Gossen's laws

As Gossen's laws are referred to two economic rules that are based on the assumption that individual preferences in the form of benefits are quantifiable. Thus, the degree of satisfaction of needs of an individual may be assigned a value, which can be calculated in units of utility and be set off against different units of utility.

The rules are of the German economist Hermann Heinrich Gossen (1810-1858) was erected in 1854 in his work " development of the laws of human intercourse and the flowing therefrom rules for human action ," were long unnoticed and were only later as Gossen's laws or " regularities of need satisfaction ", respectively.

The work was discovered after the death of Gossen's by a colleague of Stanley Jevons, who at that time still with Leon Walras about quarreled who should play the authorship of the main considerations of the subjective theory of value -. Jevons work dates back to 1871, Walras ' 1874 After they learned of Gossen's work, but both recognized its priority to.

First Gossen's law

The first law of Gossen (also law of diminishing marginal utility or saturation Act ) reads: "The size of the same enjoyment increases if we continue uninterruptedly with preparation of enjoyment, continually, until last saturation occurs. " This law states so that the consumption a commodity with increasing amount less and less additional benefit ( marginal utility ) creates.

The first law of Gossen thus picking up on the assumption cardinally measurable benefits on those deemed most activities as a valid hypothesis that the first unit of activity more (additional) benefit endows than the second, the second more than the third, the third longer than the fourth and so on. Represents one preferences over the consumption of one good only by a differentiable utility function, so says the first law of Gossen, that the second derivative of the utility function is negative.

Prime example is the consumption of food, which typically saturation occurs (and in the sequence of marginal utility can also be negative). Thus, the benefit of a first glass of water by a thirsty donates a very high value, whereas the second is already causing a slightly lower, and the third in turn slightly less added value of the fourth and perhaps bloating or nausea, that is, the marginal utility proposes to Negative order. The extreme case could go so far that you will drown in the water, if too much of it is there.

Importance

The law appears immediately plausible as an empirical regularity, but is dispensable in a wide range of microeconomic theory. It is largely replaced by the assumption that the better amounts of a preference relation is convex (clearly: decreasing marginal rate of substitution between any two goods). An exception to stochastic models in which economic agents make decisions whose consequences are random subject. Here is the assumption of a decreasing ( increasing ) marginal utility of a randomly -prone bank (or the strict concavity ( convexity ) of the utility function ) is equivalent to adopting risk-averse ( risk-prone ) behavior, since the benefits of the expected value of the possible payoffs in such a utility function is larger ( smaller) than the expected value of the respective benefits of potential payouts.

Example:

With decreasing marginal utility of benefits under U increases proportionally to the payout, for example, U ( 0) = 0; U ( 50) = 3; U ( 100) = 4 This would be the benefits of the expected value of payments = U ( 50) = 3 is greater than the expected value of the benefit of disbursements = E ( U (0 ) U ( 100 )) = E (0, 4 ) = 0.5 * 0 0.5 * 4 = 2

Note the similarity to Johann Heinrich von Thünen's law of diminishing marginal returns.

Second Gossen's law

Other names are: Equimarginalprinzip, marginal utility balancing rule, the law of compensation of the weighted marginal utility, marginal utility cal poured Compensation Act and Related Compensation Act.

"Man, the choice between several [ sic] pleasures are free, whose time is not sufficient, all the extremes of to prepare, must how different may be the absolute size of the individual flavors to the sum of his enjoyment of the greatest of bring before even the largest to the extremes of preparing, they are all partially prepare, in such a proportion that the size of each enjoyment will be canceled at the very moment in which its preparation, all remains the same. "

The second law of Gossen it comes to the distribution of income between a variety of needs, to achieve the highest total utility.

A household is thus in a household optimum when its marginal utility for all goods, each divided by the price of the good match. Otherwise, it could increase its usefulness, since a restructuring of consumption could make so that an output reduction at a good means less utility loss than a corresponding increase in spending with another good utility increase. The second law of Gossen applies to both ordinal and cardinal utility for measurement (where gutters themselves of cardinal Nutzenmessbarkeit ran out ).

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

Denoting the consumer amounts of an individual available goods with its ( differentiable ) utility function with, and the prices of goods, then the second law of Gossen be mathematically represented as follows: