Cobb–Douglas Production Cobb–Douglas Production FunctionFunction

HistoryHistoryDeveloped by

Paul Douglas and C. W. Cobb in the 1930’s

Widely used to represent the relationship of an output to inputs.

The General FormThe General FormY = ALαKβ

Where:Y = total production (the monetary value of

all goods produced in a year)L = labor inputK = capital inputA = total factor productivityα 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 ifα + β > 1 Returns to scale are increasing.