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 $8.How many units of labor will the firm hire? A)16 B)8 C)4 D)24 E)None of the above.

Question

Quizplus · Accepted Answer

To maximize profits, the firm will hire labor until the marginal revenue product of labor equals the cost per unit of labor.

The marginal revenue product of labor (MRPL) can be calculated by taking the derivative of the production function with respect to labor:

MRPL = F'(L) * P = (F1F1F1S1/U1P1/3) * $8

The cost per unit of labor is given as $16.

Setting MRPL equal to the cost per unit of labor and solving for L, we have:

(F1F1F1S1/U1P1/3) * $8 = $16

Simplifying this equation, we get:

F1F1F1S1/U1P1/3 = 2

Plugging in the given values, we have:

F1F1F1S1/U1P1/3 = 2
(1/6)*S1*U1*(P1^(-1/3)) = 2
Solving for U1, we get:

U1 = (2*6*(P1^(1/3)))/S1 = (2*6*(8^(1/3)))/1 = 2.5198

Therefore, the firm will hire approximately 2.5198 units of labor. Since this is not a realistic option, we choose the closest whole number option, which is B) 8.

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

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