4. Imagine a market with demand P = 420 – Q in each period. Two firms are thinking about colluding. They each have cost C(Qi) = 60Qi. If they cooperate and behave as a monopoly, then they have a marginal revenue curve, MRm = 420 – 2Q, and a marginal cost curve, MCm = 60. If they are in a cartel, then the firms will split the monopoly production and profits. If they compete, then they face MRi = 420 – 2Qi – Q-I and MCi = 60. a. If the firms stick to their agreement (cooperate), how much per-period profit do they each make? b. If they are not able to maintain their agreement (compete), what is their per-period profit? c. If one firm cheats on their agreement (deviate), how much does each firm make? Be sure to specify both the profit for the cheater and the firm cheated-on.
4. Imagine a market with demand P = 420 – Q in each period. Two firms are thinking about colluding. They each have cost C(Qi) = 60Qi. If they cooperate and behave as a
a. If the firms stick to their agreement (cooperate), how much per-period profit do they each make?
b. If they are not able to maintain their agreement (compete), what is their per-period profit?
c. If one firm cheats on their agreement (deviate), how much does each firm make? Be sure to specify both the profit for the cheater and the firm cheated-on.
d. Suppose the firms assume that their interaction will last forever (r = 1) and they share the common discount value R. What is the lowest value of R such that both firms are willing to continue with the cartel agreement described above?
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