9.3. Assume, as in Problem 9.2, that prices are completely unresponsive to unan- ticipated monetary shocks for one period and completely flexible thereafter. Assume also that y=c-ar and m-p= b+hy-ki hold each period. Suppose, however, that the money supply follows a random walk: m = m-1+ut, where u, is a mean-zero, serially uncorrelated disturbance.

(a) Let E, denote expectations as of period t. Explain why, for any t, EE+P+2] P+1] = 0, and thus why Em+1 - Ep+1 = b+hy - kr.

(b) Use the result in part

(a) to solve for y, pt, it, and r, in terms of mr-1 and ut.

(c) Does the Fisher effect hold in this economy? That is, are changes in ex- pected inflation reflected one-for-one in the nominal interest rate?