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 and P0 a 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 15-12, 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 in Figure 15-13.