There are two firms in the blastopheme industry.The demand curve for blastophemes is given by p = 4,200 - 3q.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 600 units, no matter which firm produces them. B)they produce a total of 466.67 units, no matter which firm produces them. C)and only if they each produce a total of 700 units. D)and only if each firm produces of 300 units in its plant. 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 profit-maximizing quantity for a monopoly is q = 2/3 * (p - MC), where p is the price and MC is the marginal cost. In this case, p = 4,200 - 3q and MC = 2q. So, q = 2/3 * (4,200 - 3q - 2q) = 2/3 * (4,200 - 5q) = 2,800/5 - 4/3 * q. Solving for q, we get q = 300. So, each firm should produce 300 units to maximize joint profits.

There Are Two Firms in the Blastopheme Industry