# Dictionary Definition

# User Contributed Dictionary

## English

### Noun

usefulness (uncountable)- the quality of being useful, to which extent something is useful
- The usefulness of his latest reorganisation has been disputed.

#### Translations

quality of being useful

- Czech: užitečnost
- Finnish: hyödyllisyys
- German: Nützlichkeit
- Icelandic: gagnsemi

# Extensive Definition

In economics, utility is a
measure of the relative satisfaction from or desirability of
consumption of goods.
Given this measure, one may speak meaningfully of increasing or
decreasing utility, and thereby explain economic behavior in terms
of attempts to increase one's utility. For illustrative purposes,
changes in utility are sometimes expressed in units called
utils.

The doctrine of utilitarianism saw the
maximization of utility as a moral criterion for the organization
of society. According to utilitarians, such as Jeremy
Bentham (1748-1832) and John
Stuart Mill (1806-1876), society should aim to maximize the
total utility of individuals, aiming for "the greatest happiness
for the greatest number".

In neoclassical economics, rationality is
precisely defined in terms of imputed utility-maximizing behavior
under economic constraints. As a hypothetical behavioral measure,
utility does not require attribution of mental states suggested by
"happiness", "satisfaction", etc.

Utility is applied by economists in such
constructs as the indifference
curve, which plots the combination of commodities that an
individual or a society requires to maintain a given level of
satisfaction. Individual utility and social utility can be
construed as the dependent
variable of a utility function (such as an indifference curve
map) and a social
welfare function respectively. When coupled with production or
commodity constraints, these functions can represent Pareto
efficiency, such as illustrated by Edgeworth
boxes and contract
curves. Such efficiency is a central concept of welfare
economics.

## Cardinal/ordinal utility

Economists distinguish between cardinal
utility and ordinal
utility. When cardinal utility is used, the magnitude of
utility differences is treated as an ethically or behaviorally
significant quantity. On the other hand, ordinal utility captures
only ranking and not strength of preferences. An important example
of a cardinal utility is the probability of achieving some
target.

Utility functions of both sorts assign real
numbers (utils) to members of a choice set. For example, suppose a
cup of coffee has utility of 120 utils, a cup of tea has a utility
of 80 utils, and a cup of water has a utility of 40 utils. When
speaking of cardinal utility, it could be concluded that the cup of
coffee is better than the cup of tea by exactly the same amount by
which the cup of tea is better than the cup of water. One is not
entitled to conclude, however, that the cup of tea is two thirds as
good as the cup of coffee, because this conclusion would depend not
only on magnitudes of utility differences, but also on the "zero"
of utility.

It is tempting when dealing with cardinal utility
to aggregate utilities across persons. The argument against this is
that interpersonal comparisons of utility are suspect because there
is no good way to interpret how different people value consumption
bundles.

When ordinal utilities are used, differences in
utils are treated as ethically or behaviorally meaningless: the
utility values assigned encode a full behavioral ordering between
members of a choice set, but nothing about strength of preferences.
In the above example, it would only be possible to say that coffee
is preferred to tea to water, but no more.

Neoclassical
economics has largely retreated from using cardinal utility
functions as the basic objects of economic analysis, in favor of
considering agent preferences over choice sets.
As will be seen in subsequent sections, however, preference
relations can often be rationalized as utility functions satisfying
a variety of useful properties.

Ordinal utility functions are equivalent up to monotone
transformations, while cardinal utilities are equivalent up to
positive linear transformations.

## Utility functions

While preferences are the
conventional foundation of microeconomics, it is
convenient to represent preferences with a utility function and
reason indirectly about preferences with utility functions. Let X
be the consumption set, the set of all mutually-exclusive packages
the consumer could conceivably consume (such as an indifference
curve map without the indifference curves). The consumer's
utility function u : X \rightarrow \textbf R ranks each package in
the consumption set. If u(x) ≥ u(y) (x R y), then the consumer
strictly prefers x to y or is indifferent between them.

