Suppose the economy is thought to be 2 percent below potential (i.e., the output gap is ?2 percent), when potential output grows 4 percent per year. Suppose the Fed is following the Taylor rule, with an inflation rate of 3 percent over the past year. The federal funds rate is currently 3 percent. The equilibrium real fed funds rate is 3 percent and the weights on the output gap and inflation gap are 0.5 each. The inflation target is 1 percent.

Question

a.Is the fed funds rate currently too high or too low? By how much? Show your work.  b.Suppose that all the conditions are the same as described above, except that the output gap is +2 percent instead of ?2 percent. Is the fed funds rate currently too high or too low? By how much? Show your work.  c.Suppose a year has gone by, output is now 3 percent above potential, and the inflation rate was 4.5 percent over the year. What federal funds rate should the Fed now set (assuming the inflation target does not change)? Show your work.

What will be an ideal response?

Answer 1

Use the equation i = r* + ? + {w1× [(Y?Y*)/Y*] × 100} + [w2× (???T)].a.i = r* + ? + {w1× [(Y?Y*)/Y*] × 100} + [w2× (???T)] = 3% + 3% + (0.5 ×?2%) + (0.5 × 2%) = 6%. So the fed funds rate is currently too low by 3 percentage points.  b.i = r* + ? + {w1× [(Y?Y*)/Y*] × 100} + [w2× (???T)] = 3% + 3% + (0.5 × 2%) + (0.5 × 2%) = 8%. So the fed funds rate is currently too low by 5 percentage points.  c.i = r* + ? + {w1× [(Y?Y*)/Y*] × 100} + [w2× (???T)] = 3% + 4.5% + (0.5 × 3%) + (0.5 × 3.5%) = 10.75%.