Question

Suppose that the natural rate of interest is 2 percent and the current rate of inflation is 4 percent. If the inflation gap is 2 percent and the rate of real GDP growth is 3 percent above its potential, the FOMC’s target fed-funds rate is:

Answer 1

Let the fed funds target rate be "i".

i= r* + pi + 0.5 (pi-pi*) + 0.5 ( y-y*)

where:

i = nominal fed funds rate
r* = real federal funds rate (usually 2%)
pi = rate of inflation
p* = target inflation rate
Y = logarithm of real output
y* = logarithm of potential output

r* = 2

pi =4

pi* = 2(since the pap is 2%, 4-2 =2)

y = log 2+3 = log 5 = 0.69897

y* =log 2 = log 2 = 0.3010

i =2 +0.5*(4-2) +0.5*(0.6989-0.3010) = 3.198 = 3.2%

FOMC’s target fed-funds rate is = 3.2%