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Wire-grid Cobb–Douglas production surface with isoquants A two-input Cobb–Douglas production function with isoquants. In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs (particularly physical capital and labor) and ...
There are three common ways to incorporate technology (or the efficiency with which factors of production are used) into a production function (here A is a scale factor, F is a production function, and Y is the amount of physical output produced):
Let's say the utility function is the Cobb-Douglas function (,) =, which has the Marshallian demand functions [2] (,) = (,) =,where is the consumer's income. The indirect utility function (,,) is found by replacing the quantities in the utility function with the demand functions thus:
Other forms include the constant elasticity of substitution production function (CES), which is a generalized form of the Cobb–Douglas function, and the quadratic production function. The best form of the equation to use and the values of the parameters ( a 0 , … , a n {\displaystyle a_{0},\dots ,a_{n}} ) vary from company to company and ...
This equation shows a Cobb–Douglas function where Y represents the total production in an economy. A represents total factor productivity , K is capital, L is labor, and the parameter a {\displaystyle a} measures the output elasticity of capital.
Gorman polar form is a functional form for indirect utility functions in economics. ... Leontief and Cobb-Douglas utilities are homothetic and thus have the Gorman form.
A Cobb-Douglas-type function satisfies the Inada conditions when used as a utility or production function.. In macroeconomics, the Inada conditions are assumptions about the shape of a function that ensure well-behaved properties in economic models, such as diminishing marginal returns and proper boundary behavior, which are essential for the stability and convergence of several macroeconomic ...
Initially, there were no utility foundations for it. In the modern era, some economists try to build models up from individual agents acting, rather than imposing a functional form on an entire economy. The Cobb–Douglas production function, if properly defined, can be applied at a micro-economic level, up to a macro- economic level."