Cobb-Douglas Production Function
Bao Hong, Tan
November 20, 2008
Figure 1: A two-input Cobb-Douglas
In economics, the Cobb-Douglas functional form of pro-
duction functions is widely used to represent the relation-
ship of an output to inputs.
It was proposed by Knut
Wicksell (1851 - 1926), and tested against statistical evi-
dence 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 Ameri-
can economy during the period 1899 - 1922. They con-
sidered a simplified view of the economy in which pro-
duction output is determined by the amount of labor in-
volved and the amount of capital invested. While there
are many other factors affecting economic performance,
their model proved to be remarkably accurate.
The function they used to model production was of the form:
P (L,K) = bLαKβ
• P = total production (the monetary value of all goods produced in a year)
• L = labor input (the total number of person-hours worked in a year)
• K = capital input (the monetary worth of all machinery, equipment, and buildings)
• b = total factor productivity
• α and β are the output elasticities of labor and capital, respectively. These values are con-
stants 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.
α + β = 1,
the production function has constant returns to scale. That is, if L and K are each increased by
20%, then P increases by 20%.
Returns to scale refers to a technical property of production that examines changes
in output subsequent to a proportional change in all inputs (where all inputs increase
by a constant factor). If output increases by that same proportional change then there
are constant returns to scale (CRTS), sometimes referred to simply as ret