Question

PRACTICE PROBLEMS FOR WEEK 6 Question: [Collusion when firms compete over time] Suppose two firms producing differentiated goods compete every day through prices. The demand for the good produced by firm i E {1,2} is qi = 24 – 5pi + 2p;. Firms can produce the goods with a constant marginal cost of production of O per unit. Hence, firm i's profit is given by T(Pi, p;) = (pi – 0) (24 – 5p; + 2p;). (a) What are firm profits for a single day in the Bertrand equilibrium? (b) What are firm profits for a single day if the firms collude? (c) What if firm 1 deviates from the collusive agreement? What are firm 1's single day profits? (d) Can collusion be sustained in this repeated game if firm 2 threatens to punish any deviation from the collusive agreement by charging in every subsequent day the Bertrand prices you found as part of solving (a)? Does it depend upon the discount factor ß? What is the intuition behind the result?

Answer 1

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