(i) Show that a utility function (u: mathbb{R} ightarrow mathbb{R}) is characterized by a constant relative...

Question:

(i) Show that a utility function $u: \mathbb{R} \rightarrow \mathbb{R}$ is characterized by a constant relative risk aversion coefficient different from 1 if and only if $u(x)=\alpha x^{1-b}+\beta$ for $\alpha>0$ and $\beta \in \mathbb{R}$, with $b eq 1$.

(ii) Show that a utility function $u: \mathbb{R} \rightarrow \mathbb{R}$ is characterized by a constant relative risk aversion coefficient equal to one if and only if $u(x)=\alpha \log (x)+\beta$ for $\alpha>0$ and $\beta \in \mathbb{R}$.

Fantastic news! We've Found the answer you've been seeking!