Diminishing returns

The law of diminishing returns describes a production- technical issue that occurs with partial factor variation. It is an economics model, which is studied both in economics and business administration, in particular the production theory and microeconomics.

Overall, this model provides a particularly vivid ( didactic ) concept, relations of use (inputs) and results (output) to describe. In everyday life, it soon becomes clear a work is performed initially faster when " some tackle together " ( division of labor), but with further increase in the number of participants decreases the efficiency and it is perhaps even less reached (" Too many cooks spoil the broth" ).

This law applies not only in agricultural production, where she was discovered and formulated as crop yield law, but is far beyond the industrial production - also applicable to other areas, again under the condition that a factor is kept constant - ceteris paribus.

Examples: If far hardly or little advertised for the product X or Y, and the party now greatly increased advertising expenses, the revenues and the voting shares initially grow progressively. At a certain point they grow only gradually decreased until they asymptotically tend to zero. This trend can be while maintaining quality by even the big expenses no longer turn back.

Conceptual delimitation

The law of diminishing returns in the real sense, also called classical law of diminishing returns, now describes a technological approach, product quantity initially proportional to the multiplication by a factor ( cp ), from a certain point at a lower rate increases and eventually decreases absolutely. This law is divided into four phases ( see section yield law # phases) and thus has the broader meaning content.

Understood in the narrow sense already the classics, that the first phase of the production is mostly irrelevant. Thus one often speaks of the distinction in classical and neo-classical law of diminishing returns. With the neo-classical law of diminishing returns, the phases are now 2 and 3 meant (also neoclassical neoclassical production area or even function). These are for the microeconomic theory of the firm is of particular interest, because only here for a competing company ( Polypol ) profit maximization is possible. The law of diminishing returns of neoclassical production theory thus assumes from the outset positive and decreasing marginal returns ( neoclassical production function ). In this area increases with each factor of production - unit additionally used, the total income, the marginal product is still positive, but in terms of value is already below the average yield.

Often, the short form is used in the German law of diminishing returns is misleading, since in fact not the law of diminishing returns as a whole, but only the special interest cutout - the neoclassical production function - is meant. Other curves can have a " statutory income " show connection between fact amounts and income. There are also statutory earnings- cost functions.

Unique is the name law of diminishing marginal returns or law of diminishing returns (if a variable factor, that is, ceteris paribus ).

It is so rather than qualitative differences in the description of the same facts. The law of diminishing returns is not a rule within the meaning of a legal norm yet it means a regulation within the meaning of an unconditional scientific method.

History

The classical law of diminishing returns is the oldest production function. When his " explorers " are independently Turgot, Thünen, James Denham - Steuart and Malthus, who came from various approaches out to comparable descriptions.

• Anne Robert Jacques Turgot

Turgot was a French statesman and economist of the Enlightenment. By observing the agricultural production he arrived 1767/68 to the realization that if one keeps all else constant factors ( eg size of the arable land, quantity of seed and fertilizer ), with the increasing use of work initially with increasing, but from is to be expected at some point with decreasing earnings growth.

• Johann Heinrich von Thünen

Thünen collected on his estate in Mecklenburg statistical evidence to draw conclusions about the rational management of an agricultural material. So that he could 1842 prove statistically the observed regularity of Turgot and formalize.

" It is " in the nature of agriculture - and this is a very observance expensive fact - that the multi- product does not increase in direct proportion to the number of more salaried workers, but any later be put workers provides a smaller product than the previous ... " "

One can state that already Thünen ( 1850) did not mean the classical law of diminishing returns in the broad sense. He probably rule out initial increase in efficiency because you can not lead a good sense with only a few workers.

Statutory earnings production function

Plausibility has the classic law of diminishing returns over its entire course (actually only ) for agricultural production processes with partial factor variation. However it is also used as a yield curve in total variation factor and other production processes. The reason for this is its high didactic potential. The functional areas to both shows as well as diminishing marginal returns. The point of the change from increasing to decreasing marginal returns ( turning point ) is called the (first) " threshold " because from this point drop the earnings growth. With the inflection point corresponds to the minimum marginal cost, which is referred to as a further (second) threshold. In the classical law of diminishing returns, the average income have there a maximum where the production elasticity is one, that is, the marginal returns are equal to the average income.

In the diagrammatic representation, it is reminiscent of the shape of a tilted to the right page in the Business Administration course is also known as statutory income production function or production function of type A. The added use of a means of production in constancy of the other factors of production first brings increasing earnings growth ( marginal or marginal products ), then from a certain quantity of decreasing and eventually even negative marginal returns.

Phase I

The first section is characterized by an above-average slope of the yield function. Marginal and average earnings also rise, but the Phase I is limited by the maximum of the marginal function. Mathematically, this can be determined by setting the second derivative of the yield function equal to zero.

Phase II

The second section is characterized by an approximately proportional to the slope of the yield function (caused by approximately constant marginal returns ). The marginal revenue function is already decreasing again, while the average yield function is still rising. 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.

Phase III

The third section is characterized by a below-average slope of the yield function. In this phase, both the marginal revenue function and the average yield function decreases. Limits the Phase III is characterized by the maximum of the yield function. At this interval limit the marginal return function intersects the abscissa. Mathematically determine this by the 1st derivative is equal to zero.

Phase IV

In the fourth section have earnings, marginal and average yield function on a negative slope.

Example

In agriculture, can the functional show (even after the French economist J. Turgot and its Turgotschem law of diminishing returns ) the example of the use of fertilizer: The continuously increased use of fertilizers ( in otherwise constant resources / conditions ( ceteris paribus ), ie for example, a constant area ) in income initially grows steadily. The revenue increase per additional seeded fertilizer quantity decreases from a certain production quantity. This eventually results in additional fertilizer application even in an overall yield reduction and even for soil poisoning: An excessive use of fertilizers will lead to earnings below the level that would have been achieved without fertilizers and eventually destroy any income. Similar observations can be made even when the factors of heat and water.

These observations go back on Eilhard Alfred Mitscherlich, who published The Law of the Minimum, and the law of diminishing yield with corresponding history charts in 1909.

Using the example of industrial production or administration can also observe the law of diminishing returns on the increased use of personnel at otherwise constant conditions, the larger is the number of employees, the greater the need for coordination and communication. However, it can be achieved situations where employees against each other only in the way or demotivate. More is moved not only by the staff augmentation so. A State of centralized controls its economy and workers allocates the production, so as to avoid the problem of unemployment can hardly increase its productivity in this way.

The classical law of diminishing returns is not necessary for the establishment of a ( short-term ) profit legal cost trend, which leads to U-shaped average cost curves. This can occur as a result of the interaction of increasing marginal and declining average fixed cost even with consistently decreasing earnings growth.