Background+information,+history+and+some+drama

=What is Cobb-Douglas Production function? = =**__General Form:__**=



where: // • F = total production (the monetary value of all goods produced in a year) //

// • L = labor input (the total number of person-hours worked in a year) //

// • K = capital input (the monetary worth of all machinery, equipment, and buildings) //

// • A = total factor productivity //

// • b and c are the output elasticities of labor and capital, respectively. //

=**__Purpose:__**= In economics, the Cobb-Douglas functional form of production is used to represent the relationship of an output to inputs

=**__Origins:__**= In 1928 Charles Cobb and Paul Douglas published a study in which they modeled the growth of the American economy during the period 1899 - 1922. Following Cobb's suggestion, they decided to use a function of the form Y=bL^(k)C^(1-k) (where b is the total level of productivity, k is the output elasticity of labor and (1-k) is the output elasticity of capital) p  reviously used by Knut Wicksell. Estimating this using the method of least squares, they obtained a result for the marginal productivity of labour, which was subsequently confirmed by the National Bureau of Economic Research. Overall, Cobb and Douglas considered a simpliﬁed view of the economy, in which production output is determined by the amount of labor involved and the amount of capital invested. However, although there are many other factors affecting economic performance, their model proved to be remarkably accurate.


 * __ Did Cobb and Douglas deserve the fame? __**

Johann Heinrich von Thunen (1783–1850), a German landowner and economist, was actually the ﬁrst to apply the differential calculus to productivity theory and perhaps the ﬁrst to use it to solve economic optimization problems. He was likewise the ﬁrst to write down the first explicit algebraic production function to appear in print. Expressed in per-worker form, his function is = // P=hq^(n) // = where: -p = output per worker -h = constant parameter determined by such considerations as the fertility of the soil and the strength and diligence of the workers who till it -q = capital per worker (the capital-to-labor ratio) -n = fraction between zero and one. It turns out that Thunen’s production function is none other than the Cobb-Douglas function in disguise. For, when one multiplies both sides of Thunen’s equation by labor L, one obtains P = pL = hLq^(n) = hL(C/L)^(n) = hL^(1−n)C^(n). The resulting function P = hL^(1−n)C^(n) is virtually the same as the Cobb-Douglas function. The conclusion is inescapable. Thus, it can be said that credit for presenting the first Cobb-Douglas function, albeit in disguised or indirect form, must go to Thunen in the late 1840s rather than to Douglas and Cobb in 1928. ==