Try the following exercises to better understand how the national debt is related to the government’s budget deficit.

 
a. Assume that the gross national debt initially is equal to $3 trillion and the federal government then runs a deficit of $300 billion:
 
i. What is the new level of gross national debt?

ii. If 100 percent of the deficit is financed by the sale of securities to federal agencies, what happens to the amount of debt held by the public? What happens to the level of gross debt?
 
iii. If GDP increased by 5 percent in the same year that the deficit is run, what happens to gross debt as a percentage of GDP? What happens to the level of debt held by the public as a percentage of GDP?
 
b. Now suppose that the gross national debt initially is equal to $2.5 trillion and the federal government then runs a deficit of $100 billion:
 
i. What is the new level of gross national debt?
 
ii. If 100 percent of this deficit is financed by the sale of securities to the public, what happens to the level of debt held by the public? What happens to the level of gross debt?
 
iii. If GDP increases by 6 percent in the same year as the deficit is run, what happens to gross debt as a percentage of GDP? What happens to the level of debt held by the public as a percentage of GDP?