In the Cagan model, if the money supply is expected to grow at some constant rate m (so that Emt+ s = mt + sm), then Equation A9 can be shown to imply that pt = mt + gm.
a. Interpret this result.
b. What happens to the price level pt when the money supply mt changes, holding the money growth rate m constant?
c. What happens to the price level pt when the money growth rate m changes, holding the current money supply mt constant?
d. If a central bank is about to reduce the rate of money growth m but wants to hold the price level pt constant, what should it do with mt? Can you see any practical problems that might arise in following such a policy?
e. How do your previous answers change in the special case where money demand does not depend on the expected rate of inflation (so that g = 0)?