Question

12. Inflation-induced tax distortions Darnell receives a portion of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 4% per year. The nominal interest rate on the bonds adjusts automatically to account for the inflation rate. The government taxes nominal interest income at a rate of 20%. The following table shows two scenarios: a low-inflation scenario and a high-inflation scenario. Given the real interest rate of 4% per year, find the nominal interest rate on Darnell's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario. Inflation Rate Real Interest Rate Nominal Interest Rate After-Tax Nominal Interest Rate After-Tax Real Interest Rate (Percent) (Percent) (Percent) (Percent) (Percent) 1.5 4.0 8.0 4.0 Compared with higher inflation rates, a lower inflation rate will the after-tax real interest rate when the government taxes nominal interest income. This tends to saving, thereby the quantity of investment in the economy and the economy's long-run growth rate.

Answer 1

Based on the given rates to Darnell, the nominal and after-tax real interest rates are:

Inflation rate 1.5%;

• Nominal rate = 5.5%.
• After-tax nominal = 4.4%.
• After-tax real = 2.9%.

Inflation rate 8%;

• Nominal rate = 12%.
• After-tax nominal = 9.6%.
• After-tax real = 1.6%.

What are the rates when inflation is 1.5%?

Nominal rate:

= Inflation + Real rate

= 1.5% + 4%

= 5.5%

After-tax nominal:

= 5.5% x (1 - 20% tax)

= 4.4%

After-tax real:

= 4.4% - 1.5% inflation

= 2.9%

What are the rates when inflation is 8%?

Nominal rate:

= Inflation + Real rate

= 8% + 4%

= 12%

After-tax nominal:

= 12% x (1 - 20% tax)

= 9.6%

After-tax real:

= 9.6% - 8% inflation

= 1.6%

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