Q817

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School
Arizona State University **We aren't endorsed by this school
Course
ECN 211
Subject
Economics
Date
Oct 21, 2023
Pages
2
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9/25/2020 Aplia: Student Question < Back to Assignment Attempts: | 0.3 | | | Keep the Highest: 0.3/ 2 8. Inflation-induced tax distortions Charles 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 Charles'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 (Percent) (Percent) (Percen (Percen |@J| [5.85] After-Tax Real Interest Rate (Percen|3 g5 2.0 4.5 | 25 | 225 |12_6\ 9.5 4.5 | 45 [X Explanation: | 4.05 |31 | 405 [X Points: 0/1 Close Explanation To maintain the level of the real interest rate, the nominal interest rate must adjust according to the Fisher equation: Nominal Interest Rate = Real Interest Rate + In flation 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 9.5% per year, the nominal interest rate is 14%, the 4.5% real rate plus the 9.5% 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 6.5% (0.1 x 6.5%) = 5.85% per year. At an inflation rate of 9.5% per year and a nominal interest rate of 14% per year, the tax reduces the nominal interest payment from 14% to an after-tax nominal interest payment of 14% (0.1 x 14%) = 12.6% per year. 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: After-Tax Real Interest Rate After-Tax Nominal Interest Rate Inflation Rate 5.85% 2% 3.85% At the higher inflation rate, the after-tax real interest rate is 12.6% 9.5% = 3.1%, which is lower than the after-tax real return at the lower inflation rate. https://ng.cengage.com/static/nb/ui/evo/index.html?deploymentld=5982802231695134071648923390&elSBN=9780357133637&id=865181431&snap... 1/2
9/25/2020 Aplia: Student Question Compared with lower inflation rates, a higher inflation rate will decrease ¥ the after-tax real interest rate when the government taxes nominal interest income. This tends to discourage v saving, thereby decreasing v the quantity of investment in the economy and decreasing ¥ the economy's long-run growth rate. Points: 0.25/1 Explanation: Close Explanation When the government taxes nominal interest income, inflation distorts the real returns to saving. Compared with a lower rate of inflation, a higher rate of inflation leads to a lower after-tax real interest rate, which tends to discourage saving. Because the economy's level of investment depends on the pool of savings available to finance investment projects (such as acquiring new tools or machinery or building new plants or office buildings), the lower volume 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. Thus, to the extent that the central bank cannot reduce inflation in an economy in which the government taxes nominal interest income, inflation will discourage saving, investment, and growth. Try Another Version Continue https://ng.cengage.com/static/nb/ui/evo/index.html?deploymentld=5982802231695134071648923390&elSBN=9780357133637&id=865181431&snap... 2/2
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