Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the expected real interest rate is unchanged at 3.0 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 after-tax expected real interest rate
A)rises by 1.8 percent.
B)rises by 0.9 percent.
C)falls by 0.9 percent.
D)falls by 1.8 percent.

Question

Quizplus · Accepted Answer

When the expected inflation rate falls from 6% to 0%, the nominal interest rate would adjust to maintain the expected real interest rate at 3.0%. The after-tax real interest rate is calculated as the real interest rate adjusted for taxes, which is $r_{after-tax} = r_{real}(1 - tax\ rate)$. With a tax rate of 30%, a decrease in inflation increases the after-tax real interest rate because the nominal interest rate would decrease less than the inflation rate, effectively increasing the real return on investments after taxes. Initially, with a 3% expected inflation, the after-tax real interest rate is $3\% \times (1 - 0.30) = 2.1\%$. When inflation falls to 0%, the nominal interest rate would adjust to still yield a real interest rate of 3%, but now the entire 3% is real return, not reduced by inflation. The after-tax real interest rate becomes $3\% \times (1 - 0.30) = 2.1\% + 1.8\% = 3.9\%$. The increase is 1.8 percentage points, from 2.1% to 3.9%.

Suppose That a Change in the Expected Inflation Rate Leads