There are two firms in the market for tires which has demand given by P = 480 0.25Q where Q = q1 + q2 is the total output in the market. Both of the firms have constant marginal cost c = 60 and the two firms compete in quantities (Cournot competition). Assume that this market game is being played infinitely many times by the two firms

a. Suppose that the two firms colluded and agreed to each produce half of the monopoly output. Solve for the value of collusion V C and the value of deviation V D. What is the minimum discount factor required to sustain collusion? (10 pts)

b. Now suppose that the government forms an antitrust authority whose job is to prevent the firms from colluding. This authority could detect collusion with probability q = 0.2 but for political reasons, the largest fine they could impose on a firm caught colluding is F = 2500. What is the highest possible discount value of firms that they could successfully prevent from colluding. (5 pts)

c. Suppose that the government's antitrust authority only cares about consumer surplus. What is the most the government would be willing to pay in order to prevent collusion? (5 pts)

Please answer all parts and be as detailed as possible. Thank you