Suppose that two firms compete in quantities (Cournot) in a market in which demand is described by P = 100 Q. Each firm incurs no fixed cost but has a marginal cost of 10. They would like to engage in collusion by acting as a monopolist (i.e. maximizing total industry profits), and sharing the profits equally between them. In order to sustain the monopoly outcome as a cartel, the firms play the following non-forgiving trigger strategy: play cooperation (i.e. monopoly outcome) in the current period so long as the other firm has cooperated in every previous period and play the Cournot 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? [15 marks] (b) What is the per-period efficiency loss due to the cartel? [5 marks] (c) Explain what is the Folk Theorem for infinitely repeated games. Illustrate this Theorem graphically using the game detailed above. [10 marks] (d) Suppose that quantities cannot be adjusted immediately: if a firm deviates from the monopoly outcome in period t, the other firm will adjust its quantity and play the Cournot Nash equilibrium from period t + 2 onward. i. 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. [7 marks] ii. Show that a cartel agreement in which firms commit to produce qi = 28 (i = 1, 2) can be sustained with a probability-adjusted discount factor of Rp = 0.55. Explain intuitively why it is the case. [8 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?