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| The output elasticities of a Cobb-Douglas function can also be characterized in terms of '''returns to scale'''. For example, if there is just one input... * ...and a 100% increase to the input causes a 100% increase to the output (i.e., '''constant''' returns to scale), then the output elasticity ''must'' be 1. * ...and a 100% increase to the input causes a >100% increase to the output (i.e., '''increasing''' returns to scale), then the output elasticity ''must'' be >1. * ...and a 100% increase to the input causes a <100% increase to the output (i.e., '''decreasing''' returns to scale), then the output elasticity ''must'' be <1. |
Cobb-Douglas Production Function
The Cobb-Douglas production function is a formulation of the production function, typically given inputs of labor and capital.
Formulation
The basic Cobb-Douglas function is:
Y(L,K) = ALaKb
Where...
L is labor and K is capital, the classical economic inputs
A is total factor productivity, essentially the catch-all residual term, generally thought of as intrinsically-productive technology or human capital
a and b represent output elasticities, generally thought of as technological effects on specific inputs' efficiencies, somewhere in the non-inclusive range of 0 and 1.
The output elasticities of a Cobb-Douglas function can also be characterized in terms of returns to scale. For example, if there is just one input...
...and a 100% increase to the input causes a 100% increase to the output (i.e., constant returns to scale), then the output elasticity must be 1.
...and a 100% increase to the input causes a >100% increase to the output (i.e., increasing returns to scale), then the output elasticity must be >1.
...and a 100% increase to the input causes a <100% increase to the output (i.e., decreasing returns to scale), then the output elasticity must be <1.
History
This production function was developed by Charles Cobb and Paul Douglas. They fit decades of aggregated U.S. economic data to this model and estimated the output elasticities for the U.S. economy.