Problem 1: Repeated Cournot and Collusion. Consider the following repeated Cournot game. The marginal cost is M C = 40. Demand is Q = 100 P. Firm 1 chooses a quantity g: at each year t = 1,2,... (similarly rm 2 chooses q). Quantities are either 20 or 15. Consider the following \"tit for tat\" strategy: Firm 1 produces 15 units in year 1. In each following year, rm 1 produces 15 units, unless rm 2 produced 20 units in the year before, in which case rm 1 produces 20 units. Firm 2's strategy is identical to rm 1's (i.e., 15 units in year 1, and 15 units in each following year unless rm 2 produced 20 units in th_e year before]. Assume the discount rate is r = 1. (a) Write down the formula for rm 1's strategy. (b) If both rms are following the above tit for tat strategy, what is the present value of the payoff of each rm? (o) Is it a Nash equilibrium for both rms to follow the above tit for tat strategy? Why? Hint. The present value of payoff of as every year starting at year T is W