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Recall the consumer utility maximization problem between consumption and saving as follows :max (1,c2 U = U(c,) + Bu(c2) + Bzu(C3)12 + (1 +r)s, = C2+ $2Ig + (1+r)$2 = C3 (a) Combine those three budget constraints into one lifetime budget constraint and give interpretation. (b) Exploiting the optimization result that the marginal rate of intertemporal substitution between ci and cj for all i # j should equal to the price, derive the optimality condition when u (c )= log c so that UAC (c) Give interpretation the optimality condition above. (d) Suppose the real interest rate r increases. What happens to c1 , c2 , c3, s1 and s2 ? (e) Suppose both 11 and 13 increase at the same time, while I1 stays the same. What

Recall the consumer utility maximization problem between consumption and saving as follows :max (1,c2 U = U(c,) + Bu(c2) + Bzu(C3)12 + (1 +r)s, = C2+ $2Ig + (1+r)$2 = C3

(a) Combine those three budget constraints into one lifetime budget constraint and give interpretation.

(b) Exploiting the optimization result that the marginal rate of intertemporal substitution between ci and cj for all i # j should equal to the price, derive the optimality condition when u (c )= log c so that UAC

(c) Give interpretation the optimality condition above.

(d) Suppose the real interest rate r increases. What happens to c1 , c2 , c3, s1 and s2 ?

(e) Suppose both 11 and 13 increase at the same time, while I1 stays the same. What happens toc1 , c2 , c3 , s1 and s2.