Problem 1: Repeated Cournot and Collusion. Consider the following repeated Cournot game. The marginal cost isMC=40. Demand isQ=100P. Firm 1 chooses a quantityq1lat each yeart=1,2,...(similarly firm 2 choosesq2t). 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, firm 1 produces 15 units, unless firm 2 produced 20 units in the year before, in which case firm 1 produces 20 units. Firm 2's strategy is identical to firm 1's (i.e., 15 units in year 1 , and 15 units in each following year unless firm 2 produced 20 units in the year before). Assume the discount rate isr=2. (a) Write down the formula for firm 1's strategy. (b) If both firms are following the above tit for tat strategy, what is the present value of the payoff of each firm? (c) Is it a Nash equilibrium for both firms to follow the above tit for tat strategy? Why? Hint. The present value of payoff ofaevery year starting at yearTisr(1r)T1a.