Suppose Huw lives for two periods, t=1,2. In each period, he consumes only two goods, x1 and x2, both of whose prices at t = 1 are I and at T = 2 are I(1+g). Thus i is the inflation rate here. Huw's income at period t=1 is I, at t= 2 is I(1+g). Thus, g represents the growth rate of his income between periods 1 and 2.

the growth rate of his income between periods 1 and 2.

Huw's life-time utility is given by:

u(x11,x21,x12,x22) = (x11 +x21)+ delta(x12 + x22)

where xit is his consumption of good i in period t and delta 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. What is Huw's optimal savings/borrowing decision?

ii) Suppose Huw can save or borrow from the bank in any period, but the savings and interest rates differ. While savings earn him an interest rate of r, he can borrow from the bank at the interest rate b, where b > r. What is Huw's optimal savings/borrowing decision now? For simplicity, assume i = 0 here.