Chapter 14, Problem 4T

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Suppose a company’s monthly production value Q in thousands of dollars is given by the Cobb-Douglas production function Q   =   10 K 0.45 L 0.55 where K is thousands of dollars of capital investment per month 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.(a) Find the monthly production value (to the nearest thousand dollars).(b) Find the marginal productivity with respect to capital investment and interpret your result.(c) Find the marginal productivity with respect to total hours of labor and interpret your result. (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=10K0.45L0.55 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.

Explanation

Given Information:

The provided production function is Q=10K0.45L0.55. Where K is the thousands of dollars of capital investment and L is the total hours of labor per month.

Formula used:

The value of a function of two variables f(x,y) at the point x=a,y=b is f(a,b).

Calculation:

Consider the provided function Q=10K0.45L0.55.

The provided function is Q(K,L)=10K0.45L0.55.

Also, the capital investment is currently $10,000 per month, and monthly work-hours of labor total 1590. Thus, K=10,L=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=10K0.45L0.55 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=10K0.45L0.55 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.

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