Question

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 \(\mathrm{d}\) with an inflation rate of \(25 \%\). Why is hyperinflation such a problem?

Short answer

Maria pays a real inflation tax of \$100, \$90, and \$81 for each of the three years with a 10% inflation rate, totaling \$271. With a 25% inflation rate, the taxes are \$250, \$187.50, and \$140.625, totaling \$578.125. Hyperinflation severely devalues currency, eroding wealth and economic stability.

Step-by-step solution

Calculate the real inflation tax for the first year

To find the real tax due to inflation for the first year, calculate the loss of purchasing power. This is done by multiplying the initial amount by the inflation rate: \(1000 \times 0.10 = \$100\). So Maria pays a real inflation tax of \$100 for the first year.

Determine the real value at the beginning of the second year

The real value of the \$1,000 at the beginning of the second year is the initial amount minus the real inflation tax paid in the first year: \(1000 - 100 = \$900\).

Calculate the real inflation tax for the second year

The inflation tax for the second year is calculated the same way as in step 1, but using the decreased value from Step 2: \(900 \times 0.10 = \$90\).

Find the real value at the beginning of the third year

The real value of the initial \$1,000 at the beginning of the third year is the amount at the beginning of the second year minus the real inflation tax paid in the second year: \(900 - 90 = \$810\).

Calculate the real inflation tax for the third year

As in previous steps, multiply the current value by the inflation rate: \(810 \times 0.10 = \$81\).

Determine the cumulative real inflation tax after three years

Add up the real inflation taxes paid each year: \(\(100 + \)90 + $81 = \$271\). This is the total real inflation tax paid over the three years.

Repeat the calculations with a 25% inflation rate

Using the same steps, calculate the real inflation tax with a 25% annual inflation rate. For the first year: \(1000 \times 0.25 = \$250\), for the second year: \((1000 - 250) \times 0.25 = \$187.50\), and for the third year: \((1000 - 250 - 187.50) \times 0.25 = \$140.625\). The total inflation tax after three years is \$578.125.

Discuss the impact of hyperinflation

Hyperinflation drastically reduces the real value of money quickly, causing people to lose purchasing power and making it hard to save or plan financially. Prices increase rapidly and currency becomes less valuable. It creates a lack of confidence in the currency as a store of value.

Key concepts

Purchasing Power

Purchasing power refers to the value of currency expressed in terms of the amount of goods or services that one unit of money can buy. It is determined by the level of prices in an economy; as prices increase, the purchasing power of money decreases.

For instance, Maria Moneybags' experience, as detailed in the exercise, features her losing purchasing power due to inflation. With an inflation rate of 10%, her \(1,000 can only purchase an equivalent of \)900 worth of goods after the first year, indicating a decline in purchasing power. This decline is a direct consequence of the currency's reduced capability to buy the same amount of goods or services over time.

Hyperinflation

Hyperinflation is an extremely high and typically accelerating rate of inflation, often exceeding 50% per month. Under hyperinflation, prices skyrocket and the real value of the currency plummets at a dramatic rate.

Examining Maria's scenario with a 25% inflation rate, a situation that is not quite hyperinflation but is illustratively high, amplifies the effect inflation has on purchasing power. Hyperinflation could ensue if that inflation rate persists or increases, rapidly eroding the real value of money. This condition creates chaos in an economy as it becomes almost impossible to set long-term financial goals, and the currency loses its function as a reliable medium of exchange and unit of account.

Real Value

The term 'real value' refers to the value of money after accounting for inflation. It reflects the actual purchasing power of money, rather than its nominal face value. The exercise involving Maria Moneybags highlights how real value changes over time with the presence of inflation.

In the exercise, the real value of Maria’s initial \(1,000 declines each year as inflation reduces its purchasing power. After three years, with inflation at 10% annually, the real value is reduced to a mere \)810, signifying a compounded effect. Understanding real value is crucial for personal finance, investment strategies, and economic planning as it reflects the true economic worth of money in an environment where prices change.