## Quick Reference

A functional form, named after its originators, that is widely used in both theoretical economics and applied economics as both a production function and a utility function. Denote aggregate output by *Y*, the input of capital by *K*, and the input of labour by *L*. The Cobb–Douglas production function is then given by

*Y* = *AK*^{α}*L*^{β}

where *A*, α, and β are positive constants. If α + β = 1 this function has constant returns to scale: if *K* and *L* are each multiplied by any positive constant λ then *Y* will also be multiplied by λ. The Cobb–Douglas production function has also been applied at the level of the individual firm. With this production function, a cost-minimizing firm will spend a proportion *α* of its total costs on capital and a proportion *β* on labour. When the Cobb–Douglas function is applied as a utility function the inputs, *K* and *L,* are replaced by the consumption levels of two types of good, say, *X* and *Y*. With this utility function a utility-maximizing consumer will spend a proportion α of their budget on good *X* and a proportion β on good *Y*. The Cobb–Douglas function can also be extended to include three or more arguments.

*Subjects:*
Economics.