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4. Suppose a market has two firms that compete by setting prices p, and p2 simultaneously, with aggregate demand at p, the lowest price, given by Q = 100 - p. The marginal cost of production is 0 and there are no fixed costs. Suppose prices can only be set in $10 increments: $0, $10, $20,$30, ... a. The firms are considering forming a cartel. i. What price would maximize the cartel's profits? Denote this price pc. What would be the profits of each firm if they split the demand at pc equally? ii. What is the best response price of a firm if it expects the other firm to price at pc? b. Suppose this game is indefinitely repeated, and the associated probability-adjusted discount factor is p. Consider the following "Grim- Trigger Strategy" for a firm: Period t=1: set price at Pc. Period t >1: set price at pc if both firms set price at Pc in all past periods. Otherwise, set price at $10. Suppose it's the first period of the game. i. Assuming that the other firm is also using this strategy, what is the discounted sum of a firm's profit stream if it sticks to this strategy? ii. Assuming that the other firm is also using this strategy, what is the discounted sum of a firm's profit stream if it deviates (optimally) from this strategy in the current period, but sticks to it in all future periods? iii. Find a condition on p that would ensure that this firm will not deviate in the first period of the game