Cobb-Douglas Production Function 发表评论(0) 编辑词条

A two-input Cobb–Douglas production function.

In economics, the Cobb–Douglas functional form of production functions is widely used to represent the relationship of an output to inputs. It was proposed by Knut Wicksell (1851–1926), and tested against statistical evidence by Charles Cobb and Paul Douglas in 1900–1928.

For production, the function is

Y = AL^α*K^β,
where:
Y = total production (the monetary value of all goods produced in a year)
L = labor input
K = capital input
A = total factor productivity
α and β are the output elasticities of labor and capital, respectively. These values are constants determined by available technology.
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 = 0.15, a 1% increase in labor would lead to approximately a 0.15% increase in output.

Further, if: α + β = 1, the production function has constant returns to scale. That is, if L and K are each increased by 20%, Y increases by 20%. If α + β < 1,
returns to scale are decreasing, and if α + β > 1 returns to scale are increasing. Assuming perfect competition and α + β = 1, α and β can be shown to be labor and capital's share 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.