Let Cara be a consumer who she exhibits no time preference = 1 and receives an endowment of W in

each of two periods.

(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 payos of {3 wf prob. P1 = D wf prob. wlvI- who Consider Cara's two-period utility maximization problem. mp}: M00) + 5E[u(Cl}] S.t.Co=WEH) Cl=w+a (a) (10} Find the rst order condition for Cara's optimization problem. (b) (10} Predictably, Csra's utility function exhibits constant absolute risk aversion 1:.(0) = 1 8\"0. Show that the number of shares she buys does not depend on her endowment W. (c) (10} Suppose that Cara has a twin sister1 Cora1 who faces the same optimization problem but whose utility function instead exhibits constant relative risk aversion 11(0) = (11:. Show that the number of shares she buys is proportional to her endowment W