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 = AKαLβ
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.