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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.
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 ...
Figure 3: This shows the utility maximisation problem with a minimum utility function. For a minimum function with goods that are perfect complements, the same steps cannot be taken to find the utility maximising bundle as it is a non differentiable function. Therefore, intuition must be used.
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.
One use of the indirect utility concept is the notion of the utility of money. The (indirect) utility function for money is a nonlinear function that is bounded and asymmetric about the origin. The utility function is concave in the positive region, representing the phenomenon of diminishing marginal utility. The boundedness represents the fact ...
In decision theory, subjective expected utility is the attractiveness of an economic opportunity as perceived by a decision-maker in the presence of risk.Characterizing the behavior of decision-makers as using subjective expected utility was promoted and axiomatized by L. J. Savage in 1954 [1] [2] following previous work by Ramsey and von Neumann. [3]