Question 8 Chapter 17 Inflation-induced tax distortions
Raphael receives a portion of his income from his holdings of interest-bearing U.S. government
... [Show More] 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 Raphael'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
Points: 0.5 / 1
Explanation: Close Explanation
To maintain the level of the real interest rate, the nominal interest rate must adjust according to the
Fisher equation:
At the lower inflation rate of 2% per year, the nominal interest rate is 6.5%, the 4.5% real rate plus
the 2% inflation rate. At the higher inflation rate of 8.5% per year, the nominal interest rate is 13%,
the 4.5% real rate plus the 8.5% inflation rate.
The government taxes 10% of the nominal interest paid on the bonds. When the inflation rate is 2%
per year and the nominal interest rate is 6.5% per year, the tax reduces the nominal interest
payment from 6.5% to an after-tax nominal interest payment
of . At an inflation rate of 8.5% per year and a nominal
interest rate of 13% per year, the tax reduces the nominal interest payment from 13% to an after-tax
(Percent)
2.0
8.5
(Percent)
4.5
4.5
(Percent) (Percent)
5.85
11.6
(Percen
4.05
13 2.4
11.7 3.2 6.5
t 3.85
decrease
discourage
Explanation: Close Explanation
When the government taxes nominal interest income, inflation distorts the real returns to saving.
Compared with lower rates of inflation, higher inflation rates lead to lower after-tax real interest rates.
A lower after-tax real return tends to discourage saving. The economy's level of investment depends
on the pool of savings available to finance investment projects like acquiring new tools or machinery or
building new plants or office buildings. The lower level of saving will decrease the quantity of
investment, thereby decreasing the economy's rate of physical capital accumulation and depressing
the long-run economic growth rate. To the extent that the central bank cannot reduce inflation in an
economy where government taxes nominal interest income, it will discourage saving, investment, and
growth.
Compared with lower inflation rates, a higher inflation rate will
when the government taxesnominal interest income. This tends to
the quantity of investment in the economy and
the after-tax real interest rate
saving, thereby
the economy's long-run
growth rate.
Points: 1 / 1
nominal interest payment of .
Rearranging the nominal interest rate equation, you can see that the real interest rate is the
difference between the nominal interest rate and the inflation rate. The after-tax real interest rate is,
therefore, the after-tax nominal interest rate minus the inflation rate. At the lower inflation rate, the
after-tax real interest rate is calculated as follows:
At the higher inflation rate, the after-tax real interest rate is , which is lower
than the after-tax real return at the lower inflation rate.
decreasing decreasing [Show Less]