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) = 56 - p.

Question

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To maximize total profit, the firms should produce where marginal cost equals marginal revenue. Firm 1's marginal cost is constant at 8, while Firm 2's marginal cost is 2y. Solving for the optimal production levels given the demand curve and cost functions, Firm 1 should produce 20 units and Firm 2 should produce 4 units to maximize total profit and then split it equally.

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