Cobb-Douglas Production Functions

scaling factor

0.5

k

0.5

ℓ

Cobb-Douglas Production Function

method

ContourPlot

Plot3D

Cobb-Douglas functions are frequently used in economics to show the relationship between input factors and the level of production. This family of functions takes on the form

a

α

ℓ

β

k

, where ℓ is one factor of production (often labor) and

k

is the second factor of production (often capital). The sum of the exponents

α+β

determines the returns to scale on factor inputs. This Demonstration visualizes Cobb-Douglas functions by letting the user select the input exponents

α

and

β

as well as a scaling factor

a

. You can also select whether the resulting production function is to be displayed as a contour plot or as a three-dimensional plot.

Details

When

α+β=1

, the Cobb-Douglas function is homogeneous, meaning that a doubling of both of the two inputs (at the same time) results in a doubling of the output.

α

and

β

are also the respective partial "output elasticities" of the production function, meaning that they measure the percent increase in production resulting from a percent increase in the particular input factor.

External Links

Homogeneous Function (Wolfram MathWorld)

Permanent Citation

Seth J. Chandler

"Cobb-Douglas Production Functions"
http://demonstrations.wolfram.com/CobbDouglasProductionFunctions/
Wolfram Demonstrations Project
Published: September 28, 2007