Assume that the IS and money demand equations each have a disturbance term. Further, assume that the central bank can control the economy's interest rate r and money supply M s except for uncontrollable disturbance terms ηt and νt , so that:
r = rT + ηt
M s = M + νt
Use Poole's analysis to derive the conditions for preferring interest rate targeting over money supply targeting, and vice versa.
Assume that the central bank chooses to target the interest rate in the preceding equation. Derive the money supply that the central bank needs to ensure for equilibrium in the money market. What would happen if it did not ensure this money supply? Discuss.