Two firms sell parking for football games and set prices at the beginning of the season. If the firms collude, they each earn a profit of $100,000 per year. If one firm cheats on the collusive agreement and sets a lower price, they earn $150,000 and the rival earns $25,000. If the firms compete, they both earn $50,000 per year. The discount factor is and firms are assumed to use a grim trigger strategy if they collude. (a) Write an equation (as a function of ) for the present value of colluding forever. (b) Write an equation (as a function of ) for the present value of cheating on the collusive agreement. (c) For what values of will firms have no incentive to cheat on the collusive agreement? 2. There are two steel companies operating in a country, Firm A and Firm B. The market demand is estimated to be Q(P ) = 1000 50P where P is price and Q is quantity. Marginal cost is $8 per unit for both firms. The firms simultaneously decide how much steel to produce at the beginning of the year and then prices adjust so that supply equals demand