Isoelastic utility

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. The isoelastic utility function is a special case of HARA and at the same time is the only class of utility functions with constant relative risk aversion, which is why it is also called the CRRA utility function.

It is

where is consumption, the associated utility, and is a constant. Since additive constant terms in objective functions do not affect optimal decisions, the term –1 in the numerator can be, and usually is, omitted (except when establishing the limiting case of as below).

When the context involves risk, the utility function is viewed as a von Neumann-Morgenstern utility function, and the parameter is a measure of risk aversion.

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.