Numerical Exercise 11
Suppose that the Fed's inflation target is 2 percent, potential outlook growth is 3.5 percent, and velocity is a function of how much interest rate differs from 5 percent:
% triangle V = 0.5 x ( i-5)
Suppose the model of the economy suggests that the real interest rate is determined by the equation where Y is the level of output, so %triangleY is the growth rate of output. Suppose that the people expect the Fed to it its inflation target.
r= 8.5- % triangle Y
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% for two years and the equation determining the real interest rate changes to r = 4.5- %triangleY, 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?
Numerical Exercise 13
Suppose that the economy is though to be 2 percent above potential (that is, the output gap is 2 percent) when potential output grows 4 percent per year. Suppose also that the Fed is following the Taylor rule , with an inflation rate of 2 percent. The federal funds rate is 3 percent. and the weights on the output gap are 0.5 each. The inflation target is 1 percent.
A: Is the Federal funds rate currently too high or too low? by how much? Show your work.
B: Suppose that a year has gone by, output is now just 1 percent above potential, and the inflation rate was 1.5 percent over the year. What federal funds rate should the Fed now set (assuming that the inflation target does not change)?