---
title: "power utility"
type: concept
related: [Power Utility, Financial Markets Intro]
source: https://www.jemoka.com/posts/kbhpower_utility/
confidence: high
status: active
---

power utility, or isoelastic utility, is a financial econometric is a utility that results absolute, constant relative risk aversion. i.e.: you tell me how risk averse you are exogenously, I tell you how much utility some consumption is.
constituents some relative risk coefficient \(\gamma \in (0,1)\), higher more risk averse consumption of some asset \(C\) requirements Utility \(U( C)\) is defined by:
\begin{equation} U( C) = \frac{c^{1-\gamma}-1}{1-\gamma} \end{equation}
additional information As you can see, the higher \(\gamma\), the lower utility some consumption brings.
log utility log utility is a special case of power utility whereby:
\begin{equation} U(x) = \log x \end{equation}
which converges to power utility where \(\lambda \to 1\).
