Search results
Results From The WOW.Com Content Network
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 ...
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 ...
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 ...
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 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.)
At its core, it is an aggregate production function, often specified to be of Cobb–Douglas type, which enables the model "to make contact with microeconomics". [1]: 26 The model was developed independently by Robert Solow and Trevor Swan in 1956, [2] [3] [note 1] and superseded the Keynesian Harrod–Domar model.
The problem is that unless we impose very strong mathematical restrictions, we cannot say that this Cobb–Douglas production function for sector i plus one for sector j (plus that for sector k, etc.) adds up to a Cobb–Douglas production function for the economy as a whole (with K and L being the sum of all of the different sectoral values).