ECON 3050 Problem Set Unit 16 Prof. Rodet Unit 16: Collusion B&P; CH 9: 5,15 1.
ID: 1108913 • Letter: E
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ECON 3050 Problem Set Unit 16 Prof. Rodet Unit 16: Collusion B&P; CH 9: 5,15 1. Amarket has an inverse demand curve P = 100-2Q and two firms, each of which has a constant marginal cost of MC- 20. a. If the firms form a profit-maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output level, what is the market price produce (assume the firms in the cartel split the and how much does each firm market evenly)? Suppose the cartel breaks down. What is the market price and how much does each firm produce (assuming Cournot competition)? b. Firm 2 Low Quantity High Quantity Firm 1 Low Quantity 15, 15 0, 20 High Quantity 20,0 10, 10 The table above represents the prisoner's dilemma faced by a duopoly in the market for diamonds. 2. a. What is the collusive outcome? b. What is the Nash equilibrium? c How valuable must future profits be relative to current profits to make collusion a stable outcome? (ie. what is the minimum discount factor Many retail stores offer to match or beat the price offered by a tival store. Explain why firms that belong to a cartel might make this offer. 3.Explanation / Answer
Question 1
Market demand is P = 100 - 2Q and MCs are each $20.
a) Under cartel, the two firms produce monopoly output and charge a monopoly price to earn monopoly profit which then is divided equally
MR = 100 - 4Q
MR = MC
100 - 4Q = 20
Q* = 20 (10 units each)
P* = 100 - 40 = $60
Profits = (60 - 20)*20 = $800 ($400 by each firm)
b) If they breach the cartel agreement and produce Cournot output, their reaction functions are
MR1 = MC and MR2 = MC
100 - 4q1 - 2q2 = 20 100 - 4q2 - 2q1 = 20
2q1 + q2 = 40 2q2 + q1 = 40
Solve them to get q1 = q2 = 40/3 and P = 100 - 2*(80/3) = 140/3
Profit = (140/3 - 20)*80/3 = 6400/3 and 3200/3 for each firm.
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