Suppose that market demand is given by P = 260 - 2Q and that firms again have a

Question

Suppose that market demand is given by P = 260 - 2Q and that firms again have a constant
marginal cost of 20, while incurring no fixed cost, but now assume that the firms are Bertrand
competitors and have unlimited capacity.
a. What is the one-period Nash equilibrium market price? Assuming that firms share the market
evenly any time they charge the same price, what is the output and profit of each firm in this
equilibrium?
b. What is the output and profit of each firm if each agrees to charge the monopoly price?
5. Return to Problem 4. Assume that the cartel is established at the monopoly price. Suppose one rm
now deviates from the agreement assuming that its rival continues to charge monopoly price.
a. Given the deviating firm's assumption, what price will maximize its profits?
b. If the deviating firm's assumption is correct, how much will the profit of the cheating rm be?
How much will be the profit of its non-cheating rival?
6. Return again to the cartel in Problems 4 and 5. Now suppose that the market game repeated
indefinitely. What is the discount factor (sigma) is necessary now in order to maintain the collusive
agreement in an indenitely repeated setting?

Explanation / Answer

P =marginal cost =20 at equilibrium hence 260 -2Q =20 hence Q =120 profit =0

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