This is a list of
production functions that have been used in the
economics literature. Production functions are a key part of modelling
national output and
national income
A variety of measures of national income and output are used in economics to estimate total economic activity in a country or region, including gross domestic product (GDP), gross national product (GNP), net national income (NNI), and adjusted nati ...
. For a much more extensive discussion of various types of production functions and their properties, their relationships and origin, see Chambers (1988) and Sickles and Zelenyuk (2019, Chapter 6).
The production functions listed below, and their properties are shown for the case of two factors of production,
capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used f ...
(K), and
labor (L), mostly for heuristic purposes. These functions and their properties are easily generalizable to include additional factors of production (like land, natural resources, entrepreneurship, etc.)
Technology
There are three common ways to incorporate technology (or the efficiency with which factors of production are used) into a production function (here ''A'' is a
scale factor, ''F'' is a production function, and ''Y'' is the amount of physical output produced):
*
Hicks-neutral technology, or "factor augmenting":
* Harrod-neutral technology, or "labor augmenting":
* Solow-neutral technology, or "capital augmenting":
Elasticity of substitution
The elasticity of substitution between
factors of production is a measure of how easily one factor can be substituted for another. With two factors of production, say, ''K'' and ''L'', it is a measure of the curvature of a production
isoquant. The mathematical definition is:
:
where "slope" denotes the slope of the isoquant, given by
:
Returns to scale
Returns to scale
In economics, returns to scale describe what happens to long-run returns as the scale of production increases, when all input levels including physical capital usage are variable (able to be set by the firm). The concept of returns to scale arises ...
can be
* Increasing returns to scale: doubling all input usages more than doubles output.
* Decreasing returns to scale: doubling all input usages less than doubles output.
* Constant returns to scale: doubling all input usages exactly doubles output.
Some widely used forms
*
Constant elasticity of substitution (CES) function:
::
, with