6.6. The central bank’s ability to control the real interest rate. Suppose the economy is described by two equations. The first is the IS equation, which for simplicity we assume takes the traditional form, Yt = −rt/θ. The second is the money-market equilibrium condition, which we can write as m − p =

L(r + πe,Y ), Lr+πe < 0, LY > 0, where m and p denote ln M and ln P .

(a) Suppose P = P and πe = 0. Find an expression for dr/dm. Does an increase in the money supply lower the real interest rate?

(b) Suppose prices respond partially to increases in money. Specifically, assume that dp/dm is exogenous, with 0 < dp/dm < 1. Continue to assume

πe = 0. Find an expression for dr/dm. Does an increase in the money supply lower the real interest rate? Does achieving a given change in r require a change in m smaller, larger, or the same size as in part (a)?