4. There are two rms in the market for tires which has demand given by P = 480 0.250 where Q = 91+ Q; is the total output in the marREt. Both of the rms have constant marginal cost c = 60 and the two rms compete in quantities (Cournot competition). Assume that this market game is being played innitely many times by the two rms a. Suppose that the two rms colluded and agreed to earth produce half of the monopoly output. Solve for the value of collusion VC and the value of deviation VD. What is the minimum discount factor ,3 required to sustain collusion? [10 pts) 13. Now suppose that the government forms an antitrust authority whose job is to prevent the rms from oolluding. This authority could detect collusion with probability q = 0.2 but for political reasons. the largest ne they could impose on a rm caught oolluding is F = 2500. What is the highest possible discount value ,6 of firms that they oould successfully prevent from oolluding. (5 pts) c. Suppose that the government's antitrust authority only cares about consumer surplus. What is the most the gavernment would be willing to pay in order to prevent collusion? (5 pts)