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(Solved) 3 Uollusion Consider two identical firms with constant marginal costs, 0, and no capacity con— straints who both discount future payoffs with...


3 Uollusion Consider two identical firms with constant marginal costs, 0, and no capacity con— straints who both discount future payoffs with discount factor 6. They interact repeat— edly in the same market, using Cournot competition. Demand is given by P(Q) = 1 — 2Q, where Q = q1 + (12. (a) (b) (d) Suppose the two firms successfully sustain a collusive game where each sets quan— tity so that price is at the monopoly level in every period and they share the monopoly profits equally. This strategy continues forever. Calculate each firm’s total discounted profits. Now suppose that one firm deviates in a single period. What is the deviating firm’s choice of quantity and what is its profit in that period? Assume that firms follow a ”trigger strategy” profile: if someone has deviated, all firms set static Cournot quantities forever. Show that collusion is sustainable provided firms are patient enough. Now suppose that the punishment (all firms 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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