   Chapter 14.3, Problem 16E Mathematical Applications for the ...

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

Solutions

Chapter
Section Mathematical Applications for the ...

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

Suppose that a company’s production function for a certain product is z = ( x + 1 ) 1 / 2 ln ( y 2 +   1 ) where x is the number of work-hours of unskilled labor and y is the number of work-hours of skilled labor.Find the marginal productivity of (a) x. (b) y.

(a)

To determine

To calculate: The marginal productivity of x if the production function for a certain product is z=(x+1)1/2ln(y2+1), where x is the number of work-hours of untrained labor and y is the number of work-hours of skilled labor.

Explanation

Given Information:

A company’s production function for a certain product is z=(x+1)1/2ln(y2+1), where x is the number of work-hours of untrained labor and y is the number of work-hours of skilled labor.

Formula used:

For a production function of the form z=f(x,y), the marginal productivity of x is given by zx and the marginal productivity of y is given by zy.

For a function f(x,y), the partial derivative of f with respect to x is calculated by taking the derivative of f(x,y) with respect to x and keeping the other variable y constant. The partial derivative of f with respect to x is denoted by fx.

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Chain rule for the function f(x)=u(v(x)) is f(x)=u(v(x))v(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

The coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Calculation:

A company’s production function for a certain product is z=(x+1)1/2ln(y2+1), where x is the number of work-hours of untrained labor and y is the number of work-hours of skilled labor

(b)

To determine

To calculate: The marginal productivity of y if the production function for a certain product is z=(x+1)1/2ln(y2+1), where x is the number of work-hours of untrained labor and y is the number of work-hours of skilled labor.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Expand each expression in Exercises 122. (2x3)(2x+3)

Finite Mathematics and Applied Calculus (MindTap Course List)

What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Differentiate. f(x)=x2exx2+ex

Single Variable Calculus: Early Transcendentals, Volume I

The critical numbers of f(x) = 3x4 = 20x3 36x2 are: a) 0, 1, 6 b) 0, 1, 6 c) 0, 1, 6 d) 0, 1, 6

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

0 1 π It does not exist.

Study Guide for Stewart's Multivariable Calculus, 8th 