For example, suppose a consumer's consumption set
is X = , and its utility function is u(nothing) = 0, u (1 apple) =
1, u (1 orange) = 2, u (1 apple and 1 orange) = 4, u (2 apples) = 2
and u (2 oranges) = 3. Then this consumer prefers 1 orange to 1
apple, but prefers one of each to 2 oranges.

In microeconomic models, there are usually a
finite set of L commodities, and a consumer may consume an
arbitrary amount of each commodity. This gives a consumption set of
\textbf R^L_+, and each package x \in \textbf R^L_+ is a vector
containing the amounts of each commodity. In the previous example,
we might say there are two commodities: apples and oranges. If we
say apples is the first commodity, and oranges the second, then the
consumption set X = \textbf R^2_+ and u (0, 0) = 0, u (1, 0) = 1, u
(0, 1) = 2, u (1, 1) = 4, u (2, 0) = 2, u (0, 2) = 3 as before.
Note that for u to be a utility function on X, it must be defined
for every package in X.

A utility function u : X \rightarrow \textbf
rationalizes a preference relation \preceq on X if for every x, y
\in X, u(x)\leq u(y) if and
only if x\preceq y. If u rationalizes \preceq, then this
implies \preceq is complete and transitive, and hence
rational.

In order to simplify calculations, various
assumptions have been made of utility functions.

- CES (constant elasticity of substitution, or isoelastic) utility is one with constant relative risk aversion
- Exponential utility exhibits constant absolute risk aversion
- Quasilinear utility
- Homothetic utility

Most utility functions used in modeling or theory
are well-behaved. They usually exhibit monotonicity, convexity, and
global non-satiation. There are some important exceptions,
however.

Lexicographic
preferences cannot even be represented by a utility
function.

## Expected utility

The expected
utility model was first proposed by Daniel
Bernoulli as a solution to the St.
Petersburg paradox. Bernoulli argued that the paradox could be
resolved if decisionmakers displayed risk
aversion and argued for a logarithmic cardinal utility
function.

The first important use of the expected utility
theory was that of John von
Neumann and Oskar
Morgenstern who used the assumption of expected utility
maximization in their formulation of game
theory.

A von Neumann-Morgenstern utility function u : X
\rightarrow \textbf assigns a real number to every element of the
outcome space in a way that captures the agent's preferences over
both simple and compound lotteries (put in category-theoretic
language, u induces a morphism between the category of preferences
under uncertainty and the category of reals). The agent will prefer
a lottery L_1 to a lottery L_2 if and only if the expected utility
(iterated over compound lotteries if necessary) of L_1 is greater
than the expected utility of L_2.

Restricting to the discrete choice context, let L
: X \rightarrow [0,1] be a simple lottery such that L(x_i) = p_i,
where p_i is the probability that x_i is won. We may also consider
compound lotteries, where the prizes are themselves simple
lotteries.

The expected utility theorem says that a von
Neumann-Morgenstern utility function exists if and only if the
agent's preference
relation on the space of simple lotteries satisfies four
axioms: completeness, transitivity, convexity/continuity (also
called the Archimedean property), and independence.

Completeness and transitivity are discussed
supra. The Archimedean property says that for simple lotteries L_1
\geq L_2 \geq L_3, then there exists a 0 \leq p \leq 1 such that
the agent is indifferent between L_2 and the compound lottery
mixing between L_1 and L_3 with probability p and 1-p,
respectively. Independence means that if the agent is indifferent
between simple lotteries L_1 and L_2, the agent is also indifferent
between L_1 mixed with an arbitrary simple lottery L_3 with
probability p and L_2 mixed with L_3 with the same probability
p.

Independence is probably the most controversial
of the axioms. A variety of
generalized expected utility theories have arisen, most of
which drop or relax the independence axiom.

