Production function

A production function describes the relationship between the inputs and the resulting outputs. Thus is a production function at the highest production volume that can produce a company with the help of the combination of inputs.

Types of production function

Income Legally

This is probably the oldest production function. It is based on observations in agriculture and was formulated by Turgot as a law of diminishing crop yield. It is assumed that two factor input quantities and output quantity. His observations showed that by increasing labor input or fertilizer production yield increases first, but after a certain amount of factor inputs the output quantity falls steadily.

Substitutional

In a substitutional production function may be a factor of production ( at least within certain limits) by another or replaces the combination of other factors of production ( substituted ) are. A further characteristic of substitutability is that the amount of output can be influenced by changes in amounts of one factor only in constancy of the other factor quantities. With regard to the substitutability can distinguish between total and peripheral substitutability. Total substitutability exists if a factor can be completely replaced by another. It can also be zero as the quantity of the factor. Calculated analytically by solving the factors of production and by the derivative of Isoquantengleichung. Peripheral substitutionality is characterized in that the exchange of factors of production is only possible within certain limits.

A sub-group are the so-called CES production functions that are characterized by a constant elasticity of substitution. The best known and most commonly used in the economics example of a substitutional production function is the Cobb -Douglas production function.

Cobb -Douglas

The Cobb -Douglas production function was developed in 1928 by Charles Wiggins Cobb and Paul Howard Douglas. Compared to the statutory earnings production function, there is no maximum in this production function, that is, it is assumed that the increase in factor inputs always has a higher application rate resulted. However, the achieved by increasing factor inputs yield decreases, that is, if you, for example, doubles the amount used, the yield increases though, but less than twofold.

Limitational

Here, the factors have a specific use ratio, that is, the yield increases only if both factors are increasingly being used. However, this applies only if both factors are present in the same degree, that is, if a factor is in excess there, so this does not apply. In this case, the increase of the other factor is sufficient to increase the output amount. This applies until the excess factor is consumed. In order to achieve a further increase in the amount of discharge, so both of these factors have to be increased again. Until that time, the income does not increase. This can be seen in the crease of the yield function. Efficient production but this is only if no factor is wasted, that is, when the correct use ratio is maintained.

Linear limitational

The factors of production are in a fixed relationship to each other and in a fixed ratio to the output (output) of a plant or a plant. A well-known representative of this type is the Leontief production function.

Nonlinear limitational

A representative nonlinear limitationaler production functions is the Gutenberg - production function.

More types and newer approaches

The theory of production functions has been especially developed by incorporating the environment as a natural factor of production.

A disadvantage is the blurring of the boundaries between the sizes of input and output (or use and application ) and the actual transformation has been established. Newer approaches to the theory of production separate the stock variables input and output of the transform sizes consumption and production. Finally, the collection of factors in the operation does not necessarily mean their consumption in production (eg due to shrinkage ). Conversely, it must not rely as output operation (eg by Committee ) produced a good.

The transformation can be well described by the engineering functions of the technical consumption and technical production, making the integration of the engineering sciences to the economic production function succeeds.

In contrast to the macro and micro- economic production functions is in the engineering functions in addition to consumption and production, in particular the technical setup and technical design of production systems in the foreground.