Steve receives a portion of his income from his holdings of interest-bearing U.S

Question

Steve receives a portion of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 3.5% per year. The nominal interest rate on the bonds adjusts automatically to the inflation rate. Suppose 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 3.5% per year, find the nominal interest rate on Steve's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario. 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.

Explanation / Answer

Working notes:

(a) Nominal interest rate = Real rate + Inflation rate

(b) After-tax nominal interest rate = Pre-tax nominal rate x (1 - tax rate) = Pre-tax nominal rate x (1 - 0.2)

= Pre-tax nominal rate x 0.8

(c) After-tax real interest rate = After-tax nominal rate - Inflation rate

Therefore:

(a) Lower inflation

Nominal interest rate = 3.5% + 2.5% = 6%

After-tax nominal rate = 6% x 0.8 = 4.8%

After-tax real rate = 4.8% - 2.5% = 2.3%

(b) Higher inflation

Nominal interest rate = 6.5% + 3.5% = 10%

After-tax nominal rate = 10% x 0.8 = 8%

After-tax real rate = 8% - 6.5% = 1.5%

(c) A lower inflation rate will increase the after-tax real rate when government taxes nominal interest income. This tends to increase saving, thereby increasing the investment and increasing long-run growth rate.

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