![]() ![]() ![]() This is the dening characteristic of constant returns to scale. The Constant Return to Scale occurs when output increases in the same proportion as the increase in input. The Cobb–Douglas function can also be extended to include three or more arguments. So if we scale both inputs by a common factor, the effect is to scale the output by that same factor. In this article we will discuss about the Cobb-Douglas production function. One is that inputs other than physical capital K and human capital H as well as knowledge (or technology, as captured by A) are relatively unimportant. 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. 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. 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. This problem has been solved Youll get a detailed solution from a subject matter expert that helps you learn core concepts. The Cobb–Douglas production function has also been applied at the level of the individual firm. For the purpose of this exercise, a simple Cobb-Douglas. 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. Model A was an unrestricted production function while Model B assumed constant returns to scale. Where A, α, and β are positive constants. The Cobb–Douglas production function is then given by 1 An Assessment of CES and Cobb-Douglas Production. The Cobb-Douglas as well as constant elasticity of substitution production function exhibit increasing returns to scale. Denote aggregate output by Y, the input of capital by K, and the input of labour by L. We see that there is a linear relation between Y and Y so we call this constant returns to scale. 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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