4. (30) Let Cara be a consumer who she exhibits no time preference 8 = 1 and receives an endowment of W in each of two periods. There exists a single risky asset currently priced at Po = 1 that next period has payoffs of 3 w/ prob. P1 = 0 w/ prob. WIH WIN Consider Cara's two-period utility maximization problem. max u (Co) + SE [u (Ci)] s.t. Co = W - & Po C1 = W+ g P1 (a) (10) Find the first order condition for Cara's optimization problem.(b) (10) Predictably, Cara's utility function exhibits constant absolute risk aversion u(C) = 1 - e'\". Show that the number of shares she buys does not depend on her endowment W. (c) (10) Suppose that Cara has a twin sister, Cora, who faces the same optimization problem (:1 ' P but whose utility function instead exhibits constant relative risk aversion u(C) = 1 _ p. Show that the number of shares she buys is proportional to her endowment W