There are two firms in the blastopheme industry.The demand curve for blastophemes is given by p = 1,500 - 2q.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)and only if each firm produces 150 units in its plant. B)they produce a total of 300 units, no matter which firm produces them. C)they produce a total of 250 units, no matter which firm produces them. D)and only if they each produce a total of 375 units. E)they shut down one of the two plants, having the other operate as a monopoly and splitting the profits.

Question

Quizplus · Accepted Answer

To maximize joint profits, the firms in the cartel will produce where marginal revenue equals marginal cost. From the demand curve, we can determine that the marginal revenue for each firm is MR = 1500 - 4q. From the cost function, we can determine the marginal cost for each firm is MC = P1 + 2q. Setting MR = MC for each firm, we get:

1500 - 4q = P1 + 2q
P1 = 1500 - 6q

Substituting this expression for P1 into each firm's cost function and solving for q, we find that each firm will produce 150 units. Therefore, the best choice is A, and only if each firm produces 150 units in its plant.

There Are Two Firms in the Blastopheme Industry