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Standard utility functions represent ordinal preferences. The expected utility hypothesis imposes limitations on the utility function and makes utility cardinal (though still not comparable across individuals). Although the expected utility hypothesis is standard in economic modeling, it is violated in psychological experiments.
A single-attribute utility function maps the amount of money a person has (or gains), to a number representing the subjective satisfaction he derives from it. The motivation to define a utility function comes from the St. Petersburg paradox: the observation that people are not willing to pay much for a lottery, even if its expected monetary gain is infinite.
Isoelastic utility for different values of . When > the curve approaches the horizontal axis asymptotically from below with no lower bound.. In economics, the isoelastic function for utility, also known as the isoelastic utility function, or power utility function, is used to express utility in terms of consumption or some other economic variable that a decision-maker is concerned with.
A utility representation theorem gives conditions on a preference relation, that are sufficient for the existence of a utility representation. Often, one would like the representing function u to satisfy additional conditions, such as continuity.
Under these requirements, every stream is equivalent to a constant-utility stream, and every two constant-utility streams are separable by a constant-utility stream with a rational utility, so condition #2 of Debreu is satisfied, and the preference relation can be represented by a real-valued function.
The utility function u(c) is defined only up to positive affine transformation – in other words, a constant could be added to the value of u(c) for all c, and/or u(c) could be multiplied by a positive constant factor, without affecting the conclusions. An agent is risk-averse if and only if the utility function is concave.
When faced with several alternatives, the person will choose the alternative with the highest utility. The utility function is not visible; however, by observing the choices made by the person, we can "reverse-engineer" his utility function. This is the goal of revealed preference theory. [citation needed] In practice, however, people are not ...
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function.