A production function provides an abstract mathematical representation of the relation between the production of a good and the inputs used. A production function is usually expressed in this general form:where: Q = quantity of production or output, L = quantity of labor input, and K = quantity of capital input. The letter "f" indicates a generic, as of yet unspecified, functional equation.
The analysis of short-run production is commonly performed at the introductory level with simple tables and graphs. These are useful abstraction methods for isolating and analyzing key aspects of short-run production. However, mathematical equations are another, often more powerful, method of abstract analysis. This is where the production function comes into play. Because a mathematical equation can extend beyond the two dimensions of a graph, it is possible to consider relations beyond just that for a variable input and total production.
If the production function takes the form of a specific equation (such as Q = 5L + 10K + 2LK), then a total product curve relating total product and the variable input can be plotted. However, to do so, one of the two inputs (L or K) must be designated as a variable input and one designated as a fixed input. For most types of production, labor is more readily changed than capital, so L is generally the variable input and K is usually the fixed input. A short-run total product curve can then be derived by "fixing" K at a particular value, then plotting the values of Q for alternative values of L.
While a great deal of economic insight into short-run production decisions of a firm and market supply curves can be analyzed with a simple graph, when economists begin using mathematical equations, such as the production function, Q = f(L, K), the possibilities are almost unlimited. A wide assortment of additional input variables can be added to this equation to make it, not only more sophisticated, but also more revealing.
For example, the effect of education and human capital on production can be seen by adding the educational attainment of workers as another input variable. In addition, the alternative impact on production of different types of capital, such as fixed structures and equipment can be identified by separating capital into two variables. In addition, to identify how public infrastructure, like highways and streets, affects production, then a variable for this input can be added to the production function.
PRODUCTION FUNCTION, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2025. [Accessed: July 18, 2025].
