Multiplicative habit utility
= Multiplicative habit utility
{title2=$g(c,h)=U(c)(c/h)^{-\alpha}$}
Multiplicative habit utility modifies current consumption utility through its ratio to habit $h>0$. With $U(c)=c^{1-R}/(1-R)$, $R>1$, and $\alpha>0$, it is $h^\alpha c^{1-R-\alpha}/(1-R)$. Its <homogeneity> in $(c,h)$ has degree $1-R$, while consumption holding habit fixed has effective relative risk aversion $R+\alpha$.