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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 hyperbolic absolute risk aversion 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 c {\displaystyle c} is consumption, u {\displaystyle u} the associated utility, and η {\displaystyle \eta } is a constant that is positive for risk averse agents. Since additive constant terms in objective functions do not affect optimal decisions, the term –1 in the numerator can be, and usually is, omitted {\displaystyle \ln} as below].
When the context involves risk, the utility function is viewed as a von Neumann–Morgenstern utility function, and the parameter η {\displaystyle \eta } is the degree of relative risk aversion.