Chapter 14, Problem 4T

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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

*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 *K* is thousands of dollars of capital investment and *L* is the total hours of labor per month. Capital investment is currently

Explanation

**Given Information:**

The provided production function is *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

**Calculation:**

Consider the provided function

The provided function is

Also, the capital investment is currently

Thus,

**(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 *K* is thousands of dollars of capital investment and *L* is the total hours of labor per month. Capital investment is currently

**(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 *K* is thousands of dollars of capital investment and *L* is the total hours of labor per month. Capital investment is currently

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