This exercise illustrates the concept of "precautionary savings"-the risk imposed by y results in higher savings w_0 = c_0. Consider the portfolio choice problem with only a risk-free asset and with consumption at both the beginning and end of the period. Suppose the investor has time-additive utility with u_0 = u and u_1 = delta u for a common function u and discount factor delta. Suppose the investor has a random endowment at the end of the period, so he chooses c_0 to maximize u (c_0) + delta E [u ((w_0 - c_0) R_f + y)] Suppose the investor has convex marginal utility (u"' > 0) and suppose that E [y] = 0. Show that the optimal c_0 is smaller than if = 0. This exercise illustrates the concept of "precautionary savings"-the risk imposed by y results in higher savings w_0 = c_0. Consider the portfolio choice problem with only a risk-free asset and with consumption at both the beginning and end of the period. Suppose the investor has time-additive utility with u_0 = u and u_1 = delta u for a common function u and discount factor delta. Suppose the investor has a random endowment at the end of the period, so he chooses c_0 to maximize u (c_0) + delta E [u ((w_0 - c_0) R_f + y)] Suppose the investor has convex marginal utility (u"' > 0) and suppose that E [y] = 0. Show that the optimal c_0 is smaller than if = 0