Question

Unlike households, governments are often able to sustain large debts. For example, in 2019, the U.S. government’s total debt reached $21.2 trillion, approximately equal to 105.3% of GDP. At the time, according to the U.S. Treasury, the average interest rate paid by the government on its debt was 1.3%. However, running budget deficits becomes hard when very large debts are outstanding.

a. Calculate the dollar cost of the annual interest on the government's total debt, assuming the interest rate and debt figures previously cited. Enter your answer in billions of dollars, and round to the nearest tenth. Annual interest: $ billion Rate of GDP growth: %
b. If the government operates on a balanced budget before interest payments are taken into account, at what rate must GDP grow for the debt-GDP ratio to remain unchanged? Enter your answer as a percentage and round to the nearest tenth of a percent.
c. Calculate the total increase in national debt if the government incurs a deficit of $600 billion in 2020. Enter your answer in billions of dollars and round to the nearest tenth. Debt increase: $ billion
d. At what rate would GDP have to grow in order for the debt-GDP ratio to remain unchanged when the deficit in 2020 is $600 billion? Enter your answer as a percentage and round your answer to the nearest hundredth of a percent. Rate of GDP growth: %
e. Why is the debt-GDP ratio the preferred measure of a country's debt rather than the dollar value of the debt? Why is it important for a country to keep its debt-GDP ratio under control?
- The size of an economy, measured by its GDP, determines a government's ability to repay debt through taxes.
- The debt- GDP ratio is a more accurate reflection of how burdened a country is by debt than the dollar value of the debt. A government should keep the debt-GDP ratio under control to keep itself from being overburdened by debt. The debt-GDP ratio shows the extent to which government debt constrains financial markets. Since this constraint depends on the size of the economy, the dollar value of the debt is a less accurate measure. Countries with high debt- GDP ratios tend to crowd out private borrowing.
- A country's debt-GDP ratio illustrates what fraction of a country's tax revenue its creditors can claim. A country with a high debt-GDP ratio risks losing the means to support essential government programs due to its obligations to its creditors.

Answer 1

The annual interest on the government's total debt is $275.6 billion. GDP must grow by at least 1.3% for the debt-GDP ratio to remain unchanged for a balanced budget before interest. With a $600 billion deficit in 2020, GDP would need to grow by 4.28% to keep the debt-GDP ratio stable.

Step-by-step explanation:

To calculate the annual interest on the government's total debt, we can use the formula Interest = Debt × Interest Rate. Given the debt of $21.2 trillion and an interest rate of 1.3%, the annual interest cost is:

Interest = $21.2 trillion × 0.013 = $0.2756 trillion or $275.6 billion.

For the debt-GDP ratio to remain the same when the government is running a balanced budget excluding interest, the GDP growth rate must be equal to the interest rate on the debt, which is 1.3%.

If the government incurs a deficit of $600 billion in 2020, the increase in national debt will be:

Debt increase = Initial Debt + Deficit = $21.2 trillion + $0.6 trillion = $21.8 trillion.

For the debt-GDP ratio to remain unchanged with a $600 billion deficit, the GDP must grow at a rate that is equal to the ratio of the deficit to the initial GDP plus the interest rate on the debt. If we denote the required GDP growth rate as G, then:

G = (Deficit / Initial GDP) + Interest Rate

G = ($0.6 trillion / $20.1 trillion) + 0.013

G = 0.0298 + 0.013 = 0.0428 or 4.28%

The debt-GDP ratio is preferred over the dollar value of the debt because it takes into account the size of the economy and its ability to repay the debt through taxation. A high debt-GDP ratio can constrain financial markets, crowd out private borrowing, and limit a country's ability to fund essential programs.