You are the manager of a firm that produces output in two plants.The demand for your firm's product is P = 78 − 15Q,where Q = Q₁ + Q₂.The marginal costs associated with producing in the two plants are MC₁ = 3Q₁ and MC₂ = 2Q₂.What price should be charged to maximize profits? A) $20.5 B) $40.5 C) $60.5 D) $80.5

Question

Quizplus · Accepted Answer

To maximize profits, the firm should produce where marginal cost equals marginal revenue: MC₁ = MR = P/(1 + ∂Q1/∂Q2) Taking the partial derivative, we get: ∂Q1/∂Q2 = (15/2)(Q₁/Q₂) Substituting this and the given marginal costs into the equation, we obtain: 3Q₁ = (78 − 15Q)/(1 + 15Q₁/2Q₂) Solving for Q, we obtain: Q = 14.25 Substituting this into the demand equation, we obtain: P = $40.5 Therefore, the best choice is B, with a price of $40.5.

You Are the Manager of a Firm That Produces Output