   Chapter 7.4, Problem 63E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Marginal Productivity Consider the Cobb-Douglas production function f ( x , y ) = 200 x 0.7 y 0.3 . When x = 1000 and y = 500 , find(a) the marginal productivity of labor, ∂ f / ∂ x .(b) the marginal productivity of capital, ∂ f / ∂ y .

(a)

To determine

To calculate: The marginal productivity that is fx at x=1000 and y=500 if the Cobb-Douglas production function is modeled by f(x,y)=200x0.7y0.3.

Explanation

Given information:

The Cobb-Douglas production function is modeled by f(x,y)=200x0.7y0.3.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided production function is,

f(x,y)=200x0.7y0.3

Partially derivative of the function f(x,y)=200x0.7y0.3 with respect to x.

fx(x,y)=x(200x0.7y0.3)=200y0.3x(x0

(b)

To determine

To calculate: The marginal productivity that is fy at x=1000 and y=500 if the Cobb-Douglas production function is modeled by f(x,y)=200x0.7y0.3.

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