Chapter 16, Problem 4P

To determine

Concept Introduction:

Deflation: When the average price level decreases continuously for a given interval in an economy then it is referred as deflation. It leads to a recession in an economy. Deflation is not healthy for an economy.

Inflation: When the price of any good increases continuously for an interval of time it is called inflation. It leads to a decrease in the purchasing power. A controlled inflation is good for an economy.

Hyper-inflation: When the inflation rate is very high and is usually for a longer duration then it is termed as hyper-inflation. It has a very harsh impact on an economy as it leads to depression.

Inflation Tax: It is a tax which is bared by the asset or the income holders due to an increase in the rate of inflation. It is a kind of capital gain tax resulting due to a rise in the price.

The formula to calculate inflation tax is,

$\text{Inflation}\text{Tax}=\text{Rate}\text{of}\text{Inflation}\times \text{Amount}\text{of}\text{Money}$

Explanation of Solution

a. Real inflation tax paid by Ms. Maria

Given,

Amount hold in stock is $1,000.

Rate of inflation is 10%.

The formula to calculate inflation tax is,

$\text{Inflation}\text{Tax}=\text{Rate}\text{of}\text{Inflation}\times \text{Amount}\text{of}\text{Money}$

Substitute $1,000 for the amount of money and 10% for the rate of inflation.

$\begin{array}{c}\text{Inflation}\text{Tax}=10\%\times \$1,000\\ =\frac{10}{100}\times \$1,000\\ =\$100\end{array}$

The real value of inflation tax paid by Ms. Maria is $100.

b. Real inflation tax paid by Ms. Maria for the second year.

Given,

Amount at the beginning of the second year is $900.

Rate of inflation after two years is 10.1%.

The formula to calculate inflation tax is,

$\text{Inflation}\text{Tax}=\text{Rate}\text{of}\text{Inflation}\times \text{Amount}\text{of}\text{Money}$

Substitute $900 for the amount of money and 10.1% for the rate of inflation.

$\begin{array}{c}\text{Inflation}\text{Tax}=10.1\%\times \$900\\ =\frac{10.1}{100}\times \$900\\ =\$90.9\end{array}$

The real value of inflation tax paid by Ms. Maria for the second year is $90.9.

c. Real inflation tax paid by Mrs. Maria for the third year.

Given,

Amount at the beginning of the third year is $809.1.

Rate of inflation after three years is 10.21%.

The formula to calculate inflation tax is,

$\text{Inflation}\text{Tax}=\text{Rate}\text{of}\text{Inflation}\times \text{Amount}\text{of}\text{Money}$

Substitute $809.1 for the amount of money and 10.21% for the rate of inflation.

$\begin{array}{c}\text{Inflation}\text{Tax}=10.21\%\times \$809.1\\ =\frac{10.21}{100}\times \$809.1\\ =\$82.6\end{array}$

The real value of inflation tax paid by Mrs. Maria for the third year is $82.6.

d. Cumulative real inflation tax paid.

Given,

Tax for the first year is $100.

Tax for the second year is $90.9.

Tax for the third year is $82.6.

The formula to calculate cumulative inflation tax paid is,

$\text{Cumulative}\text{Real}\text{Inflation}\text{Tax}=\left(\begin{array}{l}\text{Tax}\text{For}\text{First}\text{Year}+\\ \text{Tax}\text{For}\text{Second}\text{Year}+\\ \text{Tax}\text{For}\text{Third}\text{Year}\end{array}\right)$

Substitute $100 for the tax for the first year, $90.9 for the tax for the second year and $82.6 for the tax for the third year.

$\begin{array}{c}\text{Cumulative}\text{Real}\text{Inflation}\text{Tax}=\$100+\$90.9+\$82.6\\ =\$273.5\end{array}$

The cumulative inflation tax paid is $273.5.

e. Inflation tax when the inflation rate is 25%.

Real inflation tax for the first year

Given,

Amount hold in stock is $1,000.

Rate of inflation is 25%.

The formula to calculate inflation tax is,

$\text{Inflation}\text{Tax}=\text{Rate}\text{of}\text{Inflation}\times \text{Amount}\text{of}\text{Money}$

Substitute $1,000 for the amount of money and 25% for the rate of inflation.

$\begin{array}{c}\text{Inflation}\text{Tax}=25\%\times \$1,000\\ =\frac{25}{100}\times \$1,000\\ =\$250\end{array}$

The real value of inflation tax paid by Mrs. Maria is $250.

Real inflation tax for the second year.

Given,

Amount at the beginning of the second year is $750.

Rate of inflation after two years is 25.25%

The formula to calculate inflation tax is,

$\text{Inflation}\text{Tax}=\text{Rate}\text{of}\text{Inflation}\times \text{Amount}\text{of}\text{Money}$

Substitute $750 for the amount of money and 25.25% for the rate of inflation.

$\begin{array}{c}\text{Inflation}\text{Tax}=25.25\%\times \$750\\ =\frac{25.25}{100}\times \$750\\ =\$189.375\end{array}$

The real value of inflation tax paid by Mrs. Maria for the second year is $189.375.

Real inflation tax for the third year.

Given,

Amount at the beginning of the third year is $560.625.

Rate of inflation after three years is 25.525%

Hyper-inflation is such a big problem because it leads to a large amount of inflation tax. The purchasing power of money decreases which certainly leads to an instability in the market.

The formula to calculate inflation tax is,

$\text{Inflation}\text{Tax}=\text{Rate}\text{of}\text{Inflation}\times \text{Amount}\text{of}\text{Money}$

Substitute $560.625 for the amount of money and 25.525% for the rate of inflation.

$\begin{array}{c}\text{Inflation}\text{Tax}=25.525\%\times \$560.625\\ =\frac{25.525}{100}\times \$560.625\\ =\$143.09\end{array}$

The real value of the inflation tax paid for the third year is $143.09.