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: %?V - 0.5 Ã (i - 5) Suppose that a model of the economy suggests that the real interest rate is determined by the equation r = 8.5 - %?Y 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?