Notable special cases of HARA utility functions include the isoelastic utility function.
2.
Strain gauges that are not self-temperature-compensated ( such as isoelastic alloy ) can be temperature compensated by use of the dummy gauge technique.
3.
A class of utility functions which are consistent with a steady state of this model are the isoelastic or constant relative risk aversion ( CRRA ) utility functions, given by:
4.
Models of modern macroeconomics and public finance often assume the constant-relative-risk-aversion form for within period utility ( also called the power utility or isoelastic utility ).
5.
The isoelastic utility function is a special case of the hyperbolic absolute risk aversion ( HARA ) utility functions, and is used in analyses that either include or do not include underlying risk.
6.
Though isoelastic utility, exhibiting constant " relative " risk aversion, is considered more plausible ( as are other utility functions exhibiting decreasing absolute risk aversion ), exponential utility is particularly convenient for many calculations.
7.
Note the difference between CES utility and isoelastic utility : the CES utility function is an ordinal utility function that represents preferences on sure consumption commodity bundles, while the isoelastic utility function is a cardinal utility function that represents preferences on lotteries.
8.
Note the difference between CES utility and isoelastic utility : the CES utility function is an ordinal utility function that represents preferences on sure consumption commodity bundles, while the isoelastic utility function is a cardinal utility function that represents preferences on lotteries.
9.
Importantly, unlike VNM utility functions ( e . g . isoelastic utility ), Epstein-Zin preferences allow the elasticity of intertemporal substitution ( determined above by \ rho ) to be unrelated to risk aversion ( determined above by \ alpha ).
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