Ebenezer Scrooge is an expected utility maximizer who lives for two periods: t = 0,1. He consumes a single consumption good 2:. Mr. Scrooge's utility as a function of his consumption in each period (x0 and x1. respectively] is given by U = u(x) + E[u(x1)]. where u(xt) = Jxt. At the start of period 0, Mr. Scrooge is endowed with w > 0 units ofthe good, which he can either consume in period 0 or save until period 1. Let 3 denote the amount of the good he saves in 2 period [I for consumption in period 1. The return on his savings in period 1 is uncertain. With probability Tl." Mr. Scrooge will receive D5 in period 1, and with probability (1 it) he will receive d3 . where D > d 2-3 0. Mr. Scrooge has to make the savings decision before this uncertainty is realized. 1) [5 points] Set up Mr. Scrooge's expected utility maximization problem and write out the first order conditions that characterize the solution. Are the second order conditions satisfied (explain or show)? 2] [5 points] Solve Mr. Scrooge's expected utility maximization problem for the optimal amount of savings 5*. Find the maximized value of his expected utility. 3) [7 points] How does Mr. Scrooge's optimal amount of savings depend on the probability of having high return. or? Provide both the intuitive explanation and the analytical proof