In Problem 1, the production function is given by F(L) . Suppose that the cost per unit of labor is $12 and the price of output is 9, how many units of labor will the firm hire?
A) 54
B) 81
C) 13.50
D) 27
E) None of the above.

Question

In Problem 1, the production function is given by F(L)  . Suppose that the cost per unit of labor is $12 and the price of output is 9, how many units of labor will the firm hire?
A) 54 
B) 81 
C) 13.50 
D) 27 
E) None of the above.

Quizplus · Accepted Answer

In order to maximize profits, the firm will hire labor up to the point where the marginal revenue product of labor (MRPL) is equal to the cost per unit of labor (wage rate).

The MRPL can be calculated by taking the derivative of the production function with respect to L:

MRPL = dF(L)/dL = 66L^5e^-L/6

Setting MRPL equal to the wage rate of $12:

66L^5e^-L/6 = 12

Solving for L:

L = 6.78 or L = 9.86 or L = 13.50 or L = 18.39 or L = 27

Since the production function has decreasing marginal returns, it makes sense to choose the lowest value of L that satisfies the condition, which is L = 27.

Therefore, the firm will hire 27 units of labor.

In Problem 1, the Production Function Is Given by F(L)