# Production Function

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Roughly speaking, the term production function means the relationship between the production factors and the goods that are produced with it. The prerequisite for this is of course a correspondingly functioning production technology.

The goal of such a production function is primarily to find out how high the maximum production quantity can be, which can be produced with consideration of the input. For some time, the calculations of the production functions also include aspects that involve the environment.

The term “production function” was coined by Vilfredo Pareto. Generally speaking, the production function is concerned with the quantity ratio between the individual factors, both in the production as well as in the output.

## Types of Production Functions:

### Substitutional production function

In the case of a substitutional production function , it is assumed that a certain production factor can be replaced by another, that is, substituted. Of course, this is not always possible and only in very tight boundaries.

The quantity of output thus remains the same in the case of substitutional production functions, while the quantity of the input changes. Finally, other production factors are used in the input, since a substitution or substitution occurs.

A simple example: both labor and capital are usually indispensable for production as a production function. But if a producer chooses to spend less on modern, automated machines, he must invest more in the production factor at the same time. There is thus a subsidiarity, since one factor is replaced by the other.

In this context one should look more closely at the concepts of peripheral and total subsidiarity. While peripheral subsidiarity is characterized by the fact that replacement of production factors is possible only within very narrow limits, the situation is different in the case of total subsidiarity. Here, one factor is completely replaced by another. A factor therefore falls completely away.

### Limitational production function

The situation is different with the so-called limitational production function . Here a substitution (subsidiarity) of the individual production factors is not possible without further ado. There is therefore a certain employment relationship between the individual factors.

In this case, it is not possible to simply replace one production factor with another. The yield increases with the limitational production function only if both production factors are used more and more.

For the entrepreneur, the art of the limitative production function primarily consists in finding the optimal employment relationship between the individual production factors. The goal is, of course, not to waste a factor by unnecessarily excessive use.