There are two firms in the blastopheme industry.The demand curve for blastophemes is given by p = 6,600 - 5q.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 300 units in its plant. B)they produce a total of 600 units, no matter which firm produces them. C)and only if they each produce a total of 660 units. D)they produce a total of 440 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 A because under a cartel arrangement, the firms will maximize joint profits if they produce the quantity that maximizes total industry profits. The total industry profit function is given by:π = p * q - C(q₁) - C(q₂)= (6,600 - 5q) * q - q₁² - q₂²= 6,600q - 5q² - q₁² - q₂²To find the quantity that maximizes total industry profits, we take the derivative of the profit function with respect to q and set it equal to zero:dπ/dq = 6,600 - 10q = 0q = 660Therefore, the firms will maximize joint profits if they each produce 330 units in their plants.

There Are Two Firms in the Blastopheme Industry