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Concept
Utility
Summary
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of 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 ordinal preferences over a choice set, but is not necessarily comparable across consumers or possessing a cardinal interpretation. This concept of utility is personal and based on choice rather than on pleasure received, and so requires fewer behavioral assumptions than the original concept.
Consider a set of alternatives among which a person has a preference ordering. A utility function represents that ordering if it is possible to assign a real number to each alternative in such a manner that alternative a is assigned a number greater than alternative b if and only if the individual prefers alternative a to alternative b. In this situation someone who selects the most preferred alternative is necessarily also selecting the alternative that maximizes the associated utility function.
Suppose James has utility function such that x is the number of apples and y is the number of chocolates. Alternative A has apples and chocolates; alternative B has apples and chocolates. Putting the values x, y into the utility function yields for alternative A and for B, so James prefers alternative B. In general economic terms, a utility function ranks preferences concerning a set of goods and services.
Gérard Debreu derived 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 (so the individual is able to determine which of any two alternatives is preferred or that they are indifferent), and that the preference order is transitive.
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