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Chapter 28: Problem 15

Unlike households, governments are often able to sustain large debts. For example, in \(2013,\) the U.S. government's total debt reached \(\$ 17.3\) trillion, approximately equal to \(101.6 \%\) of GDP. At the time, according to the U.S. Treasury, the average interest rate paid by the government on its debt was \(2.0 \%\). 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 cited above. b. If the government operates on a balanced budget before interest payments are taken into account, at what rate must GDP grow in order for the debt-GDP ratio to remain unchanged? c. Calculate the total increase in national debt if the government incurs a deficit of \(\$ 600\) billion in 2014 . d. At what rate would GDP have to grow in order for the debt-GDP ratio to remain unchanged when the deficit in 2014 is \(\$ 600\) billion? 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 government to keep this number under control?

Short Answer

Expert verified
Answer: Maintaining a manageable debt-GDP ratio is important for a government because it ensures financial stability, long-term growth, and investor confidence. A sustainable level of debt signals a healthy economy and helps prevent crises and economic downturns. Moreover, it prevents higher interest rates, making borrowing less expensive for the government.

Step by step solution

01

a. Calculate the annual interest on the total debt

To calculate the annual interest on the total debt, we multiply the total debt by the average interest rate paid by the government. The total debt is \(\$17.3\) trillion, and the average interest rate is \(2.0 \%\): Interest = Total Debt * Average Interest Rate = \(17.3 * 0.02 = \$346\) billion So, the annual interest on the total debt is \(\$346\) billion.
02

b. GDP growth rate for constant debt-GDP ratio with balanced budget (before interest payments)

In this scenario, the government runs a balanced budget before interest payments. The interest payment is \(\$346\) billion, and the initial debt-GDP ratio is \(101.6\%\). Let x be the growth rate of GDP: \(101.6\% = \frac{(Debt + Interest)}{GDP (1 + x)}\) Solving for x, we get: \(x = \frac{(Debt + Interest)}{101.6\% \times GDP} - 1 = \frac{(17.3 + 0.346)}{1.016 \times 17.3} - 1\) \(x = 1.02014 - 1\) \(x = 0.02014\) The required GDP growth rate to keep the debt-GDP ratio constant is approximately \(2.014\%\).
03

c. Calculate the total increase in national debt if the government incurs a deficit of \(600\) billion in 2014

The total increase in national debt is the sum of the deficit and the interest payment: Total increase in National Debt = Deficit + Interest = \(600 + 346 = \$946\) billion So, the total increase in national debt in 2014 is \(\$946\) billion.
04

d. GDP growth rate for constant debt-GDP ratio with \(600\) billion deficit in 2014

Now, the government incurs a deficit of \(600\) billion in addition to the interest payment of \(346\) billion. We need to find the GDP growth rate (x) that keeps the debt-GDP ratio constant: \(101.6\% = \frac{(Debt + Deficit + Interest)}{GDP (1 + x)}\) Solving for x, we get: \(x = \frac{(Debt + Deficit + Interest)}{101.6\% \times GDP} - 1 = \frac{(17.3 + 0.6 + 0.346)}{1.016 \times 17.3} - 1\) \(x = 1.05478 - 1\) \(x = 0.05478\) The required GDP growth rate to keep the debt-GDP ratio constant when the deficit in 2014 is \(600\) billion is approximately \(5.478\%\).
05

e. Significance of the debt-GDP ratio and its importance for a government

The debt-GDP ratio is a measure of a country's government debt relative to its GDP. It is the preferred measure of a country's debt because it indicates the government's ability to pay back its debt. A high debt-GDP ratio may cause concern among investors and lead to higher interest rates, making it more expensive for the government to borrow. It is important for a government to keep the debt-GDP ratio under control because a sustainable level of debt ensures financial stability, long-term growth, and investor confidence. A high ratio may signal an unsustainable level of debt, which could lead to crises and economic downturns. By managing the debt-GDP ratio, governments can maintain healthy public finances and promote economic stability.

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Most popular questions from this chapter

Most macroeconomists believe it is a good thing that taxes act as automatic stabilizers and lower the size of the multiplier. However, a smaller multiplier means that the change in government purchases of goods and services, government transfers, or taxes needed to close an inflationary or recessionary gap is larger. How can you explain this apparent inconsistency?

In 2014 , the policy makers of the economy of Eastlandia projected the debt- GDP ratio and the ratio of the budget deficit to GDP for the economy for the next 10 years under different scenarios for growth in the government's deficit. Real GDP is currently \(\$ 1,000\) billion per year and is expected to grow by \(3 \%\) per year, the public debt is \(\$ 300\) billion at the beginning of the year, and the deficit is \(\$ 30\) billion in 2014 . a. Complete the accompanying table to show the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy if the government's budget deficit remains constant at \(\$ 30\) billion over the next 10 years. (Remember that the government's debt will grow by the previous year's deficit.) b. Redo the table to show the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy if the government's budget deficit grows by $3 \%$ per year over the next 10 years. c. Redo the table again to show the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy if the government's budget deficit grows by $20 \%$ per year over the next 10 years. d. What happens to the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy over time under the three different scenarios?

In which of the following cases does the size of the government's debt and the size of the budget deficit indicate potential problems for the economy? a. The government's debt is relatively low, but the government is running a large budget deficit as it builds a high-speed rail system to connect the major cities of the nation. b. The government's debt is relatively high due to a recently ended deficit- financed war, but the government is now running only a small budget deficit. c. The government's debt is relatively low, but the government is running a budget deficit to finance the interest payments on the debt.

Show why a \(\$ 10\) billion reduction in government purchases of goods and services will have a larger effect on real GDP than a \(\$ 10\) billion reduction in government transfers by completing the accompanying table for an economy with a marginal propensity to consume \((M P C)\) of \(0.6 .\) The first and second rows of the table are filled in for you: on the left side of the table, in the first row, the \(\$ 10\) billion reduction in government purchases decreasesa. When government purchases decrease by \(\$ 10\) billion, what is the sum of the changes in real GDP after the 10 rounds? b. When the government reduces transfers by \(\$ 10\) billion, what is the sum of the changes in real GDP after the 10 rounds? c. Using the formula for the multiplier for changes in government purchases and for changes in transfers, calculate the total change in real GDP due to the \(\$ 10\) billion decrease in government purchases and the \(\$ 10\) billion reduction in transfers. What explains the difference? (Hint: The multiplier for government purchases of goods and services is \(1 /(1-M P C)\). But since each \(\$ 1\) change in government transfers only leads to an initial change in real GDP of \(M P C \times \$ 1\), the multiplier for government transfers is $M P C /(1-M P C) .)$

How did or would the following affect the current public debt and implicit liabilities of the U.S. government? a. In 2003 , Congress passed and President Bush signed the Medicare Modernization Act, which provides seniors and individuals with disabilities with a prescription drug benefit. Some of the benefits under this law took effect immediately, but others will not begin until sometime in the future. b. The age at which retired persons can receive full Social Security benefits is raised to age 70 for future retirees. c. Social Security benefits for future retirees are limited to those with low incomes. d. Because the cost of health care is increasing faster than the overall inflation rate, annual increases in Social Security benefits are increased by the annual increase in health care costs rather than the overall inflation rate.
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