4. Cournot Duopoly A market is defined by: P(Q) = a – Q where market price is a function of aggregate quantity. There is also a constant cost per unit of c. a) Show profit (π) of a monopoly in terms of Q. b) Assume there are 3 firms that wish to collude. What would their profit function be in terms of qi c) Assume the market is perfectly competitive. What would be a firm's profit function be in terms of qi? Remember this game is symmetrical. c) Assume one firm wishes to back-stab the others and produce market quantity for one round. What would their profit function be in terms of q1, 92, and 93? d) Assume two of the three firms back-stab while one sucker still tried to collude. What would the sucker's profit function be in terms of 91, 92, and 93?
4. Cournot Duopoly A market is defined by: P(Q) = a – Q where market price is a function of aggregate quantity. There is also a constant cost per unit of c. a) Show profit (π) of a monopoly in terms of Q. b) Assume there are 3 firms that wish to collude. What would their profit function be in terms of qi c) Assume the market is perfectly competitive. What would be a firm's profit function be in terms of qi? Remember this game is symmetrical. c) Assume one firm wishes to back-stab the others and produce market quantity for one round. What would their profit function be in terms of q1, 92, and 93? d) Assume two of the three firms back-stab while one sucker still tried to collude. What would the sucker's profit function be in terms of 91, 92, and 93?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:4. Cournot Duopoly
A market is defined by: P(Q) = a – Q where market price is a function of aggregate quantity.
There is also a constant cost per unit of c.
a) Show profit (π) of a monopoly in terms of Q.
b) Assume there are 3 firms that wish to collude. What would their profit function be in terms
of qi
c) Assume the market is perfectly competitive. What would be a firm's profit function be in
terms of qi? Remember this game is symmetrical.
c) Assume one firm wishes to back-stab the others and produce market quantity for one round.
What would their profit function be in terms of q1, 92, and 93?
d) Assume two of the three firms back-stab while one sucker still tried to collude. What would
the sucker's profit function be in terms of 91, 92, and 93?
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