List of production functions

The production functions listed below, and their properties are shown for the case of two factors of production, capital (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.)

A production function can also be seen as the dynamics of national output/national income. This list is to collect production functions & the dynamics of national output/income that have been used in literature & textbooks.


There are three common ways to incorporate technology (or the efficiency with which factors of production are used) into a production function:

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 can be

Some Famous forms

, with which includes the special cases of:

  • Linear production (or perfect substitutes)

See also

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