4. [Application: Savings problem] Suppose Huw lives for two peri ods, t = 1, 2. In each period, he consumes only two goods, X1 and X2, both of whose prices at t : 1 are 1, and at t : 2 are 1 + 3'. Thus 1' is the ination rate here. Huw's income at period 1': : 1 is I, at t : 2 is I(1+g). Thus, 9 represents the growth rate of his income between periods 1 and 2. Huw's lifetime utility is given by: u(3311:$21w"'125$22) = (#3311 +1/5L'211-l- (Sb/3312 +1/r22) where 32,-; is his consumption of good i in period t and 6 is his discount factor. (i) Suppose Huw can save or borrow from the bank in any period, at the per period interest rate of r. \"That is Huw's optimal savings / borrowing decision? [Hint: Try and make use of your results from problem I to avoid redoing many of the calculations here. ] (ii) [Challenging: A problem with a non-linear budget con- straint] Suppose Huw can save or borrow from the bank in any period, but the savings and interest rates differ. W'hile savings earn him an interest rate of r, he can borrow from the bank at the interest rate 5, where l) :> r. What is Huw's optimal savings/ borrowing decision now? For simplicity, assume '5 = 0 here