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. 3 P = 10 w/ prob. Cara seeks to maximize her utility over two periods, subject to budget constraints. max u(Co) +8E[(C)], s.t. Co-W - EP C=W +EP (a) (10) Find the first order condition for Cara's optimization problem. (b) (10) Predictably, Cara's utility function exhibits constant absolute risk aversion (C)=1-e-ac. 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 (C) = Show that the number of shares she buys is proportional to her endowment W