopoly proï¬ts equally. This strategy continues forever. Calculate each ï¬rmâ€™s total discounted proï¬ts. Now suppose that one ï¬rm deviates in a single period. What is the deviating ï¬rmâ€™s choice of quantity and what is its proï¬t in that period? Assume that ï¬rms follow a â€trigger strategyâ€ proï¬le: if someone has deviated, all ï¬rms set static Cournot quantities forever. Show that collusion is sustainable provided ï¬rms are patient enough. Now suppose that the punishment (all ï¬rms setting Cournot quantitites) lasts for only T periods, with T < 00. Write down an inequality that must hold for any T that is large enough to deter deviation. Simplify the expression as much as you can.
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