Question

Inflation-induced tax distortions

Sam 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 Sam'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)
2.0	4.5
9.5	4.5

Compared with lower inflation rates, a higher inflation rate will (increase, decrease) the after-tax real interest rate when the government taxes nominal interest income. This tends to (encourage, discourage)  saving, thereby (increasing, decreasing) he quantity of investment in the economy and (increasing, decreasing) the economy's long-run growth rate.

Answer 1

Inflation rate, i	Real interest rate, r	Nominal interest rate = i+r	After-Tax Nominal Interest Rate, nt	After-Tax Real Interest Rate = nt - i
2	4.5	2+4.5 = 6.5	6.5 - 10%(6.5) = 6.5 - 0.65 = 5.85	5.85 -2 = 3.85
9.5	4.5	9.5+4.5 = 14	14 - 10%(14) = 14 - 1.4 = 12.6	12.6 - 9.5 = 3.1

decrease; discourage; decreasing; decrease
(After tax real interest rate is lower when i is higher. So, savings are discouraged which decreases investment and long run growth rate.)