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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. The parameters and are all positive constants calculated from empirical data and is a multiplicative exponential error. 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. 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. In economics, a production function is an equation that describes the relationship between input and output, or what goes into making a certain product, and a Cobb-Douglas production function is a specific standard equation that is applied to describe how much output two or more inputs into a production process make, with capital and labor being the typical inputs described. Where A, α, and β are positive constants. The Cobb–Douglas production function is then given by Important Points The Cobb Douglas production function exhibits the three types of returns: If a+b>1, there are increasing returns to scale. A, a and are positive parameters where a > O, > O. Denote aggregate output by Y, the input of capital by K, and the input of labour by L. The Cobb-Douglas production function is expressed as Q AK a L where Q is output and L and are inputs of labour and capital, respectively. The general form of the Cobb-Douglas production function is, A>0. Certainly, the Cobb Douglas production function is a very popular type of production function. In 1928, Charles Cobb and Paul Douglas presented the view that production output is the result of the amount of labor and physical capital invested. There are three main types of production function. A is a positive constant (Called Total Factor Productivity). The basic form of the Cobb-Douglas production function is as follows: Q (L,K) A L K. 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. Types of Production Function: Cobb Douglas production function. The Formula of Cobb-Douglas production function.