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2. (Long Q : Total 4 Points) Recall the consumer utility maximization problem between consumption and saving as follows: max U = u(c1) + Bu (c2) + Bu (cs) C1,C2 11 = C1 +81 12+(1+r) s1 = c2 + $2 13 +(1+r) s2 = 13 (a) (1 Point) Combine those three budget constraints into one life time budget constraint and give interpre- tation. (b) (1 Point) Exploiting the optimization result that the marginal rate of intertemporal substitution between 4 and c; for all i # j should equal to the price, derive the optimality condition when u (c) = log c so that (c) (1 Point) Give interpretation the optimality condition above. (d) (1 Point) Suppose both 12 and 13 increase at the same time, while I stays the same. What happens to C1, C2, C3, 81 and sz? 2. (Long Q : Total 4 Points) Recall the consumer utility maximization problem between consumption and saving as follows: max U = u(c1) + Bu (c2) + Bu (cs) C1,C2 11 = C1 +81 12+(1+r) s1 = c2 + $2 13 +(1+r) s2 = 13 (a) (1 Point) Combine those three budget constraints into one life time budget constraint and give interpre- tation. (b) (1 Point) Exploiting the optimization result that the marginal rate of intertemporal substitution between 4 and c; for all i # j should equal to the price, derive the optimality condition when u (c) = log c so that (c) (1 Point) Give interpretation the optimality condition above. (d) (1 Point) Suppose both 12 and 13 increase at the same time, while I stays the same. What happens to C1, C2, C3, 81 and sz