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The summarised formula for expected utility is () = where is the probability that outcome indexed by with payoff is realized, and function u expresses the utility of each respective payoff. [1] Graphically the curvature of the u function captures the agent's risk attitude.
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.
Robert Hall was the first to derive the effects of rational expectations for consumption. His theory states that if Milton Friedman’s permanent income hypothesis is correct, which in short says current income should be viewed as the sum of permanent income and transitory income and that consumption depends primarily on permanent income, and if consumers have rational expectations, then any ...
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.
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.
Bernoulli's imaginary logarithmic utility function and Gabriel Cramer's U = W 1/2 function were conceived at the time not for a theory of demand but to solve the St. Petersburg's game. Bernoulli assumed that "a poor man generally obtains more utility than a rich man from an equal gain" [ 3 ] an approach that is more profound than the simple ...
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.
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).