A monopoly has two production plants with cost functions C₁ = 50 + 0.1Q₁² and C₂ = 30 + 0.05Q₂².The demand it faces is Q = 500 − 10P.What is the profit-maximizing level of output? A) Q₁ = 62.5; Q₂ = 125. B) Q₁ = 125; Q₂ = 62.5. C) Q₁ = Q₂ = 125. D) Q₁ = Q₂ = 62.5.

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Quizplus · Accepted Answer

To find the profit-maximizing level of output, we first determine the total cost and revenue functions. The total cost (TC) is the sum of the costs of both plants: TC = CS1 + CS2 = 50 + 0.1QS1 + 30 + 0.05QS2. The demand function is Q = 500 - 10P, which can be rearranged to find the price as a function of quantity: P = 50 - 0.1Q. Total revenue (TR) is P*Q, which becomes (50 - 0.1Q)Q. To maximize profit, we set marginal cost (MC) equal to marginal revenue (MR). Since the cost functions of the plants differ, we allocate production to the more efficient plant (with lower marginal cost) first. Plant 2 has a lower marginal cost (0.05 per unit) than Plant 1 (0.1 per unit), so we maximize output from Plant 2 before using Plant 1. The correct allocation that maximizes profit given the constraints and cost structures is QS1 = 62.5 and QS2 = 125, as it balances the marginal costs with the overall demand and price structure efficiently.

A Monopoly Has Two Production Plants with Cost Functions C1

A Monopoly Has Two Production Plants with Cost Functions C₁