4. (30) Let Cara be a consumer who she exhibits no time preference 5 = 1 and receives an endowment of W in each of two periods. There exists a single risky asset currently priced at P0 = 1 that next period has payoffs of 7 3 w/ prob. P1 = 0 w/ prob. MIHMIN Cara seeks to maximize her utility over two periods, subject to budget constraints. mgax u(Co) + 6E[u(C'1)], S.t. Co = W{Pm 01 = W+P1. (a) (10) Find the rst order condition for Cara's optimization problem. (b) (10) Predictably, Cara's utility function exhibits constant absolute risk aversion 21(0) 2 1 600. Show that the number of shares she buys does not depend on her endowment W. (c) (10) Suppose that Cara's sister Corra faces the same optimization problem and has a utility function that exhibits constant relative risk aversion 11(0) = 011:. Show that the number of shares she buys is proportional to her endowment W