3. Two firms compete in the market for a homogeneous product. Market demand is given by P(Q) = 240 -Q, where P is the market price and Q is the aggregate market output. Each firm has a constant margina costs of c and no fixed costs: C(q) = cq, where c = 12Y and Y is the number you calculated earlier based on your SID. The firms compete by simultaneously choosing output. (a) Suppose a single firm operates in the market. Find the profit-maximising price and quantity of the monopolist. Label the monopoly output qm. What are the monopolist's profits, Im? [3 marks] (b) Suppose the two firms interact for a single period. i. Find the reaction function for each firm. [3 marks] ii. Solve for the Nash equilibrium outputs of each firm. [2 marks] c) Suppose instead the two firms compete by simultaneously choosing output over an infinite horizon. Both firms have the same discount factor, 8. We want to find the sustainability of collusion on the monopoly output using a variation of the grim trigger strategy. Define qc = 9m/2 as half of the monopoly output you calculated earlier. The firms consider the following collusive strategies: . produce q = qe in the first period OR if both firms produced q last period OR if both firms produced qm last period; . produce q = 9m otherwise. These strategies involve a single period of harsh punishment in which both firms each produce the monopoly output (so that Q = 2qm) before returning to the collusive output. Punishment is said to be credible if all players have an incentive to carry out the punishment. i. Assume that the punishment is credible. For what values of o do both players have an incentive to cooperate? Explain carefully how you derived your answer. [6 marks] ii. For what values of o is the punishment credible? Explain carefully how you derived your answer. [6 marks]