   Chapter 7.3, Problem 45E ### 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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# Cobb-Douglas Production Function Use the Cobb-Douglas production function ∫ ( x ,   y ) = c x a y 1 − a to show that when both the number of units of labor and the number of units of capital are doubled, the production level is also doubled.

To determine

To prove: In the production function f(x,y)=cxay1a, if number of units of labour and

capital is doubled, the production level is also doubled.

Explanation

Given Information:

A production function is given as f(x,y)=cxay1a.

Proof:

Consider the primary equation

f(x,y)=cxay1a

Now, as per the question if x and y are doubled,

Thus, numbers will be 2x and 2y, then production function becomes:

f(2x,2y)=c(2x)a(2y)1a=c2axa21a

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