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 trade 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.)

1. 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.)

2. 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?

3. 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 developed in class, 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 analysis in class.