Income Act

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Curve according to the law of yield: Change in the application rate Y by varying the factor r1.

The law of income (also the law of decreasing marginal income ) is an economic model that describes the relationship between effort / use ( English input ) and yield ( English output ) when one production factor is changed and all the others remain the same ( partial factor variation ).


It was originally defined by Anne Robert Jacques Turgot for agriculture as the land yield law: If you steadily increase the labor input on the same piece of land , the yield initially increases quickly, then only slowly, then it remains the same, and finally it even increases again from. This law applies not only to agricultural production , but also to industrial production and other areas.


If the product X or the party Y is hardly or little advertised and the advertising expenditure is now increased sharply, then the sales revenues or the voting shares initially grow progressively . From a certain point they only grow degressively until they finally tend asymptotically towards zero. This trend can no longer be reversed if the quality remains the same, no matter how great the expenditure.

Definition of terms

The income law in the true sense, also known as the classic income law, describes a technology in which by increasing a factor ( cp ), the product quantity initially increases disproportionately, from a certain point onwards disproportionately and finally decreases absolutely. This law is divided into 4 phases (see section Income Law # Income Law Production Function ) and thus carries the broader meaning.

In the narrower sense, the classics understood that the first phase is mostly irrelevant for production . One often speaks of the distinction between classic and neoclassical income law. The neoclassical income law now refers to phases 2 and 3 (also neoclassical area or even neoclassical production function ). These are of particular interest for microeconomic company theory, because only here is profit maximization possible for a competing company (Polypol) . The income law of the neoclassical production theory assumes positive and decreasing marginal yields from the beginning ( neoclassical production function ). In this area, the total yield increases with each additional unit of production factor used, the marginal yield is still positive, but is already below the average yield in terms of value.

Often the abbreviated form of Earnings Act is used in a misleading manner in German, since what is actually meant here is not the Earnings Act as a whole, but only the particular section of interest - the neoclassical production function. Other curve progressions can also show a “statutory income” relationship between factual input quantities and yields. There are also cost functions under income law .

The designation law of decreasing marginal yield or law of decreasing yield growth (when using a variable factor , i.e. ceteris paribus ) is clearer .

It is more a question of qualitative differences in the description of one and the same factual situation. The income law is neither a rule in the sense of a legal norm nor does it designate a rule in the sense of an unconditional scientific method.


The classic income law is considered the oldest production function . His "discoverers" are Turgot , Thünen , Denham-Steuart and Malthus , who came from different approaches to comparable descriptions.

Anne Robert Jacques Turgot
Turgot was a French statesman and Enlightenment economist. By observing agricultural production in 1767/68 he came to the conclusion that if all other factors are kept constant (e.g. size of the arable land, amount of seeds and fertilizer), with increasing use of work, initially with increasing, but decreasing at a certain point a decreasing increase in yield can be expected.
Johann Heinrich von Thünen
Thünen collected statistical material on his estate in Mecklenburg in order to draw conclusions about the sensible management of an agricultural property. This enabled him to statistically prove and formalize the regularity observed by Turgot in 1842.

"It is" in the nature of agriculture - and this is a very noteworthy circumstance - that the surplus product does not increase in direct proportion to the number of more employed workers, but each later employed worker delivers a smaller product than the previous one ... ""

- Thünen, 1850, p. 416; Secondary quote according to Reiss
It can be said that Thünen (1850) did not mean the classic income law in the broad sense. He probably ruled out an initial increase in efficiency, since you cannot reasonably manage a property with only a few workers.

Production function under income law

Phases of the income law

The classic yield law has plausibility over its entire course (actually only) for agricultural production processes with partial factor variation . Nevertheless, it is also used as a yield curve for total factor variation and for other production processes. The reason for this is its high didactic potential. The functional shows areas of increasing as well as decreasing marginal yields. The point of change from increasing to decreasing marginal yields (turning point) is referred to as the (first) “threshold”, since from this point the yield increases fall. The minimum of marginal costs, which is referred to as the further (second) threshold, corresponds to the turning point. With the classic yield law, the average yields have a maximum where the production elasticity is one, i.e. H. the marginal yields are equal to the average yields.

In the diagrammatic representation, it is reminiscent of the shape of an S. inclined to the right. In business administration , the course is also known as the production function under the law of income or type A production function. The increased use of a means of production with constancy of the other production factors brings first increasing yields (marginal yields or marginal products), then from a certain input quantity onwards decreasing and finally even negative marginal yields.

Phase I.

The first section is characterized by a disproportionate increase in the yield function. Marginal and average yield also increase, but phase I is limited by the maximum of the marginal yield function. This can be determined mathematically by setting the 2nd derivative of the yield function equal to zero.

