As we observed in this chapter, central banks, rather than purposefully setting the level of the money supply, usually set a target level for a short-term interest rate by standing ready to lend or borrow whatever money people wish to hold at that interest rate. (When people need more money for a reason other than a change in the interest rate, the money supply therefore expands, and it contracts when they wish to hold less.)
a. Describe the problems that might arise if a central bank sets monetary policy by holding the market interest rate constant. (First, consider the flexible-price case, and ask yourself if you can find a unique equilibrium price level when the central bank simply gives people all the money they wish to hold at the pegged interest rate. Then consider the sticky-price case.)
b. Does the situation change if the central bank raises the interest rate when prices are high, according to a formula such as R - R0 = a(P - P0), where a is a positive constant andP0a target price level?
c. Suppose the central bank€™s policy rule is R €“ R0 = a(P €“ P0) + u, where u is a random movement in the policy interest rate. In the overshooting model shown in Figure describe how the economy would adjust to a permanent one-time unexpected fall in the random factor u, and say why. You can interpret the fall in u as an interest rate cut by the central bank, and therefore as an expansionary monetary action. Compare your story with the one depicted inFigure.

Dollarleuro exchange rate, E Doliar return Dollar return 2' 2' 3' 4 Expected euro return euro return Rates of return in0 dollar terms) LIRg Yus LIRs Yus) US US 4 U.S. real money supply U.S. real money holdings U.S. real money holdings (a) Short-run effects (b) Adjustment to long-run equilibrium