Editing Risk aversion (section)

=== Relative risk aversion ===
The '''Arrow–Pratt measure of relative risk aversion''' (RRA) or '''coefficient of relative risk aversion''' is defined as<ref name="SB">{{cite book|author1=Simon, Carl and Lawrence Blume|title=Mathematics for Economists|year=2006|publisher=Viva Norton|isbn=978-81-309-1600-2|pages=363|edition=Student}}</ref>
: <math>R(c) = cA(c)=\frac{-cu''(c)}{u'(c)}</math>.

Unlike ARA whose units are in $<sup>−1</sup>, RRA is a dimensionless quantity, which allows it to be applied universally. Like for absolute risk aversion, the corresponding terms ''constant relative risk aversion'' (CRRA) and ''decreasing/increasing relative risk aversion'' (DRRA/IRRA) are used. This measure has the advantage that it is still a valid measure of risk aversion, even if the utility function changes from risk averse to risk loving as ''c'' varies, i.e. utility is not strictly convex/concave over all ''c''. A constant RRA implies a decreasing ARA, but the reverse is not always true. As a specific example of constant relative risk aversion, the utility function <math>u(c) = \log(c)</math> implies {{nowrap|1=RRA = 1}}.

In [[intertemporal choice]] problems, the [[elasticity of intertemporal substitution]] often cannot be disentangled from the coefficient of relative risk aversion. The [[isoelastic utility]] function
: <math>u(c) = \frac{c^{1-\rho}-1}{1-\rho}</math>
exhibits constant relative risk aversion with <math>R(c) = \rho </math> and the elasticity of intertemporal substitution <math>\varepsilon_{u(c)} = 1/\rho</math>. When <math>\rho = 1,</math> using [[l'Hôpital's rule]] shows that this simplifies to the case of ''log utility'', {{nowrap|1=''u''(''c'') = log ''c''}}, and the [[income effect]] and [[substitution effect]] on saving exactly offset.

A time-varying relative risk aversion can be considered.<ref>{{cite journal |last1=Benchimol |first1=Jonathan |title=Risk aversion in the Eurozone |journal=Research in Economics |date=March 2014 |volume=68 |issue=1 |pages=39–56 |doi=10.1016/j.rie.2013.11.005 |s2cid=153856059 }}</ref>