Phase II

The second section is characterized by an almost proportional slope of the yield function (caused by almost constant marginal yields). The marginal yield function is already falling again, while the average yield function is still increasing. Phase II is limited by the maximum of the average yield function. Mathematically, this can be determined by equating the average yield with the marginal yield.

Phase III

The third section is characterized by a disproportionate slope of the yield function. In this phase, both the marginal yield function and the average yield function decrease. Phase III is limited by the maximum of the income function. The marginal yield function intersects the abscissa at this interval limit . This can be determined mathematically by setting the 1st derivative equal to zero.

Phase IV

In the fourth section, the yield, marginal and average yield functions show a negative slope.


In agriculture, this can be demonstrated functionally (also after the French economist J. Turgot and his Turgot income law ) using the example of the use of fertilizers : through the continuously increasing use of fertilizers (with otherwise constant resources / conditions (ceteris paribus) , i.e. e.g. constant area) the yield initially increases steadily. The increase in yield per additional amount of fertilizer applied decreases from a certain application amount. If the fertilizer continues to be applied, this ultimately leads to a reduction in overall yield and even to soil poisoning: Excessive use of fertilizers will bring the yield below the level that would have been achieved without fertilizers and ultimately destroy any yield. Similar observations can be made for the factors heat and water.

These observations can also be traced back to Eilhard Alfred Mitscherlich , who published The Law of the Minimum and the Law of Decreasing Land Yield with corresponding progression diagrams in 1909.

Using the example of industrial production or in administration , the income law can also be observed on the increased use of personnel with otherwise constant framework conditions: the larger the number of employees, the greater the need for communication and coordination. However, situations can be reached where employees only stand in each other's way or become demotivated. The increase in staff will not move more. A state that controls its economy centrally and allocates workers to the production facilities in order to avoid the problem of unemployment can hardly increase its productivity in this way.

The classic income law is not necessary to justify a (short-term) income law cost curve that leads to U-shaped average cost curves. These can also occur with consistently decreasing earnings growth as a result of the interplay of increasing marginal and decreasing average fixed costs .


  • Günter Fandel: Production. Volume 1: Production and Cost Theory. 7th edition. Springer, Berlin et al. 2007, ISBN 978-3-540-73140-5 , pp. 191f. Chapter.
  • Günter Wöhe , Ulrich Döring: Introduction to general business administration. 24th revised and updated edition. Vahlen, Munich 2010, ISBN 978-3-8006-3795-9 , p. 396f. Section “Income-related production function”.

Web links

Individual evidence

  1. a b c Income Act - definition in the Gabler Wirtschaftslexikon
  2. Income law  ( page no longer available , search in web archivesInfo: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. - Definition on 2Template: Dead Link /  
  3. ^ Wolfgang Cezanne: Allgemeine Volkswirtschaftslehre , Oldenbourg Wissenschaftsverlag; Edition: revised edition (March 14, 2005), ISBN 3486577700 , p. 115
  4. Neoclassical production functions ( Memento of the original from July 3, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. - short economics article  @1@ 2Template: Webachiv / IABot /
  5. Compare this: Paul Anthony Samuelson, William D. Nordhaus: Volkswirtschaftslehre. The international standard work of macro and microeconomics , mi-Fachverlag; Edition: N.-A. (November 2005), ISBN 3636030337 , page 164: The Income Act states that we continuously receive lower additional income if we continue to increase an input with unchanged other factors.
  6. Arthur Woll: General Economics . Vahlen Franz GmbH; Edition: 12th, 1996, ISBN 3800629739 , page 174f
  7. ^ Günter Wöhe / Ulrich Döring : Introduction to General Business Administration , Vahlen; Edition: 24th, revised and updated edition. (September 13, 2010), ISBN 3800637952 , p. 396
  8. Income Act - definition in the dictionary of the Federal Agency for Civic Education
  9. a b Bernd Schiemenz, Olaf Schönert: Decision and Production , Oldenbourg Wissenschaftsverlag; Edition: revised edition (March 23, 2005), ISBN 3486577166 , p. 106
  10. Horst Siebert, Oliver Lorz: Introduction to Economics , Kohlhammer; Edition: 15th, completely revised. Edition (May 2007), ISBN 3170194372 , p. 72
  11. ^ A b Winfried Reiss: Microeconomic Theory: Historically founded introduction , Oldenbourg Wissenschaftsverlag; Edition: 6. completely revised. u. verb. A (September 1, 2007), ISBN 3486585444 , page 90f