 Multiplicative habit utility

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 $R+\alpha$.