11.3. Assume, as in Problem 11.2, that prices are completely unresponsive to unanticipated 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: mt = mt −1+ ut, where ut is a mean-zero, serially uncorrelated disturbance.

(a) Let Et denote expectations as of period t. Explain why, for any t, Et [E t +1

[pt +2] − pt +1] = 0, and thus why Etmt +1 − Et pt +1 = b+ hy − k r, where y and r are the flexible-price levels of y and r.

(b) Use the result in part

(a) to solve for yt, pt, it, and rt in terms of mt−1 and ut.

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