There are two firms in the blastopheme industry.The demand curve for blastophemes is given by p = 4,500 - 4q.Each firm has one manufacturing plant and each firm i has a cost function C(q_i)= q²i, where q_i is the output of firm i.The two firms form a cartel and arrange to split total industry profits equally.Under this cartel arrangement, they will maximize joint profits if A)they produce a total of 375 units, no matter which firm produces them. B)and only if each firm produces 250 units in its plant. C)and only if they each produce a total of 562.50 units. D)they produce a total of 500 units, no matter which firm produces them. E)they shut down one of the two plants, having the other operate as a monopoly and splitting the profits.

Question

Quizplus · Accepted Answer

The correct answer is B because under a cartel arrangement, firms will maximize joint profits if they produce at the quantity where the marginal cost of the industry equals the industry's marginal revenue. In this case, the marginal cost of the industry is MC = 2q, and the industry's marginal revenue is MR = 4,500 - 8q. Setting MC = MR, we get 2q = 4,500 - 8q, which implies q = 500. Since there are two firms, each firm should produce 250 units to maximize joint profits.

There Are Two Firms in the Blastopheme Industry