If the production function is Q = K^.5L^.5 and capital is fixed at 9 units,then the marginal product of labor when L = 49 is: A) 3. B) 9/98. C) 3/14. D) None of the answers are correct.

Question

Quizplus · Accepted Answer

To find the marginal product of labor, we take the partial derivative of the production function with respect to labor (holding capital constant):

MP_L = (dQ/dL) = K*S1*U1*P1.5*S1*S1*P0*L^-0.5*U1*P1.5*S1*S1*P0

Substituting K = 9 and L = 49, we get:

MP_L = 9*S1*U1*P1.5*S1*S1*P0*49^-0.5*U1*P1.5*S1*S1*P0

Simplifying, we get:

MP_L = 3/14

Therefore, the correct answer is C.

If the Production Function Is Q = K