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Chapter 31: Problem 4

Answer the following questions about the (real) inflation tax, assuming that the price level starts at 1 . a. Maria Moneybags keeps \(\$ 1,000\) in her sock drawer for a year. Over the year, the inflation rate is \(10 \%\). What is the real inflation tax paid by Maria for this year? b. Maria continues to keep the \(\$ 1,000\) in her drawer for a second year. What is the real value of this \(\$ 1,000\) at the beginning of the second year? Over the year, the inflation rate is again \(10 \%\). What is the real inflation tax paid by Maria for the second year? c. For a third year, Maria keeps the \(\$ 1,000\) in the drawer. What is the real value of this \(\$ 1,000\) at the beginning of the third year? Over the year, the inflation rate is again \(10 \%\). What is the real inflation tax paid by Maria for the third year? d. After three years, what is the cumulative real inflation tax paid? e. Redo parts a through d with an inflation rate of \(25 \%\). Why is hyperinflation such a problem?

Short Answer

Expert verified
Answer: The main problem with hyperinflation is the rapid erosion of purchasing power. In Maria's example, her real inflation tax more than doubled with the 25% inflation rate compared to the 10% inflation rate, illustrating that higher inflation rates lead to a higher loss of purchasing power. This can have serious consequences for individuals and the economy as a whole.

Step by step solution

01

Calculate the real value of Maria's money at the end of the first year

To do this, we can use the following formula: Real value = Nominal value / (1 + Inflation rate). Real value = \(1,000 / (1 + 0.10) = \)909.09.
02

Calculate the real inflation tax for the first year

Real inflation tax = Nominal value - Real value. Real inflation tax = \(1,000 - \)909.09 = $90.91. #b. Calculating real inflation tax for the second year#
03

Calculate the real value of Maria's money at the beginning of the second year

The real value of her money at the beginning of the second year is the same as the real value at the end of the first year, which is $909.09.
04

Calculate the real value of Maria's money at the end of the second year

Real value = \(909.09 / (1 + 0.10) = \)826.45.
05

Calculate the real inflation tax for the second year

Real inflation tax = Real value at the beginning of the year - Real value at the end of the year. Real inflation tax = \(909.09 - \)826.45 = $82.64. #c. Calculating real inflation tax for the third year#
06

Calculate the real value of Maria's money at the beginning of the third year

The real value of her money at the beginning of the third year is the same as the real value at the end of the second year, which is $826.45.
07

Calculate the real value of Maria's money at the end of the third year

Real value = \(826.45 / (1 + 0.10) = \)751.32.
08

Calculate the real inflation tax for the third year

Real inflation tax = Real value at the beginning of the year - Real value at the end of the year. Real inflation tax = \(826.45 - \)751.32 = $75.13. #d. Calculating cumulative real inflation tax#
09

Add the real inflation taxes for all three years

Cumulative real inflation tax = \(90.91 + \)82.64 + \(75.13 = \)248.68. #e. Redo parts a through d with an inflation rate of 25%# #a. Calculating real inflation tax for the first year at 25% inflation#
10

Calculate the real value of Maria's money at the end of the first year at 25% inflation

Real value = \(1,000 / (1 + 0.25) = \)800.
11

Calculate the real inflation tax for the first year at 25% inflation

Real inflation tax = Nominal value - Real value. Real inflation tax = \(1,000 - \)800 = $200. #b. Calculating real inflation tax for the second year at 25% inflation#
12

Calculate the real value of Maria's money at the beginning of the second year

The real value of her money at the beginning of the second year is the same as the real value at the end of the first year, which is $800.
13

Calculate the real value of Maria's money at the end of the second year

Real value = \(800 / (1 + 0.25) = \)640.
14

Calculate the real inflation tax for the second year

Real inflation tax = Real value at the beginning of the year - Real value at the end of the year. Real inflation tax = \(800 - \)640 = $160. #c. Calculating real inflation tax for the third year at 25% inflation#
15

Calculate the real value of Maria's money at the beginning of the third year

The real value of her money at the beginning of the third year is the same as the real value at the end of the second year, which is $640.
16

Calculate the real value of Maria's money at the end of the third year

Real value = \(640 / (1 + 0.25) = \)512.
17

Calculate the real inflation tax for the third year

Real inflation tax = Real value at the beginning of the year - Real value at the end of the year. Real inflation tax = \(640 - \)512 = $128. #d. Calculating cumulative real inflation tax at 25% inflation#
18

Add the real inflation taxes for all three years

Cumulative real inflation tax = \(200 + \)160 + \(128 = \)488.
19

e. Discuss the problem with hyperinflation

The main problem with hyperinflation is the rapid erosion of purchasing power. As we can see from the calculations, Maria's real inflation tax more than doubled with the 25% inflation rate compared to the 10% inflation rate. This demonstrates that higher inflation rates lead to a higher loss of purchasing power, which can have serious consequences for individuals and the economy as a whole.

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Most popular questions from this chapter

Who are the winners and losers when a mortgage company lends \(\$ 100,000\) to the Miller family to buy a house worth \(\$ 105,000\) and during the first year prices unexpectedly fall by \(10 \%\) ? What would you expect to happen if the deflation continued over the next few years? How would continuing deflation affect borrowers and lenders throughout the economy as a whole?

The economy of Brittania has been suffering from high inflation with an unemployment rate equal to its natural rate. Policy makers would like to disinflate the economy with the lowest economic cost possible. Assume that the state of the economy is not the result of a negative supply shock. How can they try to minimize the unemployment cost of disinflation? Is it possible for there to be no cost of disinflation?

After experiencing a recession for the past two years, the residents of Albernia were looking forward to a decrease in the unemployment rate. Yet after six months of strong positive economic growth, the unemployment rate has fallen only slightly below what it was at the end of the recession. How can you explain why the unemployment rate did not fall as much although the economy was experiencing strong economic growth?

Due to historical differences, countries often differ in how quickly a change in actual inflation is incorporated into a change in expected inflation. In a country such as Japan, which has had very little inflation in recent memory, it will take longer for a change in the actual inflation rate to be reflected in a corresponding change in the expected inflation rate. In contrast, in a country such as Zimbabwe, which has recently had very high inflation, a change in the actual inflation rate will immediately be reflected in a corresponding change in the expected inflation rate. What does this imply about the short- run and long-run Phillips curves in these two types of countries? What does this imply about the effectiveness of monetary and fiscal policy to reduce the unemployment rate?

Concerned about the crowding-out effects of government borrowing on private investment spending, a candidate for president argues that the United States should just print money to cover the government's budget deficit. What are the advantages and disadvantages of such a plan?
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