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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.
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 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.
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.
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.
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.
Note that since utility is not observable, the substitution effect is not directly observable. Still, it can be calculated by referencing the other two observable terms in the Slutsky equation. This process is sometimes known as the Hicks decomposition of a demand change. [2] The equation can be rewritten in terms of elasticity:
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.