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Paul Douglas explained that his first formulation of the Cobb–Douglas production function was developed in 1927; when seeking a functional form to relate estimates he had calculated for workers and capital, he spoke with mathematician and colleague Charles Cobb, who suggested a function of the form Y = AL β K 1−β, previously used by Knut Wicksell, Philip Wicksteed, and Léon Walras ...
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 ...
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 ...
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;
The AK model production function is a special case of a Cobb–Douglas production function: 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.
The production functions listed below, and their properties are shown for the case of two factors of production, capital (K), and labor (L), mostly for heuristic purposes. These functions and their properties are easily generalizable to include additional factors of production (like land, natural resources, entrepreneurship, etc.)
Charles Wiggins Cobb (September 17, 1875 – March 2, 1949) was an American mathematician and economist and a 1912 Ph.D. graduate of the University of Michigan.He published many works on both subjects, however he is most famous for developing the Cobb–Douglas production function in economics.