7.4. A framework for investigating excess smoothness. Suppose that C, equals [r/(1+][+ ElYs/(1+r], and that A+1-(1+r)A, + Y - Cr).

(a) Show that these assumptions imply that EICC, (and thus that con- sumption follows a random walk) and that ElCl/(1+r) = A, - EY/(1+r).

(b) Suppose that AY, AY-1+, where u is white noise. Suppose that Y exceeds E-[Y] by one unit (that is, suppose u 1). By how much does consumption increase?

(c) For the case of > 0, which has a larger variance, the innovation in in- come, u,, or the innovation in consumption, C-E-11C]? Do consumers use saving and borrowing to smooth the path of consumption relative to income in this model? Explain.