Suppose a firm is a monopolist in its output market and a perfect competitor in its input market.The demand for its output is
.The firm's production is given by and the market wage is $50.The profit maximizing level of labor input is

Question

Suppose a firm is a monopolist in its output market and a perfect competitor in its input market.The demand for its output is

.The firm's production is given by Suppose a firm is a monopolist in its output market and a perfect competitor in its input market.The demand for its output is<sub> </sub> <sub> </sub> .The firm's production is given by and the market wage is $50.The profit maximizing level of labor input is A) 100 B) 1,000 C) 3,600 D) 5,000

and the market wage is $50.The profit maximizing level of labor input is

Quizplus · Accepted Answer

To find the profit maximizing level of labor input, we need to equate the marginal revenue product (MRP) of labor to the market wage rate. Since the firm is a monopolist in the output market, its marginal revenue (MR) will be less than the price (P) of the output. Therefore, to find the MRP, we need to multiply the marginal product of labor (MPL) by the marginal revenue (MR) of the output.

MPL = 10(300/L)^(1/2) = 3000/L^(1/2)

MR = ∂TR/∂Q = 600 - Q

MRP = MPL x MR
    = 3000Q/L^(1/2) - Q^2/L^(1/2)

Setting MRP equal to the market wage rate of $50, we get:

3000Q/L^(1/2) - Q^2/L^(1/2) = 50

Solving for Q, we get:
Q = 3600

Substituting Q back into the production function to find the corresponding level of labor input, we get:

L = 300(3600/10)^(1/2)
  = 1800

Therefore, the profit maximizing level of labor input is 1800, which corresponds to choice C.

Suppose a Firm Is a Monopolist in Its Output Market