There are two firms in the market for tires which has demand given byP= 4800.25QwhereQ=q1+q2is the total output in the market. Both of the firms have constant marginal costc= 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 collusionVCand the value of deviationVD. What is the minimum discount factorrequired to sustain collusion?

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 probabilityq= 0.2 but for political reasons, the largest fine they could impose on a firm caught colluding isF= 2500. What is the highest possible discount valueof firms that they could successfully prevent from colluding.

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?