## \Aplia-PROD-SRVMaterialsmarc.lieberman-0046_E100ps_8-F15-LONG-Run_Fiscal_(National_Debt)

• November 30, 2020

Introduction to Macroeconomics                                                                        New York University

Marc Lieberman                                                                                                Fall, 2015

Supplemental Problem Set #8

Fiscal Policy and the National Debt

Note: To learn more about solving these types of problems, attend one of the recitations Friday Nov 20 or Monday Nov 23.

When dealing with the impact of the national debt on the economy, we have an issue: The debt itself is a stock variable (measured at a moment in time), while GDP , the budget deficit and interest payments are flows (measured over a period of time). This can create problems when we mix the two types of variables in the same problem. So for simplicity and consistency, we’ll make the following assumptions in this problem:

• During any year, the government pays a flow of interest on the amount of debt that it owed at the beginning of that year.
• The “Debt-GDP” ratio for any given year is the National Debt (a stock) at the beginning of that year, divided by GDP (a flow) during that year.

We’ll also make the following assumption about the interest rate:

• The interest rate the government must pay on its national debt is a constant 5%.

1. Suppose that, at the beginning of 2015, a country’s National Debt is \$7.5 trillion, and its GDP in 2015 is \$15 trillion.

1. What is the debt-GDP ratio for 2015? (State your answer in decimal form)
• How much interest, in dollars, must the government pay on the debt in 2015?
• What is the “burden of the debt” for 2015? (State your answer in both decimal and percent form)

Note: As discussed in class, the burden of the debt is the ratio of interest payments to GDP  It is called the “burden of the debt” because it’s the fraction of our total income that must be collected as net taxes just to pay interest on the debt.

2.  Now suppose that GDP grows by 10% (that is, 2016 GDP is 10% greater than 2015 GDP), and during 2015, the government ran a budget deficit of \$750 billion.

1. What is the GDP in 2016?
• What is the government’s National Debt in 2016?

[Hint: Remember that we’re measuring national debt at the beginning of each year.  So how does the budget deficit during 2015 affect the national debt at the beginning of 2016?]

• By what percentage did the National Debt grow (from the beginning of 2015 to the beginning of 2016)?
• What is the debt-GDP ratio for 2016? (State your answer in decimal form).  How does it compare to the ratio for 2015?
• How much interest, in dollars, must the government pay on the debt in 2016?
• What is the “burden of the debt” for 2016? (State your answer in both decimal and percent form)  How does it compare to the “burden of the debt” in 2015?

3. Suppose once again that 2016 GDP is 10% greater than 2015 GDP.  But this time, assume that in 2015, the government ran a budget deficit of \$1 trillion (instead of the \$750 billion we assumed before). What would be the burden of the debt in 2016? (Go through the same process as in 2. above to find the answer).

4. Suppose once again that 2016 GDP is 10% greater than 2015 GDP.  But this time, assume that in 2015, the government ran a budget deficit of \$500 billion (instead of the \$750 billion  or  \$1 trillion  we assumed previously). What would be the burden of the debt in 2016? (Go through the same process again.)

5. Based on the values for the burden of the debt you found in 2, 3, and 4, evaluate the following two statements:

a. “Whenever the government runs a budget deficit and adds to the national debt, the burden of the debt rises.”  True or false?

b. “Whenever the government runs a budget deficit, it adds to the national debt.  But if GDP is also growing, and the national debt grows more slowly than GDP, the burden of the debt will fall.  With a growing GDP, the national debt has to grow at a faster rate than GDP to cause the burden of the debt to rise.”  True or false?

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