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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 ...
The AK model production function is a special case of a Cobb–Douglas function with constant returns to scale. Y = A K a L 1 − a {\displaystyle Y=AK^{a}L^{1-a}\,} This equation shows a Cobb–Douglas function where Y represents the total production in an economy.
A Cobb–Douglas production function is an example of a production function that has an expansion path which is a straight line through the origin. [6]
The equation below (in Cobb–Douglas form) is often used to represent total output (Y) as a function of total-factor productivity (A), capital input (K), labour input (L), and the two inputs' respective shares of output (α and β are the share of contribution for K and L respectively). As usual for equations of this form, an increase in ...
As its name suggests, the CES production function exhibits constant elasticity of substitution between capital and labor. Leontief, linear and Cobb–Douglas functions are special cases of the CES production function. That is, If approaches 1, we have a linear or perfect substitutes function;
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.
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 ...
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 ...