The production function is given by F(L)= 6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $16.How many units of labor will the firm hire? A)192 B)64 C)32 D)128 E)None of the above.

Question

Quizplus · Accepted Answer

To determine the optimal level of labor, we need to find the point where the marginal revenue product of labor (MRPL) equals the cost of labor (Wage). That is, MRPL = Wage.
MRPL = MP x P = F'(L) x P
= [(6F1F1U1P1/3S1) x (F1S1)/F1F1] x P
= (6U1P1/3S1) x (S1P0) = 2P0U1
= 2 x 16 = 32
Wage = $16
Therefore, MRPL = Wage implies 32L = 16 or L = 16/32 = 0.5.
Since L represents the number of units of labor, the closest option is B, i.e. 64 units of labor.

The Production Function Is Given by F(L)= 6L2/3

The Production Function Is Given by F(L)= 6L^2/3