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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.
Inverting this formula gives the indirect utility function (utility as a function of price and income): (,) = (),where is the amount of income available to the individual and is equivalent to the expenditure ((,)) in the previous equation.
Exponential utility implies constant absolute risk aversion (CARA), with coefficient of absolute risk aversion equal to a constant: ″ ′ =. In the standard model of one risky asset and one risk-free asset, [1] [2] for example, this feature implies that the optimal holding of the risky asset is independent of the level of initial wealth; thus on the margin any additional wealth would be ...
A multi-utility representation (MUR) of a relation is a set U of utility functions, such that : (). In other words, A is preferred to B if and only if all utility functions in the set U unanimously hold this preference. The concept was introduced by Efe Ok.
The term E-utility for "experience utility" has been coined [2] to refer to the types of "hedonistic" utility like that of Bentham's greatest happiness principle. Since morality affects decisions, a VNM-rational agent's morals will affect the definition of its own utility function (see above).
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.
The right-hand side of the equation equals the change in demand for good i holding utility fixed at u minus the quantity of good j demanded, multiplied by the change in demand for good i when wealth changes. The first term on the right-hand side represents the substitution effect, and the second term represents the income effect. [1]