Chapter 14, Problem 4T

(a)

To determine

To calculate: The monthly production value (to the nearest thousand dollars). Suppose a company’s monthly production value Q in thousands of dollars is given by the Cobb-Douglas production function $Q=10K^{0.45}{L}^{0.55}$ where K is thousands of dollars of capital investment and L is the total hours of labor per month. Capital investment is currently $\$10,000$ per month, and monthly work-hours of labor total $1590$.

(b)

To determine

To calculate: The marginal productivity with respect to capital investment. Suppose a company’s monthly production value Q in thousands of dollars is given by the Cobb-Douglas production function $Q=10K^{0.45}{L}^{0.55}$ where K is thousands of dollars of capital investment and L is the total hours of labor per month. Capital investment is currently $\$10,000$ per month, and monthly work-hours of labor total $1590$. Interpret the result.

(c)

To determine

To calculate: The marginal productivity with respect to total hours of labor. Suppose a company’s monthly production value Q in thousands of dollars is given by the Cobb-Douglas production function $Q=10K^{0.45}{L}^{0.55}$ where K is thousands of dollars of capital investment and L is the total hours of labor per month. Capital investment is currently $\$10,000$ per month, and monthly work-hours of labor total $1590$. Interpret the result.