3. Suppose that a risk averse investor with wealth w> 0 can invest a proportion 2 (0,1) of their wealth in a risky asset that gives a random rate of return r. a. Show that when 2 is chosen optimally WE[ rU'(W(1 + 2r))]= 0, where E is an expectations operator with respect to r, and U' is marginal utility. [5 marks] b. Using your answer in (a), and noting that it implies E[ ru'(W(1 + r))]=0, show that, if relative risk aversion is decreasing, then the investor optimally holds a higher proportion of the risky asset as they get richer. [10 marks] 3. Suppose that a risk averse investor with wealth w> 0 can invest a proportion 2 (0,1) of their wealth in a risky asset that gives a random rate of return r. a. Show that when 2 is chosen optimally WE[ rU'(W(1 + 2r))]= 0, where E is an expectations operator with respect to r, and U' is marginal utility. [5 marks] b. Using your answer in (a), and noting that it implies E[ ru'(W(1 + r))]=0, show that, if relative risk aversion is decreasing, then the investor optimally holds a higher proportion of the risky asset as they get richer. [10 marks]