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.What is the profit-maximizing price that the firm should charge? A) $8 B) $9 C) $11 D) $12

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Quizplus · Accepted Answer

To find the profit-maximizing price, we first need to determine the quantity that maximizes profit. The total quantity produced, Q, is the sum of quantities produced in both plants: Q = Q1 + Q2. Given the demand function P = 20 - Q and the marginal costs MC1 = 2 and MC2 = 2Q2, we equate marginal revenue (MR) to marginal cost (MC) for each plant. For a linear demand curve, MR = 20 - 2Q. Setting MR equal to MC for each plant and solving for Q1 and Q2 gives us the quantities that maximize profit. Since MC1 is constant and MC2 increases with Q2, we find the optimal Q by equating MR to the sum of MCs. Without the specific calculations here, the key is recognizing that the firm's profit maximization involves setting MR equal to the aggregate MC, and then using the demand function to find the corresponding price. Given the information and the options provided, the correct calculation leads to a profit-maximizing price of $11, which corresponds to the equilibrium where the firm's total marginal cost equals its marginal revenue, taking into account the output levels from both plants.

You Are the Manager of a Firm That Produces Output