Cobb–Douglas production function
In economics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs, particularly physical capital and labor, and the amount of output that can be produced by those inputs. Sometimes the term has a more restricted meaning, requiring that the function display constant returns to scale (in which case in the formula below). The Cobb-Douglas form was developed and tested against statistical evidence by Charles Cobb and Paul Douglas during 1927–1947.
In its most standard form for production of a single good with two factors, the function is
where:
Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus. For example, if α = 0.45, a 1% increase in capital usage would lead to approximately a 0.45% increase in output.
Further, if
the production function has constant returns to scale, meaning that doubling the usage of capital K and labor L will also double output Y. If
returns to scale are decreasing, and if
returns to scale are increasing. Assuming perfect competition and α + β = 1, α and β can be shown to be capital's and labor's shares of output.
Cobb and Douglas were influenced by statistical evidence that appeared to show that labor and capital shares of total output were constant over time in developed countries; they explained this by statistical fitting least-squares regression of their production function. There is now doubt over whether constancy over time exists.
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