Cobb douglas constant returns to scale9/13/2023 ![]() The Cobb–Douglas function can also be extended to include three or more arguments. At first the two economists have applied their principle to. ![]() Such a form of the CobbDouglas production function assumes constant returns to scale of K and H, which can be thought of as combining two assumptions. 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. This is similar to linear homogeneous production function showing constant returns to scale. A simple aggregated CobbDouglas production function, with no natural resources, was the starting point for the estimation of the stock of human capital in the 19th century in Brazil. 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. 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 function can be either increasing, decreasing or constant. In order to estimate the Cobb-Douglas production function the cross sectional farm data at a point of time are transformed into natural log form. Refer to the definitions of returns to scale in the text and in the lecture slides 1. Where A, α, and β are positive constants. The estimate of returns to scale, sum of the output elasticities of labour and capital 0.29710 + 0.669 0.966 is 0.966 showing that there are decreasing returns to scale. 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. If there are two inputs and the technology is described by a Cobb-Douglas production functionthen the production function takes the form F (z1,z2) Az1uz2v. 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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