the production function is given by F(L)= 6L^2/3.Suppose that the cost per unit of labor is $8 and the price of output is 4, 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 profit, the firm will hire labor up to the point where the marginal product of labor (MPL) equals the wage rate. The MPL can be found by taking the derivative of the production function with respect to labor, which gives: MPL = F1F1F10 6^2/3 Plugging in the given values for the price of output and cost per unit of labor, we get: MPL = F1F1F10 6S1U11/3S1S1 To find the level of labor that maximizes profit, we need to equate MPL with the wage rate. Since the wage rate is $8 per unit of labor, we have: MPL = 8 F1F1F10 6S1U11/3S1S1 = 8 Solving for L, we get: L = (F1F1F10 6S1U11/3S1S1)/(8) Plugging in the given values, we get: L = (4*6*1*1^(1/3))/(8) L = 8 Therefore, the firm will hire 8 units of labor to maximize profit.

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

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