9.2. Consider a discrete-time model where prices are completely unresponsive to unanticipated monetary shocks for one period and completely flexible there- after. Suppose the IS and LM curves are y = car and m - p = b+ hy-ki, where y, m, and p are the logs of output, the money supply, and the price level; r is the real interest rate; i is the nominal interest rate; and

a, h, and k are positive parameters. Assume that initially m is constant at some level, which we normalize to zero, and that y is constant at its flexible-price level, which we also normalize to zero. Now suppose that in some period-period 1 for simplicity-the monetary authority shifts unexpectedly to a policy of increasing m by some amount g>0 each period.

(a) What are r,

e, i, and p before the change in policy?

(b) Once prices have fully adjusted, period 2. g. Use this fact to find r, i, and p in

(c) In period 1, what are i, r, p, and the expectation of inflation from period 1 to period 2, Ep2] - p?

(d) What determines whether the short-run effect of the monetary expansion is to raise or lower the nominal interest rate?