## Utility of money

One of the most common uses of a utility
function, especially in economics, is the utility of
money. The utility function for money is a nonlinear function that
is bounded and
asymmetric about the origin. These properties can be derived from
reasonable assumptions that are generally accepted by economists and decision
theorists, especially proponents of rational
choice theory. The utility function is concave in
the positive region, reflecting the phenomenon of
diminishing marginal utility. The boundedness reflects the fact
that beyond a certain point money ceases being useful at all, as
the size of any economy at any point in time is itself bounded. The
asymmetry about the origin reflects the fact that gaining and
losing money can have radically different implications both for
individuals and businesses. The nonlinearity of the utility
function for money has profound implications in decision making
processes: in situations where outcomes of choices influence
utility through gains or losses of money, which are the norm in
most business settings, the optimal choice for a given decision
depends on the possible outcomes of all other decisions in the same
time-period.

## Discussion and criticism

Different value systems have different
perspectives on the use of utility in making moral judgments. For example,
Marxists,
Kantians, and
certain libertarians
(such as Nozick) all believe
utility to be irrelevant as a moral standard or at least not as
important as other factors such as natural rights, law, conscience and/or
religious doctrine. It is debatable whether any of these can be
adequately represented in a system that uses a utility model.

## See also

- Allais paradox
- behavioral economics
- Choice Modelling
- consumer surplus
- convex preferences
- cumulative prospect theory
- decision theory
- efficient market theory
- expectation utilities
- Ellsberg paradox
- game theory
- list of economics topics
- marginal utility
- microeconomics
- prospect theory
- risk aversion
- risk premium
- Transferable utility
- Utility Maximization Problem
- utility (patent)
- utility model

## References and additional reading

- Neumann, John von and Morgenstern, Oskar Theory of Games and Economic Behavior. Princeton, NJ. Princeton University Press. 1944 sec.ed. 1947
- Nash Jr., John F. The Bargaining Problem. Econometrica 18:155 1950
- Anand, Paul. Foundations of Rational Choice Under Risk Oxford, Oxford University Press. 1993 reprinted 1995, 2002
- Kreps, David M. Notes on the Theory of Choice. Boulder, CO. Westview Press. 1988
- Fishburn, Peter C. Utility Theory for Decision Making. Huntington, NY. Robert E. Krieger Publishing Co. 1970. ISBN 978-0471260608
- Plous, S. The Psychology of Judgement and Decision Making New York: McGraw-Hill, 1993
- Virine, L. and Trumper M., Project Decisions: The Art and Science. Management Concepts. Vienna, VA, 2007. ISBN 978-1567262179

## External links

usefulness in Czech: Užitek

usefulness in German: Nutzenfunktion

usefulness in Spanish: Utilidad
(desambiguación)

usefulness in Persian: مطلوبیت

usefulness in French: Utilité

usefulness in Korean: 효용

usefulness in Hungarian: Hasznossági
függvény

usefulness in Indonesian: Utilitas

usefulness in Japanese: 効用

usefulness in Lao: ຜົນປະໂຫຍດ

usefulness in Portuguese: Função de
utilidade

usefulness in Romanian: Funcţie de
utilitate

usefulness in Russian: Полезность
(экономика)

usefulness in Finnish: Hyöty

usefulness in Swedish: Nytta

usefulness in Vietnamese: Thỏa dụng

usefulness in Chinese: 效用

# Synonyms, Antonyms and Related Words

account, advantage, advantageousness,
advisability,
agreeableness,
applicability,
appropriateness,
auspiciousness,
availability,
beneficialness,
benefit, benevolence, benignity, class, cogency, convenience, decency, desert, desirability, effectiveness, efficacy, efficiency, excellence, expedience, expediency, fairness, favorableness, feasibility, fineness, first-rateness,
fitness, fittingness, fruitfulness, functionality, gain, goodliness, goodness, grace, healthiness, help, helpfulness, kindness, merit, niceness, operability, opportuneness, percentage, pleasantness, point, politicness, practicability, practical
utility, practicality, profit, profitability, profitableness, propriety, prudence, purpose, purposefulness, quality, relevance, rewardingness, rightness, seasonableness, seemliness, service, serviceability, skillfulness, soundness, suitability, superiority, timeliness, usability, use, utility, utilizability, validity, value, virtue, virtuousness, wholeness, wisdom, worth, worthwhileness