|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, =...

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|Recall the consumer utility maximization problem between consumption and savingas 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 life time budget constraint and giveinterpre-tation.(b) Exploiting the optimization result that the marginal rate of intertemporal substitutionbetweenci and cj for all i # j should equal to the price, derive the optimality condition when u (c )= log c so thatauac(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. Whathappens toc1 , c2 , c3 , s1 and s2 ?