The demand for a monopoly's output is p = 200

Question

The demand for a monopoly's output is p = 200 - Q.The monopoly's production function is Q = 2L,and the market wage is $4.How many units of labor will the monopolist employ at its profit maximization level of output?
A) L = 49.5
B) L = 4623
C) L = 198
D) L = 10

Quizplus · Accepted Answer

To find the profit-maximizing level of output for the monopolist, we first need to determine the marginal revenue (MR) and marginal cost (MC) and set them equal to each other. The demand function is given as p = 200 - Q. To find MR, we differentiate the total revenue (TR = p*Q) with respect to Q. Since TR = (200 - Q)Q, MR = 200 - 2Q. The production function is Q = 2L, implying that the marginal product of labor (MPL) is 2. The marginal cost (MC) is the wage (W) divided by the MPL, so MC = W/MPL = 4/2 = 2. Setting MR = MC gives 200 - 2Q = 2. Solving for Q gives Q = 99. Since Q = 2L, solving for L gives L = 99/2 = 49.5.