2. Suppose that two rms selling homogeneous products compete in prices (Bertrand) in a market in which demand is described by P = 100 Q. Each rm incurs no xed cost but has a marginal cost of 20. They would like to engage in collusion by acting as a monopolist (i.e. maximizing total industry prots), and sharing the prots equally between them. In order to sustain the monopoly outcome as a cartel1 the rms play the following non-forgiving trigger strategy: play cooperation [i.e. monopoly outcome) in the current period so long as the other rm has cooperated in every previous period and play the Bertrand Nash equilibrium if there has ever been a deviation from the monopoly outcome. Let p be the probability that the game continues the next period and R be the discount factor. (a) What probability adjusted discount factor Rp is necessary to sustain a cartel agreement on the monopoly outcome? Hint: When a rm cheats, it needs to undercut the other rm only slightly to capture almost the entire monopoly prot (as rms haue unlimited capacity and sell homogeneous products). Therefore, to answer this question, assume that if one rm cheats, it captures the entire monopoly prot. [10 marks] (b) What is the per-period efciency loss due to the cartel? [10 marks] (c) Explain what is the Folk Theorem for innitely repeated games. Illustrate this Theorem graphically using the game detailed above. [10 marks] (d) Suppose that prices cannot be adjusted immediately: if a rm deviates from the monopoly outcome in period t, the other rm will adjust its price and play the Bertrand Nash equilibrium from period t + 2 onward. Show that an adjusted discount factor of Rp = 0.55 is not large enough to sustain a cartel on the monopoly outcome. Explain the intuition. [10 marks] (e) Explain why a non-forgiving trigger strategy is potentially too harsh in a world where the market demand is uncertain. How can we modify the trigger strategy to overcome this issue? [10 marks]