3 Precautionary Saving (Bonus) You can get partial points. Try the question and see how far you can get. Question 3.[5pt] Consider an economy with a discount factor of S = 1 and interest rate r = 0 and log utility, where income in period t is Yt and income in period t + 1 is either high Y141 or low Yet, with a chance of 1/2 each. In this case consumption in the second period will either be high or low: Ch+1 = YI + Y4 - C+= I" - Ct where I is lifetime income. The expected utility as a function of Ct = c then becomes: U (c ) = In(c) + - In(1" - c) + = In(1' - c) a) Show that optimal consumption c* in period t is C* = 0.75E(1) - 0.25 * VE(1)2 + 80} where E(I) is the expected lift-time income E(I) = !"+ and of is the variance of life-time income of = E(12) - (E(1))2 = [242 - ( ItI')2