Recall the consumer utility maximization problem between consumption and saving as follows :

maxU =u(c1)+u(c2)+2u(c3) c1 ,c2

I1 = c1 + s1

I2 + (1 + r) s1 = c2 + s2 I3 + (1 + r) s2 = c3

(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

ci and cj for all i = j should equal to the price, derive the optimality condition when u (c) = log c so that u 1

c =c.

(c) (1 Point) Give interpretation the optimality condition above.

(d) (1 Point) Suppose both I2 and I3 increase at the same time, while I1 stays the same. What happens to

c1, c2, c3, s1 and s2