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 1928.

In 1928 Charles Cobb and Paul Douglas published a study in which they modeled the growth of the American manufacturing industry during the period 1899-1922. They considered a simplified view of the economy in which production output is determined by the amount of labor involved and the amount of capital invested. The conclusion drawn from this famous statistical study is that labour contributed about 3/4th and capital about 1/4th of the increase in the manufacturing production. The function they used to model production was of the form:

Q = KLαC1-α,

where: Q = total output/production, L = Quantity of labor, K and α are the positive constants and C is the amount of capital.

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, α and β can be shown to be labor and capital’s share of output. For Cobb-Douglas production function, elasticity of substitution is equal to one (Unity).  