1. Consider two firms (i=1,2) interacting in the market. Assume that firms compete in quantities and therefore they choose either to cooperate or not in each round. If a firm deviates it earns monopoly profit for a round and a punishment phase will follow from next round onwards (for ever) where both firms choose the Cournot quantity. Assume a discounting factor & and that firms meet in the market in every period. The demand facing the industry is p = 1 92. Let Q = q1 + 92 denote the aggregate industry output - 91 - level. Assume further that production is costless. i. Derive the Cournot equilibrium (quantity, price, profits). (5 marks) ii. Derive the Cooperative equilibrium (quantity, price, profits). (5 marks) iii. Derive quantities, prices and profits if firm 2 deviates. (5 marks) iv. Find the discounting factor that sustains collusion. (5 marks) v. Now assume that firms meet in the market every two periods. Find the new discounting factor that sustains collusion. (5 marks) vi. Now allow for two identical and independent markets. Both firms participate in both markets. Assume that in market 1 firms meet every period and in market 2 they meet every second period. Derive the incentive constraint for collusion in both markets and the value of the discounting factor. Assume that a deviation in a market will be punished in the next period in both markets forever, by choosing the Cournot quantity. (10 marks) vii. Now assume a single market and that firms meet every period in the market but the punishment phase last for T rounds before firms revert to the collusive outcome. Write the incentive constraint and: 1-8Ꭲ 1-8 a. show that S ≥ 1.125 (10 marks) b. For a discounting factor 8 = 0.1 find the T that sustains collusion. (5 marks)
1. Consider two firms (i=1,2) interacting in the market. Assume that firms compete in quantities and therefore they choose either to cooperate or not in each round. If a firm deviates it earns monopoly profit for a round and a punishment phase will follow from next round onwards (for ever) where both firms choose the Cournot quantity. Assume a discounting factor & and that firms meet in the market in every period. The demand facing the industry is p = 1 92. Let Q = q1 + 92 denote the aggregate industry output - 91 - level. Assume further that production is costless. i. Derive the Cournot equilibrium (quantity, price, profits). (5 marks) ii. Derive the Cooperative equilibrium (quantity, price, profits). (5 marks) iii. Derive quantities, prices and profits if firm 2 deviates. (5 marks) iv. Find the discounting factor that sustains collusion. (5 marks) v. Now assume that firms meet in the market every two periods. Find the new discounting factor that sustains collusion. (5 marks) vi. Now allow for two identical and independent markets. Both firms participate in both markets. Assume that in market 1 firms meet every period and in market 2 they meet every second period. Derive the incentive constraint for collusion in both markets and the value of the discounting factor. Assume that a deviation in a market will be punished in the next period in both markets forever, by choosing the Cournot quantity. (10 marks) vii. Now assume a single market and that firms meet every period in the market but the punishment phase last for T rounds before firms revert to the collusive outcome. Write the incentive constraint and: 1-8Ꭲ 1-8 a. show that S ≥ 1.125 (10 marks) b. For a discounting factor 8 = 0.1 find the T that sustains collusion. (5 marks)
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.6P
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Transcribed Image Text:1. Consider two firms (i=1,2) interacting in the market. Assume that firms compete in
quantities and therefore they choose either to cooperate or not in each round. If a firm
deviates it earns monopoly profit for a round and a punishment phase will follow from next
round onwards (for ever) where both firms choose the Cournot quantity. Assume a
discounting factor & and that firms meet in the market in every period. The demand facing
the industry is p = 1 92. Let Q = q1 + 92 denote the aggregate industry output
-
91
-
level. Assume further that production is costless.
Transcribed Image Text:i. Derive the Cournot equilibrium (quantity, price, profits). (5 marks)
ii. Derive the Cooperative equilibrium (quantity, price, profits). (5 marks)
iii. Derive quantities, prices and profits if firm 2 deviates. (5 marks)
iv. Find the discounting factor that sustains collusion. (5 marks)
v. Now assume that firms meet in the market every two periods. Find the new discounting
factor that sustains collusion. (5 marks)
vi. Now allow for two identical and independent markets. Both firms participate in both
markets. Assume that in market 1 firms meet every period and in market 2 they meet every
second period. Derive the incentive constraint for collusion in both markets and the value
of the discounting factor. Assume that a deviation in a market will be punished in the next
period in both markets forever, by choosing the Cournot quantity. (10 marks)
vii. Now assume a single market and that firms meet every period in the market but the
punishment phase last for T rounds before firms revert to the collusive outcome. Write the
incentive constraint and:
1-8Ꭲ
1-8
a. show that S ≥ 1.125 (10 marks)
b. For a discounting factor 8 = 0.1 find the T that sustains collusion. (5 marks)
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