An industry has two colluding firms that act so as to maximize total profit in the industry and then split the profits equally. Firm 1 has cost function c(y) = 8y. Firm 2 has cost function c(y) = y². Each firm produces an integer number of units. Market demand is given by Y(p) = 72 - p.

Question

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First, we need to find the industry's total profit-maximizing output level. We can do this by finding the output level where marginal revenue (MR) is equal to marginal cost (MC). The market demand function is given as Y(p) = 72 - p. Solving for p, we get p = 72 - Y. The total revenue (TR) for the industry is then TR = pY = (72 - Y)Y = 72Y - Y^2. Differentiating TR with respect to Y, we get MR = 72 - 2Y. For Firm 1, we have c1(y1) = 8y1. Its marginal cost (MC1) is then 8. Setting MR equal to MC1, we get 72 - 2Y = 8, or Y = 32. For Firm 2, we have c2(y2) = y2². Its marginal cost (MC2) is then ². Setting MR equal to MC2, we get 72 - 2Y = ². Substituting Y = 32, we get ² = 4. Now we need to check whether this output level yields the same profit for both firms. The profit for Firm 1 is (p1 - MC1)y1 = (72 - 32 - 8)16 = 576. The profit for Firm 2 is (p2 - MC2)y2 = (72 - 4 - ²)16 = 576. Therefore, both firms earn equal profits of 576, which they split equally. Therefore, the best choice is D: Firm 1 should produce 28 units and firm 2 should produce 4 units, which yields a total industry output of 32 units and total profits of 1152, split equally between the two firms.

An Industry Has Two Colluding Firms That Act So as to Maximize