The Basic Cobb-Douglas Production (Aggregate Supply) Function
Cobb-Douglas
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A two-input Cobb-Douglas production function
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 1900-1928.
For production, the function is
Y = ALαKβ,
where:
· Y = total production (the monetary value of all goods produced in a year)
· L = labor input
· K = capital input
· A = total factor productivity
· α and β are the output elasticities of labor and capital, respectively. These values are constants determined by available technology.
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%, Y increases by 20%. If
α + β < 1,
returns to scale are decreasing, and if
α + β > 1
returns to scale are increasing.
Source: http://en.wikipedia.org/wiki/Cobb-Douglas
Total factor productivity
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In economics, total-factor productivity (TFP) is a variable which accounts for effects in total output not caused by inputs. For example, a year with unusually good weather will tend to have higher output, because bad weather hinders agricultural output. A variable like weather does not directly relate to unit inputs, so weather is considered a total-factor productivity variable.
The equation below (in Cobb-Douglas form) represents total output (Y) as a function of total-factor productivity (A), capital input (K), labor input (L), and the two inputs' respective shares of output (α is the capital input share of contribution). An increase in either A, K and L will lead to an increase in output. While capital and labor input are tangible, total-factor productivity appears to be more intangible as it can ranch from technology to knowledge of worker (human capital). The reason why Cobb-Douglas equation is used in this function is because it exhibits constant return to scale. That is, if we double input, we get a double output.
Technology Growth and Efficiency are regarded as two of the biggest sub-sections of Total Factor Productivity, the former possessing "special" inherent features such as positive externalities and non-rivalness which enhance its position as a driver of economic growth.
Total Factor Productivity is often seen as the real driver of growth within an economy and studies reveal that whilst labour and investment are important contributors, Total Factor Productivity may account for up to 60% of growth within economies.
Source: http://en.wikipedia.org/wiki/Total_Factor_Productivity
(Compiled for ECON 5000, Production Theory. Dept. of Economics, East Carolina Univ., Spring 2009.)
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