3. Infinitely Repeated Bertrand Game Suppose that, just as in the previous problem, two firms compete in a market in which inverse demand is given by P = 260 - 2Q. Each firm incurs no fixed cost and has a marginal cost of 20. However, instead of competing in quantities, they compete in price.

a. What is the one period Nash equilibrium output, price and profits? b. What is the output of each firm if they collude to produce the monopoly output? How much profit does each firm earn from such collusion? c. If one firm decides to cheat on the agreement in which each firm produces half of the monopoly output, how much will it produce? What will be the industry price and profits of the two firms? d. Suppose the market game described above is now repeated forever. Find a pair of trigger strategies (i.e., carrot and stick) which can support the collusive agreement and show that it can be maintained if the discount factor is greater than 0.5