Gossen's law

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As Gossen laws are called two economic rules based on the assumption that individual preferences in the form of benefits are quantifiable. Accordingly, a value can be assigned to the degree of satisfaction of an individual's needs , which can be calculated in utility units and, if necessary, offset against various utility units.

The rules were drawn up by the German economist Hermann Heinrich Gossen (1810–1858) in 1854 in his work Development of the Laws of Human Intercourse and the Rules for Human Action Flowing from it . They were ignored for a long time and only became later as Gossen's laws or laws for the satisfaction of needs designated.

The work was discovered after Gossen's death by a colleague of Stanley Jevons , who at that time was still arguing with Leon Walras about who should be the copyright holder of the essential considerations of subjective value theory - Jevon's work dates to 1871, Walras' 1874. After they learned of Gossen's work, but both recognized his priority.

First Gossen's Law

Decrease in marginal utility (u = utility, Δu = marginal utility, q = amount consumed)

The first Gossen law (also the law of diminishing marginal utility or saturation law) reads: "The size of one and the same enjoyment, if we continue with the preparation of the enjoyment, continually decreases until the last time saturation occurs." The law says that consumption of a good with increasing quantity creates ever less additional benefit (marginal benefit).

Assuming cardinally measurable benefit, Gossen's first law takes up the hypothesis, which is considered valid for most activities, that the first activity unit creates more (additional) benefits than the second, the second more than the third, the third more than the fourth and so on. If one represents preferences about the consumption of only one good by a differentiable utility function, then Gossen's first law says that the second derivative of the utility function is negative.

A prime example is the consumption of foods, which typically become saturated (and as a result the marginal utility can also become negative). For example, the consumption of a first glass of water by a thirsty person is very beneficial, whereas the second is already somewhat less, the third is somewhat less additional and the fourth may already cause a feeling of fullness or nausea, i.e. H. the marginal utility turns negative. The extreme case could go as far as drowning in the water if there is too much of it.

Mathematical formulation of Gossen's 1st law (decreasing marginal utility) in the 2-goods case:

meaning

The law appears to be immediately plausible as empirical regularity, but can be dispensed with in large areas of microeconomic theory. It is largely replaced by the assumption that the better quantities of a preference relation are convex (illustrative: decreasing marginal rate of substitution between two goods). An exception are stochastic models, in which economic subjects make decisions, the consequences of which are random. Here the assumption of a decreasing (increasing) marginal utility of a random disbursement (or the strict concavity (convexity) of the utility function) is equivalent to the assumption of risk-averse ( risk-affine ) behavior, since the utility of the expected value of the possible disbursements is greater (smaller) with such a utility function. is than the expected value of the respective benefits of the possible payouts.

Example:

Possible payouts: and
Probabilities: Each
Expected value of the payouts:

With decreasing marginal utility, the utility rises disproportionately to the payout, e.g. B. . Here the benefit of the expected value of the payments would be greater than the expected value of the benefits of the payments .

Note the similarity to Johann Heinrich von Thünen's Law of Declining Marginal Yield .

Second Gossen's Law

Other terms are: Equimarginalprinzip, Marginal utility equalization rule, Law of the equalization of the weighted marginal utility, Gossen's marginal utility equalization law and Genussausgleichsgesetz.

"" The person who has the choice between several [ sic! ] Enjoyment is free, but the time is insufficient to fully prepare all of them, however different the absolute size of the individual enjoyments may be, in order to bring the sum of his enjoyment to the greatest before he even fully prepares the greatest , prepare them all partially, and indeed in such a ratio that the size of each enjoyment at the moment in which its preparation is interrupted, remains the same for all. ""

- Hermann Heinrich Gossen (1854)

Gossen's second law is about distributing income over a variety of needs in order to achieve the highest overall benefit.

A household is therefore in a household optimum when its marginal utility for all goods, divided by the price of the good, match. Otherwise it could increase its utility, since consumption could be restructured in such a way that a reduction in expenditure for one good means less loss of utility than a corresponding increase in expenditure for another good. Gossen's second law applies to both ordinal and cardinal utility measurement (where Gossen himself assumed cardinal utility measurability).

The statement that in the household optimum the price ratio of any two goods must agree with the ratio of their marginal rate of substitution (slope of the indifference curve) is equivalent to Gossen's second law.

If one denotes the consumer goods quantities of the goods available to an individual with , his (differentiable) utility function with , and the prices of the goods with , then Gossen's second law can be represented mathematically as follows:

Scope and Criticism

Gossen's work, the development of the laws of human intercourse and the resulting rules for human action , describes consumption in a natural economy in which the individual produces only for himself. Consumption is planned according to the subjective appreciation of the goods. The value is purely individual character in gutters. In Gossen's society there is neither division of labor nor production of goods for exchange. In this respect, Gossen describes a psychological benefit theory of the isolated individual, instead of "traffic" in the goods-producing society of his time - in the industrial revolution .

literature

  • Hermann Heinrich Gossen: Development of the laws of human intercourse, and the rules for human action that flow from them. Brunswick 1854

Web links

Individual evidence

  1. Ulrich van Suntum: The invisible hand. 3. Edition. Springer, 2005, page 36
  2. ^ Hermann Heinrich Gossen: Development of the Laws of Human Intercourse, and the rules for human action that flow from it. Braunschweig 1854, p. 4f.
  3. ^ Hermann Heinrich Gossen: Development of the Laws of Human Intercourse, and the rules for human action that flow from it. Braunschweig 1854, p. 12