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 the 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 percent of GDP?
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i. To find the new level of gross national debt, you would add the initial debt of $2.5 trillion with the deficit of $100 billion:
New level of gross national debt = Initial debt + Deficit
= $2.5 trillion + $100 billion
Remember that 1 trillion is equal to 1,000 billion, so you will need to convert the deficit from billion to trillion before adding:
$100 billion = $100 billion / $1 trillion per 1,000 billion
= $0.1 trillion
Therefore, the new level of gross national debt is:
New level of gross national debt = $2.5 trillion + $0.1 trillion
= $2.6 trillion
ii. If 100 percent of the deficit is financed by the sale of securities to the public, the level of debt held by the public would increase by the same amount as the deficit. In this case, the deficit is $100 billion, or $0.1 trillion:
Level of debt held by the public = Initial debt + Deficit
= $2.5 trillion + $0.1 trillion
= $2.6 trillion
The level of gross debt would also increase by the same amount, as the deficit was completely financed by the sale of securities to the public.
iii. To calculate the gross debt and debt held by the public as a percentage of GDP, you need to divide the respective debt levels by the GDP and then multiply by 100 to get the percentage.
Gross debt as a percentage of GDP = (Gross debt / GDP) * 100
Debt held by the public as a percentage of GDP = (Debt held by the public / GDP) * 100
To determine the impact on these percentages, we need to know the GDP growth rate. It is given that the GDP increased by 6 percent in the same year as the deficit is run.
Let's assume that the initial GDP is "G". With a 6 percent increase, the new GDP is:
New GDP = G + (6% of G)
= G + 0.06G
= 1.06G
Now we can calculate the changes in the debt ratios:
Change in gross debt as a percentage of GDP = (New gross debt / New GDP) * 100 - (Initial gross debt / Initial GDP) * 100
Change in debt held by the public as a percentage of GDP = (New debt held by the public / New GDP) * 100 - (Initial debt held by the public / Initial GDP) * 100
Let's substitute the values:
Change in gross debt as a percentage of GDP = ($2.6 trillion / 1.06G) * 100 - ($2.5 trillion / G) * 100
Change in debt held by the public as a percentage of GDP = ($2.6 trillion / 1.06G) * 100 - ($2.5 trillion / G) * 100
Please note that this is a simplified calculation since we assumed the initial GDP as "G" and the increase as 6 percent. In reality, accurate data for year-on-year GDP growth would be needed to obtain precise values.