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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 ...
For a utility function with perfect substitutes, the utility maximising bundle can be found by differentiation or simply by inspection. Suppose a consumer finds listening to Australian rock bands AC/DC and Tame Impala perfect substitutes. This means that they are happy to spend all afternoon listening to only AC/DC, or only Tame Impala, or ...
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.
A consumer's indirect utility (,) can be computed from their utility function (), defined over vectors of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector (,) by solving the utility maximization problem, and second, computing the utility ((,)) the consumer derives from that ...
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.
Formally, the expenditure function is defined as follows. Suppose the consumer has a utility function defined on commodities. Then the consumer's expenditure function gives the amount of money required to buy a package of commodities at given prices that give utility of at least ,
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 modelling, it has been found to be violated in psychological experiments.
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility function.