Collusion with n Firms: Suppose there are n firms, each with cost c(q) = q, playing the repeated Cournot quantity setting game. All firms discount future periods at rate be (0, 1). Assume the inverse market demand is p(q) = a - bq. Consider the following profile of strategies: . Each firm sets quantity qi = 2 in the first period, and continues setting this quantity as long as nobody has deviated from it in the past. . If any firm has deviated from this strategy, all firms play the Cournot Nash Equilibrium quantity in all future periods. We are interested in knowing when this profile of strategies constitute a Subgame Perfect Equilibrium. (a) What are the profits of each firm in the current period if all firms choose the Cournot Nash Equilibrium quantities? (b) If the firms collude to maximize collective profits in the current period, what are the profits of each firm? (c) If the other n-1 firms in the market were all choosing the collusive level of output, what quantity of output maximizes the profits of the n-th firm in the current period? What are the profits this firm would receive in the current period? (d) Based on your answers to part (a)-(c), determine the level of patience necessary to support the above strategies as a Subgame Perfect Equilibrium. (e) How does your answer to part (d) vary with n? What does this tell you about how easy or difficult it is to support collusion when the number of firms increases? (f) Can you think of other reasons, outside this model, for why collusion may be more difficult in a repeated model if the number of firms increased