Question

The relation between the real and the nominal interest rates is given by

                                                                   r=i-πe

1. Suppose that the nominal interest rate is 0.05. Compute the real interest rate
   1. when the expected inflation rate is 0.07.
   2. when the expected inflation rate is 0.05.
   3. when the expected inflation rate is 0.03.
   4. The nominal interest rate is subject to the zero lower bound constraint. Find the lowest real interest rate
      1. when the expected inflation rate is 0.03.
      2. when the expected inflation rate is 0.01.
      3. when the expected inflation rate is -0.03.
      4. when the expected inflation rate is -0.05.

Answer 1

(1) Nominal interest rate is 0.05

r=i-πe

where 'r' is the real interest rate

'i' is the nominal interest rate

'πe' is the expected inflation rate.

(a) when the expected inflation rate is 0.07.

r = 0.05 - 0.07

r = -0.02

(b) when the expected inflation rate is 0.05

r = 0.05 - 0.05

r = 0

(c) when the expected inflation rate is 0.03.

r = 0.05 - 0.03

r = 0.02

(2) The nominal interest rate is subject to the zero lower bound constraint.  It is also called zero nominal bounds and its the nominal rates which get close to zero.

So the nominal interest rate would be 0.

(a) when the expected inflation rate is 0.03.

r = 0 - 0.03

r = -0.03

lowest real interest rate is -0.03

(b) when the expected inflation rate is 0.01.

r = 0 - 0.01

r = -0.01

lowest real interest rate is -0.01

(c) when the expected inflation rate is -0.03.

r = 0 -(- 0.03)

r = 0.03

lowest real interest rate is 0.03

(d) when the expected inflation rate is -0.05.

r = 0 -(- 0.05)

r = 0.05

lowest real interest rate is 0.05