Question

Inflation rate is 7,8, target inflation rate is 2,1, GDP growth is 5,2, potential GDP growth is 2,7, equilibrium real fed funds rate is 1,8. Given this, what should the target level of the Federal funds rate?

Answer 1

Answer :

Calculation of Federal funds rate :-

As per Taylor Rule,

ff^t = π + ff^*r + ½(π gap) + ½(Y gap)

where

ff^t = federal funds target

π = inflation

ff^*r = the real equilibrium fed funds rate

π gap = π – π target

Y gap = actual output − output potential

*actual output is GDP rate in the question

Inflation Rate	Target inflation rate	GDP growth	Potential GDP growth	Equilibrium real fed funds rate	Answer : Federal funds rate
7	2	5	2	1	12 (note 1)
8	1	2	7	8	17(note 2)

Note 1 :

Calculation of federal fund rate when inflation is 7,Target inflation rate is 2, GDP rate is 5, GDP growth rate is 2, Equilibrium real fed funds rate is 1

as per above formula

Federal funds rate = inflation rate +Equilibrium real fed funds rate+ 1/2(inflation gap)+ 1/2(GDP gap)

= 7+1+1/2(5)+1/2(3)

=7+1+2.5+1.5

= 12

where inflation gap = Inflation rate - Target inflation rate =7-2 = 5

GDP gap = GDP growth - Potential GDP growth = 5-2 = 3

therefore Federal fund rate is 12.

Note 2 :

Calculation of federal fund rate when inflation is 8,Target inflation rate is 1, GDP rate is 2, GDP growth rate is 7, Equilibrium real fed funds rate is 8

as per above formula

Federal funds rate = inflation rate +Equilibrium real fed funds rate+ 1/2(inflation gap)+ 1/2(GDP gap)

= 8+8+1/2(7)+1/2(-5)

=8+8+3.5-2.5

= 17

where inflation gap = Inflation rate - Target inflation rate =8-1 = 7

GDP gap = GDP growth - Potential GDP growth = 2-7 = -5

therefore Federal fund rate is 17.