Question

Two oligopolies (Firm A and Firm B) have access to the same the same technology and have similar costs. FC = 0 MC = AVC = ATC = $100 Assume the demand of the product is given below: P=1000-Q Remember Q= q_A+ q_B Where q_(A ) is production by firm A and q_B-is production by firm B (a) Assume that they compete with price. i. How low can the price would go? Explain ii. Obtain the competitive price, quantity produced and profits for each firm. (b) Assume not that the firm now can agree on production and decides to behave like a monopoly. i. Obtain the price of the product if they can keep the monopoly agreement and the qa and qb. ii. Obtain Economic profit for each firm iii. Using the logic of prisoner’s dilemma explain why it is difficult to maintain these agreements.

Answer 1

Given that

FC = 0 MC = AVC = ATC = $100

Demand is P=1000-Q, Q= qA+ qB

(a) i. The price would not fall below the marginal cost because then the firms will have no incentive to sell. Since MC = AVC, it is the minimum price that they would be willing to sell.

ii. Since they compete on prices and are selling identical goods, competition will bring price to its minimum acceptable level which is 100. Hence, the competitive price is 100, quantity produced by the market is 1000 - 100 = 900 and by each firm is 900/2 = 450 units. Profits for each firm is 0 because P = AC = 100.

(b) i. As a monopoly they would produce using MR = MC. Here MR = 1000 - 2Q so we have 1000 - 2Q = 100 or Q = 900/2 = 450 units. Each firm produces 225 units. Price is 1000 - 450 = $550

ii. Economic profit for each firm = (550 - 100)*225 = 101250.

iii. Here it is difficult to maintain these agreements because if one of them cheats and supply more at a slightly reduced price, it will be able to sell everything and so each firm has an incentive to cheat and break the agreement.