Example Firm Production Functions
Overview
Although it is unlikely to get an exact analytical form for the production function of any given firm,
it is useful to have a set of examples that can be fit to the firms data, or used for instructional purposes.
Cobb Douglas Production Function
A common function used to model production is the Cobb Douglas Production function
{% Y = AL^{\beta}K^{\alpha} %}
- {% Y %} - total production
- {% L %} - labor input
- {% K %} - capital input
- {% A %} - total factor productivity
- {% \alpha %},{% \beta %} elasticities
The cobb douglas productin function is typically used for explanatory purposes in micro economic theory, but
the function could be fit to a firms data, if the company feels that it approximates their production curves well.
The cobb douglas function can be recast as follows:
{% log Y = log A + \beta \times L + \alpha \times K %}
from which the coefficients can be estimated using
standard
regression techniques.
The challenge to fitting Cobb Douglas is to define the variables K and L in a way that is measurable.
