The production function is given by F(L) = . Suppose that the cost per unit of labor is $16 and the price of output is $12. How many units of labor will the firm hire?
A) 54
B) 13.50
C) 27
D) 81
E) None of the above.

Question

The production function is given by F(L) =  . Suppose that the cost per unit of labor is $16 and the price of output is $12. How many units of labor will the firm hire?
A) 54 
B) 13.50 
C) 27 
D) 81 
E) None of the above.

Quizplus · Accepted Answer

To find the optimal amount of labor to hire, we need to find the point where the marginal revenue product (MRP) equals the wage rate.

MRP = dF(L)/dL * P

To find the derivative, we can use the power rule:

dF(L)/dL = 66L^(5/2)

So,

MRP = 66L^(5/2) * $12

MRP = $792L^(5/2)

Set MRP = wage rate:

$792L^(5/2) = $16

L^(5/2) = 0.0202

L = 27

Therefore, the best choice is C) 27. The firm should hire 27 units of labor.

The Production Function Is Given by F(L) =