Cobb–Douglas Production Function

A Cobb–Douglas Production Function is an economic model that represents the technological relationship between the amounts of inputs and the amount of output that can be produced by those inputs in production.

• Context:
  • It can (typically) involve inputs such as Physical Capital Measure and Labor Measure.
  • It can be used to analyze Scale of Production, Returns to Scale, and Factor Substitutability.
  • It can be characterized by a mathematical formula: [math]\displaystyle{ Y = A \times L^\beta \times K^\alpha }[/math], where:
    • [math]\displaystyle{ Y }[/math] is the total production (the real value of all goods produced in a year).
    • [math]\displaystyle{ L }[/math] and [math]\displaystyle{ K }[/math] are the inputs for labor and capital, respectively.
    • [math]\displaystyle{ \alpha }[/math] and [math]\displaystyle{ \beta }[/math] are the output elasticities of capital and labor, respectively.
    • [math]\displaystyle{ A }[/math] is total factor productivity.
  • It can exhibit constant returns to scale if [math]\displaystyle{ \alpha + \beta = 1 }[/math].
  • It can be extended to include more inputs like human capital, technology, and natural resources.
  • It can be used in microeconomic analysis of individual firms and macroeconomic analysis of a national economy.
  • ...
• Example(s):
  • CES Production Function, which allows for different substitution possibilities between inputs (vs. a fixed substitution ratio).
  • ...
• Counter-Example(s):
  • A Linear Production Function, where output increases linearly with input.
  • A Leontief Production Function, where inputs are used in fixed proportions.
  • ...
• See: Econometrics, Production Function, Input-Output Model.

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References

2023

• (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Cobb–Douglas_production_function Retrieved:2023-11-14.
  • In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs (particularly physical capital and labor) and the amount of output that can be produced by those inputs. The Cobb–Douglas form is developed and tested against statistical evidence by Charles Cobb and Paul Douglas between 1927 and 1947; according to Douglas, the functional form itself was developed earlier by Philip Wicksteed.

1928

• (Cobb & Douglas, 1928) ⇒ Charles W. Cobb, and Paul H. Douglas. (1928). “A Theory Of Production.” Internet Archive. Retrieved: 1972-07-23.

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