8. (Certainty approximation ) There is a useful approximation to the certainty equivalent that is easy to derive A second-order expansion near = E(x) gives U(x) UT)+U')(x)+U")(x) - Hence, E[U()])+U"(F)var(r)

On the other hand, if we let c denote the certainty equivalent and assume it is close to ., we can use the first-order expansion U

(c) U)+U' (T) (c). Using these approximations, show that U" (F) c+ var(r) UI()