Consider a discrete-time model where prices are completely unresponsive to unanticipated monetary shocks for one period and completely flexible thereafter. Suppose the IS equation is y = c − ar and that the condition for equilibrium in the money market is m − p = b + hy − ki. Here 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

To incorporate the effects of the knowledge that the money growth is temporary into our formal analysis, we would have to let the change in real money holdings at a given time depend not just on current holdings and current inflation, but on current holdings and the entire expected path of inflation. See n. 32. Monetary authority shifts unexpectedly to a policy of increasing m by some amount g > 0 each period.

(a) What are r, π^e, i, and p before the change in policy?

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

c) In period 1, what are i, r, p, and the expectation of inflation from period 1 to period 2, E₁[p₂] − p₁?

Sol:

(a) Substituting the normalized, flexible-price level of output, y₀ = 0, into the IS equation, y₀ = c - ar₀, gives us 0 = c - ar₀.