. (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 P1 : {3 w/ prob. wh-'wlto O w/ prob. Consider Cara's two-period utility maximization problem. mg): \"(00) + 5E[u(01)] S.t. Co : W 5P0 01 = Wl 131 (a) (10) Find the rst order condition for Cara's optimization problem. (b) (10) Predictably, Cara's utility function exhibits constant absolute risk aversion 11(0) 2 1 6_QC. 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 but whose utility function instead exhibits constant relative risk aversion MC) 2 q:_:. Show that the number of shares she buys is proportional to her endowment W