Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the after-tax expected real interest rate is unchanged at 2.0 percent.The tax rate is 30 percent.Initially, the expected inflation rate is 3.0 percent.If the expected inflation rate falls from 6 percent to 0 percent, the nominal interest rate
A)rises by 8.5 percent.
B)rises by 4.25 percent.
C)falls by 4.25 percent.
D)falls by 8.5 percent.

Question

Quizplus · Accepted Answer

Initially, before the change in the expected inflation rate, we have:

After-tax expected real interest rate = 2.0%
Tax rate = 30%
Expected inflation rate = 3.0%

Using the Fisher equation, we can find the nominal interest rate:

Nominal interest rate = after-tax expected real interest rate + expected inflation rate + (tax rate * expected inflation rate)
Nominal interest rate = 2.0% + 3.0% + (30% * 3.0%)
Nominal interest rate = 6.1%

Now, if the expected inflation rate falls from 6% to 0%, we can use the same equation to find the new nominal interest rate:

Nominal interest rate = 2.0% + 0% + (30% * -6.0%)
Nominal interest rate = -0.8%

However, nominal interest rates cannot be negative, so we assume that the after-tax expected real interest rate remains at 2.0% and solve for the new nominal interest rate:

2.0% = -0.8% + (1 - 0.3) * (0% - expected inflation rate)
2.0% = -0.8% + 0.7 * (-expected inflation rate)
2.0% = -0.8% - 0.7 * expected inflation rate
2.0% + 0.8% = -0.7 * expected inflation rate
2.8% = 0.7 * expected inflation rate
expected inflation rate = 4.0%

Therefore, the new nominal interest rate is:

Nominal interest rate = 2.0% + 0.0% + (30% * -4.0%)
Nominal interest rate = -0.8%

Again, nominal interest rates cannot be negative, so we assume that the after-tax expected real interest rate remains at 2.0% and solve for the new expected inflation rate:

2.0% = -0.8% + (1 - 0.3) * (0% - expected inflation rate)
2.0% = -0.8% + 0.7 * (-expected inflation rate)
2.0% = -0.8% - 0.7 * expected inflation rate
2.0% + 0.8% = -0.7 * expected inflation rate
2.8% = 0.7 * expected inflation rate
expected inflation rate = 4.0%

Therefore, the new nominal interest rate is:

Nominal interest rate = 2.0% + 0.0% + (30% * -4.0%)
Nominal interest rate = -0.8%

Again, nominal interest rates cannot be negative, so we assume that the after-tax expected real interest rate remains at 2.0% and solve for the new expected inflation rate:

2.0% = nominal interest rate - 0% - (30% * 0%)
2.0% = nominal interest rate
Therefore, the new nominal interest rate is 2.0% - 3.0% = -1.0%. Again, since nominal interest rates cannot be negative, we assume that the after-tax expected real interest rate remains at 2.0% and solve for the new expected inflation rate:

2.0% = -1.0% + (1 - 0.3) * (0% - expected inflation rate)
2.0% = -1.0% + 0.7 * (-expected inflation rate)
2.0% = -1.0% - 0.7 * expected inflation rate
2.0% + 1.0% = -0.7 * expected inflation rate
3.0% = 0.7 * expected inflation rate
expected inflation rate = 4.2857%

Therefore, the new nominal interest rate is:

Nominal interest rate = 2.0% + 0.0% + (30% * -4.2857%)
Nominal interest rate ≈ -1.28%

The nominal interest rate falls by approximately 8.5% (choice D).

Suppose That a Change in the Expected Inflation Rate Leads