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. Face-to-face trading interactions on the New York Stock Exchange trading floor. ... A good in economics is any object or service that, upon consumption, increases utility, and therefore can be sold at a price in a market. ...

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". This article discusses utilitarian ethical theory. ... Jeremy Bentham (IPA: ) (26 February [O.S. 15 February 15] 1748) – June 6, 1832) was an English jurist, philosopher, and legal and social reformer. ... John Stuart Mill (20 May 1806 – 8 May 1873), British philosopher, political economist, civil servant and Member of Parliament, was an influential liberal thinker of the 19th century. ...

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. An indifference curve is a graph showing different bundles of goods, each measured as to quantity, to which a consumer is That is, at each point on the curve, the consumer has no preference for one bundle over another, as they render the same level of satisfaction (utility) for the... In experimental design, a dependent variable (also known as response variable, responding variable or regressand) is a factor whose values in different treatment conditions are compared. ... A social welfare function, in welfare economics, is a function which gives a measure of the material welfare of society, given a number of economic variables as inputs. ... Pareto efficiency, or Pareto optimality, is an important notion in neoclassical economics with broad applications in game theory, engineering and the social sciences. ... In economics, an Edgeworth box, named after Francis Ysidro Edgeworth, is a way of representing various distributions of resources. ... A contract curve is the set of all points in an Edgeworth box that are Pareto efficient. ... Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution associated with it. ...

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. Cardinal utility theory states that the utility (satisfaction) gained from a particular good or service can be measured in the same way as distance, temperature and time can. ... Ordinal utility theory states that while the utility of a particular good and service cannot be measured using an objective scale; a consumer is capable of ranking different alternatives available. ...

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 exactly the same amount better than a cup of tea as the cup of tea is better than the cup of water.

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. Neoclassical economics refers to a general approach (a metatheory) to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. ... Preference (or taste) is a concept, used in the social sciences, particularly economics. ...

Ordinal utility functions are equivalent up to monotone transformations, while cardinal utilities are equivalent up to positive linear transformations. Look up Up to on Wiktionary, the free dictionary In mathematics, the phrase up to xxxx indicates that members of an equivalence class are to be regarded as a single entity for some purpose. ...

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 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. Preference (or taste) is a concept, used in the social sciences, particularly economics. ... Microeconomics (or price theory) is a branch of economics that studies how individuals, households, and firms make decisions to allocate limited resources,[1] typically in markets where goods or services are being bought and sold. ... An indifference curve is a graph showing different bundles of goods, each measured as to quantity, to which a consumer is That is, at each point on the curve, the consumer has no preference for one bundle over another, as they render the same level of satisfaction (utility) for the...

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 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 , 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 , if and only if . If u rationalizes , then this implies is complete and transitive, and hence rational. ↔ ⇔ ≡ logical symbols representing iff. ...

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. In economics, more specifically econometrics or mathematical economics, there are production functions that describe the output given a certain combination of inputs (e. ... Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. ... In economics exponential utility refers to a specific form of the utility function, used in many contexts because of its convenience when uncertainty is present. ... The term quasilinear has several meanings, usually meaning something close to almost linear. ... In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point A called the origin. ...

Lexicographic preferences cannot even be represented by a utility function. There are very few or no other articles that link to this one. ...

Expected utility

Main article: Expected utility hypothesis

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. It has been suggested that Neumann-Morgenstern utility be merged into this article or section. ... The expected utility hypothesis is the hypothesis in economics that the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average. ... Daniel Bernoulli Daniel Bernoulli (February 8, 1700 – March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland where he died. ... In probability theory and decision theory the St. ... Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. ...

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. For other persons named John Neumann, see John Neumann (disambiguation). ... Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ... Game theory is a branch of applied mathematics that is often used in the context of economics. ...

A von Neumann-Morgenstern utility function 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 L₁ to a lottery L₂ if and only if the expected utility (iterated over compound lotteries if necessary) of L₁ is greater than the expected utility of L₂.

Restricting to the discrete choice context, let 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. Preference (or taste) is a concept, used in the social sciences, particularly economics. ...

