Minimum punishment amount to thwart that cheating


Problem: Consider an oligopolistic market wherein firms are setting quantity. The 3 firms in this industry have identical cost structures: MC = 10, and each have a capacity of 9 units. The market demand curve is P = 100-5Q. Suppose a collusive agreement at the monopolistic equilibrium has been established. However, one of the firms is now considering cheating by producing at full capacity. What is the minimum punishment amount to thwart that cheating? (You may assume the punishment threat is credible and that a punishment equal to the incentive to cheat is successful at thwarting cheating).

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