Question

8. Inflation-induced tax distortions Andrew receives a portion of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 4.5% 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 10%. The following table shows two scenarios: a low-inflation scenario and a high- inflation scenario. Given the real interest rate of 4.5% per year, find the nominal interest rate on Andrew's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario. Inflation Rate (Percent) Real Interest Rate (Percent) Nominal Interest Rate (Percent) After-Tax Nominal Interest Rate (Percent) After-Tax Real Interest Rate (Percent) 4.5 7.0 4.5 Compared with higher inflation rates, a lower inflation rate will nominal interest income. This tends to saving, thereby the economy's long-run growth rate. the after-tax real interest rate when the government taxes the quantity of investment in the economy and

Answer 1

Nominal interest rate= inflation+ real interest rate

So the first two columns would be filled with this formula

Inflation rate	Real interest rate	Nominal interest rate	after tax nominal interest rate	after tax real interest rate
2.0	4.5	2+4.5=6.5	5.85%	5.85-2= 3.85%
7	4.5	7+4.5=11.5	10.35%	10.35-7=3.35%

After tax interest rate of 6.5%= 6.5-10% of 6.5= 5.85%

After tax interest rate of 11.5%= 11.5%-10%of 11.5= 10.35%

The formula After tax real interest rate= nominal after tax interest rate- inflation

A lower inflation rate would increase the after tax rate real interest rate when the government taxes nominal interest income. This tends to encourage savings which increases quantity of investment and increases the economy's long run growth rate.

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