*See
also: List of Economic Topics *

**UTILITY**
- microeconomics

In
economics, **utility** is a measure of the happiness or satisfaction gained
from a good or service.

The
concept is applied by economists in such topics as the indifference curve, which
measures the combination of a basket of commodities that an individual or a community
requests at a given level(s) of satisfaction. The concept is also used in utility
functions, social welfare functions, Pareto maximization, Edgeworth boxes and
contract curves. It is a central concept of welfare economics.

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

Utility
theory assumes that humankind is rational. That is, people maximize their utility
wherever possible. For instance, one would request more of a good if it is available
and if one has the ability to acquire that amount, if this is the rational thing
to do in the circumstances.

**Cardinal
and ordinal utility**

There
are mainly two kinds of measurement of utility implemented by economists: cardinal
utility and ordinal utility.

Utility
was originally viewed as a measurable quantity, so that it would be possible to
measure the utility of each individual in the society with respect to each good
available in the society, and to add these together to yield the total utility
of all people with respect to all goods in the society. Society could then aim
to maximise the total utility of all people in society, or equivalently the average
utility per person. This conception of utility as a measurable quantity that could
be aggregated across individuals is called cardinal utility.

Cardinal
utility quantitatively measures the preference of an individual towards a certain
commodity. Numbers assigned to different goods or services can be compared. A
utility of 100 units towards a cup of vodka is twice as desirable as a cup of
coffee with a utility level of 50 units.

The
concept of cardinal utility suffers from the absence of an objective measure of
utility when comparing the utility gained from consumption of a particular good
by one individual as opposed to another individual.

For
this reason, neoclassical economics abandoned utility as a foundation for the
analysis of economic behaviour, in favour of an analysis based upon preferences.
This led to the development of tools such as indifference curves to explain economic
behaviour.

In
this analysis, an individual is observed to prefer one choice to another. Preferences
can be ordered from most satisfying to least satisfying. Only the ordering is
important: the magnitude of the numerical values are not important except in as
much as they establish the order. A utility of 100 towards an ice-cream is not
twice as desirable as a utility of 50 towards candy. All that can be said is that
ice-cream is preferred to candy. There is no attempt to explain why one choice
is preferred to another; hence no need for a quantitative concept of utility.

It
is nonetheless possible, given a set of preferences which satisfy certain criteria
of reasonableness, to find a utility function that will explain these preferences.
Such a utility function takes on higher values for choices that the individual
prefers. Utility functions are a useful and widely used tool in modern economics.

A
utility function to describe an individual's set of preferences clearly is not
unique. If the value of the utility function were to be, eg, doubled, squared,
or subjected to any other strictly monotonically increasing function, it would
still describe the same preferences. With this approach to utility, known as ordinal
utility it is not possible to compare utility between individuals, or find the
total utility for society as the Utilitarians hoped to do.

**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 packages
the consumer could conceivably consume. The consumer's utility function
assigns a happiness score to each package in the consumption set. If u(x) >
u(y), then the consumer strictly prefers x to y.

For
example, suppose a consumer's consumption set is X = {nothing, 1 apple, 1 orange,
1 apple and 1 orange, 2 apples, 2 oranges}, 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
microeconomics 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 , and each
package 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
= 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
rationalizes a preference relation <= on X if for every ,
u(x) <= u(y) if and only if x <= y. If u rationalizes <=, then this implies
<= is complete and transitive, and hence rational.

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