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Suppose that N 3 firms produce the same good at the same constant marginal cost c = 20 and compete la Cournot. There are no fixed costs. The market demand that the firms face is P(Q) = 14010Q (each period). The horizon is infinite (T = +), and all firms discount the future by the same discount factor (0, 1). If these firms compete repeatedly, they may be able to earn higher profits by engaging in tacit collusion. Let be the minimum discount factor that sustains collusion. Answer the following questions. (a) Calculate the (per-period) quantities, price, and profits in the one-shot (non-collusive) Cournot equilibrium and in the case when all firms merge. [8 marks] (b) How can the N firms use tacit collusion in the repeated game to jointly earn the same profit each period as the merged firm from part (a)? Write down explicitly the grim trigger strategies that the firms follow to achieve this. Do not yet attempt to verify whether these strategies form an equilibrium or to compute . [5 marks] (c) Given your answer to part (b), determine , the minimum discount factor that sustains this collusive outcome, for the special case when N = 3. [6 marks] (d) Suppose that initially there are N = 3 firms, as in part (c), but then two of the three firms merge. Determine , the minimum discount factor that sustains the collusive outcome after the merger. Is collusion now easier or harder to sustain than in the baseline case?

Question 1 Suppose that N 3 firms produce the same good at the same constant marginal cost c = 20 and compete la Cournot. There are no fixed costs. The market demand that the firms face is P(Q) = 140-10Q (each period). The horizon is infinite (T= +), and all firms discount the future by the same discount factor & (0, 1). If these firms compete repeatedly, they may be able to earn higher profits by engaging in tacit collusion. Let ** be the minimum discount factor that sustains collusion. Answer the following questions. (a) Calculate the (per-period) quantities, price, and profits in the one-shot (non-collusive) Cournot equilibrium and in the case when all firms merge. (8 marks) (b) How can the N firms use tacit collusion in the repeated game to jointly earn the same profit each period as the merged firm from part (a)? Write down explicitly the grim trigger strategies that the firms follow to achieve this. Do not yet attempt to verify whether these strategies form an equilibrium or to compute 8*. (5 marks) (c) Given your answer to part (b), determine 8*, the minimum discount factor that sus- tains this collusive outcome, for the special case when N = 3. (6 marks) (d) Suppose that initially there are N = 3 firms, as in part (c), but then two of the three firms merge. Determine 8 **, the minimum discount factor that sustains the collusive outcome after the merger. Is collusion now easier or harder to sustain than in the baseline case? (6 marks) (Total 25 marks) Question 1 Suppose that N 3 firms produce the same good at the same constant marginal cost c = 20 and compete la Cournot. There are no fixed costs. The market demand that the firms face is P(Q) = 140-10Q (each period). The horizon is infinite (T= +), and all firms discount the future by the same discount factor & (0, 1). If these firms compete repeatedly, they may be able to earn higher profits by engaging in tacit collusion. Let ** be the minimum discount factor that sustains collusion. Answer the following questions. (a) Calculate the (per-period) quantities, price, and profits in the one-shot (non-collusive) Cournot equilibrium and in the case when all firms merge. (8 marks) (b) How can the N firms use tacit collusion in the repeated game to jointly earn the same profit each period as the merged firm from part (a)? Write down explicitly the grim trigger strategies that the firms follow to achieve this. Do not yet attempt to verify whether these strategies form an equilibrium or to compute 8*. (5 marks) (c) Given your answer to part (b), determine 8*, the minimum discount factor that sus- tains this collusive outcome, for the special case when N = 3. (6 marks) (d) Suppose that initially there are N = 3 firms, as in part (c), but then two of the three firms merge. Determine 8 **, the minimum discount factor that sustains the collusive outcome after the merger. Is collusion now easier or harder to sustain than in the baseline case? (6 marks) (Total 25 marks)

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