Activity analysis

The activity analysis is an economics approach of production theory , to analyze production systems , which in the 1950s by the two Nobel laureate economist Tjalling Koopmans and Debreu was developed. Together with the Gutenberg production function, it is one of the two most important developments in production theory. In business administration , individual production sites up to entire companies are analyzed; In the national economy, larger production systems from regions to entire states to the world economy . It is one of the so-called static-deterministic production theories, which consider the consumption of raw materials and the amount of goods produced within a certain period of time and assume that constant conditions prevail within this period ("static", no technical progress , no learning effects) and all production options are known in advance (“deterministic”, no random effects such as machine failures). The named activities are mathematically interpreted as points in an n-dimensional space and are therefore also referred to as production points. Each coordinate of these points then indicates how much of a good is produced (positive coordinate) or consumed (negative coordinate) in the corresponding production. The amount of all technically possible activities is called the technology amount.

Previous production theories made highly limiting assumptions about the shape of the amount of technology. It was often assumed that it can be described by a function that can be differentiated twice . Activity analysis, on the other hand, makes very few, simple basic assumptions, which are therefore also known as axioms. This includes, for example, the assumption that it is always technically possible not to produce. Mathematically, this means that the origin of coordinates always belongs to the technology. Because of these minor restrictions, activity analysis is a very abstract concept that is suitable for modeling many different production systems. For example, productions that produce several goods from a single good, as in chemical analysis , assembly processes that produce only one from several goods, and also multi-stage or cyclical productions that use some of the products again themselves. This concerns z. B. yeast at a bakery or machines from a machine manufacturer. But the world economy is also a self-contained economic system.

The modeling takes place in several steps: starting from all technically possible activities, activities that are economically nonsensical are gradually excluded from further consideration. This applies, for example, to activities that only consume goods but do not produce them, or those that consume an unnecessarily large amount. With the remaining activities, the goods can then be valued with prices in order to arrive at costs and revenues. It is then possible to calculate optimal production programs or transfer prices . Also needs assessments and efficiency analyzes. The activity analysis also serves as the theoretical foundation for process costing .

Environment-oriented extensions expressly include the generation of undesirable objects such as waste , noise , pollutants or exhaust gases . This makes it possible to model the effects of legal limit values, environmental taxes or emission certificates and to predict their ecological and economic consequences. Furthermore, planning of recycling and material flow management is possible on the basis of cyclical models .

activities

Productions in which k different types of goods are involved are represented in the activity analysis in a k-dimensional real space , which is also referred to as goods space. It is irrelevant whether these goods are consumed or generated in production. The quantities of goods consumed (factor quantities, input quantities, input quantities) are represented by the vector x.

${\displaystyle x={\begin{pmatrix}x_{1}\\\vdots \\x_{k}\end{pmatrix}}}$

The individual entries of the vector are positive if the corresponding good is consumed and zero otherwise. The quantities of goods produced (production quantities, output quantities, output quantities) are represented by the vector y.

${\displaystyle y={\begin{pmatrix}y_{1}\\\vdots \\y_{k}\end{pmatrix}}}$

Here the entries are positive if the good is generated and zero otherwise. In order not to confuse these quantities with the mathematical concept of a quantity , they are often referred to as factor quantities or product quantities. Often, however, only changing the quantities is of interest. They are combined in the vector z, which results as

${\displaystyle z=y-x={\begin{pmatrix}y_{1}-x_{1}\\\vdots \\y_{k}-x_{k}\end{pmatrix}}={\begin{pmatrix}z_{1}\\\vdots \\z_{k}\end{pmatrix}}}$.

This vector is referred to as activity or also as production point or production for short. Graphically, the xy representation is often used, while the z representation is more used for mathematical descriptions.

Technologies

The amount of all technically possible activities is called technology (amount) or technique . It is a subset of the goods space. ${\displaystyle T}$

${\displaystyle T=\{z|{\text{z ist technisch möglich}}\}}$

Five basic assumptions are made for technologies, which are also referred to as axioms and partly result from scientific principles, partly also emerged from economic or practical considerations.

1. Isolation of technology
2. Possibility of inaction
3. Impossibility of the land of milk and honey
4. Irreversibility of production
5. Possibility of high-yield production

Isolation of technology

Isolation means that edge points are elements of the technology set. This assumption results from mathematical considerations of expediency.

Impossibility of the land of milk and honey

The basic assumption described as the impossibility of the land of milk and honey results from the conservation of energy and the first law of thermodynamics . It excludes productions that only produce goods and do not consume any goods.

Irreversibility of production

The irreversibility of production results from the law of entropy . It is true that parts used during assembly can be recovered by dismantling, but not the time that has passed. In mathematical terms, the intersection of a technology and its reversal is inactivity.

Possibility of profitable production

Productions that only consist of the destruction of goods and inactivity are of no economic interest. Therefore the existence of at least one activity that produces goods is assumed.

literature

• Harald Dyckhoff: Production Theory . Basics of industrial production management. 5th, revised edition. Springer, Berlin et al. 2006, ISBN 3-540-32600-6 .
• Günter Fandel: Production I. Production and cost theory. 3rd, revised edition. Springer, Berlin et al. 1991, ISBN 3-540-53526-8 .
• Klaus-Peter Kistner: Production and Cost Theory. 2nd, completely revised and expanded edition. Physica-Verlag, Heidelberg 1993, ISBN 3-7908-0644-7 .
• Tjalling C. Koopmans : Analysis of production as an efficient combination of activities. In: Tjalling C. Koopmans (Ed.): Activity Analysis of Production and Allocation. Proceedings of a Conference (= Cowles Commission monograph. 13, ZDB -ID 254454-4 ). Wiley, New York NY et al. 1951, pp. 33-97.
• Waldemar Wittmann : Production theory (= econometrics and corporate research. 11, ISSN  0078-3390 ). Springer, Berlin et al. 1968.