You are the manager of a firm that produces output in two plants.The demand for your firm's product is P = 20 − Q,where Q = Q₁ + Q₂.The marginal costs associated with producing in the two plants are MC₁ = 2 and MC₂ = 2Q₂.How much output should be produced in plant 1 in order to maximize profits? A) 1 B) 4 C) 8 D) 11

Question

Quizplus · Accepted Answer

To maximize profits, we must equate marginal revenue to marginal cost in each plant. The marginal revenue is given by MR = P(1+1/ε), where ε is the price elasticity of demand. In this case, ε = -1, so MR = 10 - Q/2. For plant 1, we have: MR = MC₁ 10 - Q/2 = 2 Q/2 = 8 Q = 16 Therefore, plant 1 should produce 8 units of output to maximize profits.

You Are the Manager of a Firm That Produces Output