8. Let R(W) = -wu" (W)/U'w) and a(w) = ArgmaxE[u(w+ar) be the optimal investment choice relative to the utility function u(). Suppose w > 0, u'() > 0, u" () 0. Prove the following proposition: (a) If I > 1, given the utility function u() and R'(W) > 0. Define u(w) = u(w), U2 = u(w) then, R1(w) > R2w). (b) Given the conclusion in (a), we have aj(w) (w2). (Hint: Let 1 = wi/w2. The economic implication of this question is that for an investor with a monotonously increasing relative risk aversion, the proportion of his investment in risky assets decreases as wealth increases.) 8. Let R(W) = -wu" (W)/U'w) and a(w) = ArgmaxE[u(w+ar) be the optimal investment choice relative to the utility function u(). Suppose w > 0, u'() > 0, u" () 0. Prove the following proposition: (a) If I > 1, given the utility function u() and R'(W) > 0. Define u(w) = u(w), U2 = u(w) then, R1(w) > R2w). (b) Given the conclusion in (a), we have aj(w) (w2). (Hint: Let 1 = wi/w2. The economic implication of this question is that for an investor with a monotonously increasing relative risk aversion, the proportion of his investment in risky assets decreases as wealth increases.)