M & B 4th Edition by Dean Croushore

Exercise 17

Suppose that the Fed's inflation target is 2 percent, potential output growth is 3.5 percent, and velocity is a function of how much the interest rate differs from 5 percent:

Suppose that a model of the economy suggests that the real interest rate is determined by the equation

where Y is the level of output, so %? Y is the growth rate of output. Suppose that people expect the Fed to hit its inflation target.
a Calculate the optimal money growth rate needed for the Fed to hit its inflation target in the long run.
b In the short run, if output growth is just 2 percent for two years and the equation determining the real interest rate changes to r = 4.5 - %? Y , what money growth rate should the Fed aim for to hit its inflation target in that period?
c If the Fed instead maintained the money growth rate from part a, what is likely to happen to inflation?
d Which policy do you think is better in the short run? Which is better in the long run?