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Utility

Within economics, the concept of utility is used to model worth or value. Its usage has evolved over time; the term was introduced as a measure of pleasure or satisfaction within the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a consumer's preference ordering over a choice set, it is devoid of its original interpretation as a measurement of the pleasure or satisfaction obtained by the consumer from that choice. Consider a set of alternatives facing an individual, over which the individual has a preference ordering. A utility function is able to represent those preferences if it is possible to assign a real number to each alternative, in such a way that alternative a is assigned a number greater than alternative b if, only if, the individual prefers alternative a to alternative b. In this situation an individual that selects the most preferred alternative available is also selecting the alternative that maximises the associated utility function.

In general economic terms, a utility function measures preferences concerning a set of goods and services. Utility is correlated with words such as happiness and welfare, these are hard to measure mathematically. Thus, economists utilize consumption baskets of preferences in order to measure these abstract, non quantifiable ideas. Gérard Debreu defined the conditions required for a preference ordering to be representable by a utility function. For a finite set of alternatives these require only that the preference ordering is complete, that the preference order is transitive. Utility is applied by economists in such constructs as the indifference curve, which plot the combination of commodities that an individual or a society would accept to maintain a given level of satisfaction. Utility and indifference curves are used by economists to understand the underpinnings of demand curves, which are half of the supply and demand analysis, used to analyze the workings of goods markets. Individual utility and social utility can be construed as the value of a utility function and a social welfare function respectively.

When coupled with production or commodity constraints, under some assumptions these functions can be used to analyze Pareto efficiency, such as illustrated by Edgeworth boxes in contract curves. Such efficiency is a central concept in welfare economics. In finance, utility is applied to generate an individual's price for an asset called the indifference price. Utility functions are related to risk measures, with the most common example being the entropic risk measure. In the field of artificial intelligence, utility functions are used to convey the value of various outcomes to intelligent agents; this allows the agents to plan actions with the goal of maximizing the utility of available choices. It was recognized that utility could not be measured or observed directly, so instead economists devised a way to infer underlying relative utilities from observed choice. These'revealed preferences', as they were named by Paul Samuelson, were revealed e.g. in people's willingness to pay: Utility is taken to be correlative to Desire or Want.

It has been argued that desires cannot be measured directly, but only indirectly, by the outward phenomena to which they give rise: and that in those cases with which economics is chiefly concerned the measure is found in the price which a person is willing to pay for the fulfillment or satisfaction of his desire. There has been some controversy over the question whether the utility of a commodity can be measured or not. At one time, it was assumed that the consumer was able to say how much utility he got from the commodity; the economists who made this assumption belonged to the'cardinalist school' of economics. Today utility functions, expressing utility as a function of the amounts of the various goods consumed, are treated as either cardinal or ordinal, depending on whether they are or are not interpreted as providing more information than the rank ordering of preferences over bundles of goods, such as information on the strength of preferences; when cardinal utility is used, the magnitude of utility differences is treated as an ethically or behaviorally significant quantity.

For example, suppose a cup of orange juice has utility of 120 utils, a cup of tea has a utility of 80 utils, a cup of water has a utility of 40 utils. With cardinal utility, it can be concluded that the cup of orange juice is better than the cup of tea by the same amount by which the cup of tea is better than the cup of water. Formally speaking, this means that if one has a cup of tea, she would be willing to take any bet with a probability, p, greater than.5 of getting a cup of juice, with a risk of getting a cup of water equal to 1-p. One cannot conclude, that the cup of tea is two thirds of the goodness of the cup of juice, because this conclusion would depend not only on magnitudes of utility differences, but on the "zero" of utility. For example, if the "zero" of utility was located at -40 a cup of orange juice would be 160 utils more than zero, a cup of tea 120 utils more than zero. Cardinal utility, to economics, can be seen as the assumption that utility can be measured through quantifiable characteristics, such as height, temperature, etc.

Neoclassical economics has retreated from using cardinal utility functions as the basis of economic behavior. A notable exception is in the context of analyzing choice under conditions of r

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