Question

A firm has the Cobb-Douglas production function $Q(K, L) = K^{\frac{1}{4}}L^{\frac{1}{2}}$, and $K$ is fixed at 81 units. What is the marginal product of labor if $L$ is equal to 100 units? 3.0 None of the answers is correct. 0.05 0.3 0.15

          A firm has the Cobb-Douglas production function $Q(K, L) = K^{\frac{1}{4}}L^{\frac{1}{2}}$, and $K$ is fixed at 81 units. What is the marginal product of labor if $L$ is equal to 100 units?
3.0
None of the answers is correct.
0.05
0.3
0.15

A firm has the Cobb-Douglas production function Q(K, L) = K^(1)/(4)L^(1)/(2), and K is fixed at 81 units. What is the marginal product of labor if L is equal to 100 units?
3.0
None of the answers is correct.
0.05
0.3
0.15

Added by Stacy E.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Jennifer Stoner

02/22/2022

Step 1

The marginal product of labor (MPL) is the partial derivative of the production function with respect to L: $\text{MPL} = \frac{\partial Q}{\partial L} = \frac{1}{2}K^{\frac{1}{4}}L^{\frac{1}{2}-1} = \frac{1}{2}K^{\frac{1}{4}}L^{-\frac{1}{2}} = \frac{1}{2} Show more…

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A firm has the Cobb-Douglas production function $Q(K, L) = K^{\frac{1}{4}}L^{\frac{1}{2}}$, and $K$ is fixed at 81 units. What is the marginal product of labor if $L$ is equal to 100 units? 3.0 None of the answers is correct. 0.05 0.3 0.15