The Cobb–Douglas function can also be extended to include three or more arguments. 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. 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 production function, a cost-minimizing firm will spend a proportion α of its total costs on capital and a proportion β on labour. The Cobb–Douglas production function has also been applied at the level of the individual firm. Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus. ![]() In their paper they proved that the Inada conditions force the production func-tion to be asymptotically Cobb-Douglas that is, its elasticity of substitution is asymptotically equal to. The second one is attributed to Barelli and Pessoa (2003). 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. See for example the papers of Solow (1958), Newman and Read (1691) and, Ferguson and Pfouts (1962). Where A, α, and β are positive constants. The Cobb–Douglas production function is then given by ![]() ![]() Denote aggregate output by Y, the input of capital by K, and the input of labour by L. 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.
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