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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.
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, 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.
For every utility function v, there is a unique preference relation represented by v. However, the opposite is not true: a preference relation may be represented by many different utility functions. The same preferences could be expressed as any utility function that is a monotonically increasing transformation of v. E.g., if
The sign of the second derivative of a differentiable utility function that is cardinal, is the same for all the numerical representations of a particular preference structure. Given that this is usually a negative sign, there is room for a law of diminishing marginal utility in cardinal utility theory.
where E is the expectation operator, u is a known utility function (which applies both to consumption and to the terminal wealth, or bequest, W T), ε parameterizes the desired level of bequest, ρ is the subjective discount rate, and is a constant which expresses the investor's risk aversion: the higher the gamma, the more reluctance to own ...
The utility function whose expected value is maximized is concave for a risk averse agent, convex for a risk lover, and linear for a risk neutral agent. Thus in the risk neutral case, expected utility of wealth is simply equal to the expectation of a linear function of wealth, and maximizing it is equivalent to maximizing expected wealth itself.
One extra unit of utility for a starving person is not seen to be of any greater value than an extra unit of utility for a millionaire. At the other extreme is the Max-Min, or Rawlsian utility function. [8] According to the Max-Min criterion, welfare is maximized when the utility of those society members that have the least is the greatest.