But we can argue also that if the individuals i are somewhat homogenous (regarding income, tastes, and priorities, for example, the people of the same socioeconomic stratum) we might be able to proceed with the estimation of the function to model the consumer behavior toward the goods. A multiplicative function, with 2 essential factors, and a scaling. One could argue that each individual i has a different utility function to maximize, and also that the elasticities for each good are different across individuals. A useful production function: Cobb-Douglas. They have developed this equation between years 1927-1947. where Q is output, A,, b are constants, and L and K are labor and capital, respectively. Cobb-Douglas production function shows physical output as the Douglas labor and capital inputs that is: Q AL K b. Given the basic form of the Cobb-Douglas production function, we'll find the partial derivatives with respect to capital, K, and labor, L. This production function is developed by Paul Douglas and Charles Cobb, as also shown in the image too. The CobbDouglas form was developed and tested against statistical evidence by Charles Cobb and Paul Douglas during 19271947. This function deals with the relationship between input and output used to produce a product. Since we’re doing macroeconomics we will be considering. This concept can be applied at the level of individual rms, industries, or entire economies. There are different forms of production functions that can be applied at the level of individual firms, industries or entire economies one form is the Cobb-Douglas Production Function. CobbDouglas production function is used in both microeconomics and macroeconomics. The CobbDouglas Production Function 1 Introduction In general, a productionfunctionis a specication of how the quantity of output behaves as a func-tion of the inputs used in production. However, some assumptions must be noted: 1) We’re assuming that our sample (or subsample) containing the set of individuals i tend to have a similar utility function, 2) the estimation of the elasticity for each good, would also be a generalization of the individual behavior as an aggregate. A production function is a function that specifies how the quantity of output relates with the quantity of inputs used in production.
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