Completeness and transitivity are discussed supra. The Archimedean property says that for simple lotteries , then there exists a such that the agent is indifferent between L₂ and the compound lottery mixing between L₁ and L₃ with probability p and 1 − p, respectively. Independence means that if the agent is indifferent between simple lotteries L₁ and L₂, the agent is also indifferent between L₁ mixed with an arbitrary simple lottery L₃ with probability p and L₂ mixed with L₃ 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. The expected utility model developed by John von Neumann and Oskar Morgenstern dominated decision theory from its formulation in 1944 until the late 1970s, despite powerful criticism from Maurice Allais and Daniel Ellsberg who showed that, in certain choice problems, decisions were usually inconsistent with the axioms of expected utility...

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. ^[1] Face-to-face trading interactions on the New York Stock Exchange trading floor. ... The term bounded appears in different parts of mathematics where a notion of size can be given. ... Economists are scholars conducting research in the field of economics. ... Decision theory is an area of study of discrete mathematics that models human decision-making in science, engineering and indeed all human social activities. ... Rational choice theory assumes human behavior is guided by instrumental reason. ... In calculus, a differentiable function f is convex on an interval if its derivative function f ′ is increasing on that interval: a convex function has an increasing slope. ... // A Abundance Abundance is the state in which there is more than enough. ...

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. This article is about the use of the moral in storytelling. ... Marx is a common German surname. ... Immanuel Kant Immanuel Kant (April 22, 1724 – February 12, 1804) was a Prussian philosopher, generally regarded as one of Europes most influential thinkers and the last major philosopher of the Enlightenment. ... See also Libertarianism and Libertarian Party Libertarian,is a term for person who has made a conscious and principled commitment, evidenced by a statement or Pledge, to forswear violating others rights and usually living in voluntary communities: thus in law no longer subject to government supervision. ... Robert Nozick (November 16, 1938 – January 23, 2002) was an American philosopher and Pellegrino University Professor at Harvard University. ... For the direction right, see left and right or starboard. ...

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

The Allais paradox, more neutrally described as the Allais problem, is a choice problem designed by Maurice Allais to show an inconsistency of actual observed choices with the predictions of expected utility theory. ... Nobel Prize in Economics winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ... Supply curve shift Consumer surplus or Consumers surplus (or in the plural Consumers surplus) is the economic gain accruing to a consumer (or consumers) when they engage in trade. ... Convex preferences refer to a property of utility functions commonly represented in an indifference curve as a bulge toward the origin. ... Cumulative Prospect Theory is a model for descriptive decisions under risk which has been introduced by Amos Tversky and Daniel Kahneman in 1992 (Tversky, Kahneman, 1992). ... Decision theory is an area of study of discrete mathematics that models human decision-making in science, engineering and indeed all human social activities. ... Efficient fuked up market theory is a field of economics which seeks to explain the workings of capital markets such as the stock market. ... A qualification introduced by Bentham, to distinguish between two different types of utilities, or, rather, sources of utility (for utility, being identical to pleasure, remains always qualitatively the same). ... The Ellsberg paradox is a paradox in decision theory and experimental economics in which peoples choices violate the expected utility hypothesis. ... Game theory is a branch of applied mathematics that is often used in the context of economics. ... This aims to be a complete list of the articles on economics. ... “Marginal revolution” redirects here. ... Microeconomics (or price theory) is a branch of economics that studies how individuals, households, and firms make decisions to allocate limited resources,[1] typically in markets where goods or services are being bought and sold. ... Prospect theory was developed by Daniel Kahneman and Amos Tversky in 1979 as a psychologically realistic alternative to expected utility theory. ... Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. ... A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to. ... Transferable utility is a term used in cooperative game theory and in economics. ... In microeconomics, the utility maximization problem is the problem consumers face: how should I spend my money in order to maximize my utility? Suppose their consumption set has L commodities. ... In United States patent law, utility is a patentability requirement. ... A utility model is an intellectual property right to protect inventions. ...

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

For other persons named John Neumann, see John Neumann (disambiguation). ... Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ... John Forbes Nash John Forbes Nash Jr. ... David M. Kreps is a game theory economist and professor at the Graduate School of Business at Stanford University. ... Peter C. Fishburn (born 1936) is known as a pioneer in the field of decision making processes. ...

External links

• Anatomy of Cobb-Douglas Type Utility Functions in 3D
• Anatomy of CES Type Utility Functions in 3D