3. Two firms are operating as a cartel. The stage game is very similar to the one in Question 1. Firms engage in Bertrand pricing, each firm has a constant marginal cost equal to c = 4, and the firms sell a homogenous, perfectly substitutable output. Demand is given by D(P) = 12 P, and the collusive arrangement has it that they split the market evenly. Unlike question 1, there are no demand shocks. The firms decide that the grim trigger strategy punishes collusion too harshly. Instead, they decide that the punishment should only last for T periods. This means that if in any period t, one of the firms cheats on the agreement, then the firms will revert back to Bertrand pricing for the next T periods (i.e. in period t +1, +2, all the way to period t +T). Once the T periods of punishment have elapsed, the firms will then go back to cooperating For example, if T = 2, that means that after a firm cheats, the two firms charge the Bertrand price for 2 periods, and go back to cooperating thereafter. (a) Suppose T = 1. For what values of 8, the discount factor, will the above collusive strategy be a SPNE? (Remember to calculate the present value of profits for each firm if it cooperates and if it deviates from the agreement.) (b) Suppose T = 2. For what values of 8, the discount factor, will the above collusive strategy be a SPNE? (c) Suppose T = 5. For what values of 8, the discount factor, will the above collusive strategy be a SPNE? 3. Two firms are operating as a cartel. The stage game is very similar to the one in Question 1. Firms engage in Bertrand pricing, each firm has a constant marginal cost equal to c = 4, and the firms sell a homogenous, perfectly substitutable output. Demand is given by D(P) = 12 P, and the collusive arrangement has it that they split the market evenly. Unlike question 1, there are no demand shocks. The firms decide that the grim trigger strategy punishes collusion too harshly. Instead, they decide that the punishment should only last for T periods. This means that if in any period t, one of the firms cheats on the agreement, then the firms will revert back to Bertrand pricing for the next T periods (i.e. in period t +1, +2, all the way to period t +T). Once the T periods of punishment have elapsed, the firms will then go back to cooperating For example, if T = 2, that means that after a firm cheats, the two firms charge the Bertrand price for 2 periods, and go back to cooperating thereafter. (a) Suppose T = 1. For what values of 8, the discount factor, will the above collusive strategy be a SPNE? (Remember to calculate the present value of profits for each firm if it cooperates and if it deviates from the agreement.) (b) Suppose T = 2. For what values of 8, the discount factor, will the above collusive strategy be a SPNE? (c) Suppose T = 5. For what values of 8, the discount factor, will the above collusive strategy be a SPNE