![]() ![]() 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. So, this type of production function exhibits constant returns to scale over the entire range of output. 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. Returns to Scale and the Aggregate Production Function By Simone Clemhout X I he relationship between product exhaustion and the linear homo-I geneity of the firm production function was a hotly debated- issue years ago. 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. Where A, α, and β are positive constants. The Cobb–Douglas production function is then given by The Cobb-Douglas function in the Technology sheet obeys the Law of Diminishing Returns for each input (with 0<<1), yet it has constant returns. Therefore, If +1, it exhibits constant returns to scale (CRS) If +>1, it exhibits increasing returns to scale (IRS) If +<1, it exhibits decreasing returns to scale (DRS) 2. Denote aggregate output by Y, the input of capital by K, and the input of labour by L. The sum of the powers/exponents of factors in Cobb-Douglas production function, that is + measures the 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. can exhibit constant, increasing, or decreasing returns to scale. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |