I don't know how to solve this question

4. [SA] Here, we'll consider a modification to the repeated Bertrand duopoly ex- ample from class. We still have D(p) = 1000 - 20p and MC = 10. There are no fixed costs. Recall that a monopoly results in p" = 30, (" = 400, II" = 8000 here. Consider the following Grim-Trigger strategy: . Firms collude and play p, = p2 = 30, with Firm 1 serving = of the market (and Firm 2 serving = of the market) in every period until either firm deviates. . After a deviation, firms play p1 = p2 = 10 forever. (The market split doesn't matter at this point.) (a) How much profit per period does each firm receive when colluding? (Hint: they should differ.) If a firm deviates in some period, what is its deviation strategy and how much profit does the firm receive in that period? (b) Suppose both firms have a common discount factor, 6. For what range of values of 6 can this Grim-Trigger strategy sustain collusive pricing? (Hint: Both firms must be willing to collude. Your answer should not include a range of o where one of the firms is willing but the other isn't.)