Cobb-Douglas Production Functions

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 (ℓ^α)(k^β), 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.

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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.

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Contributed by: Seth J. Chandler

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