Cobb-Douglas Production Function

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Cobb-Douglas Production Function Bao Hong, Tan November 20, 2008 1 Introduction In economics, the Cobb-Douglas functional form of production functions is widely used to represent the relationship of an output to inputs. It was proposed by Knut Wicksell (1851 - 1926), and tested against statistical evidence by Charles Cobb and Paul Douglas in 1928. 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. They 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. While there Figure 1: A two-input Cobb-Douglas are many other factors affecting economic performance, production function their model proved to be remarkably accurate. The function they used to model production was of the form: P (L, K ) = bLα K β where: • P = 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) • b = total factor productivity • α and β are the output elasticities of labor and capital, respectively. These values are constants determined by available technology. 1 Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus. For example if α = 0.15, a 1% increase in labor would lead to approximately a 0.15% increase in output. Further, if: α + β = 1, the production function has constant returns to scale. That is, if L and K are each increased by 20%, then P increases by 20%. Returns to scale refers to a technical property of production that examines changes in output subsequent to a proportional change in all inputs (where all

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