The gross national debt initially is equal to $2.5 trillion and the federal government then runs a defict of $100 billion:
1. What is the new level of gross national debt?
2. If 100 percent of this deficit is financed by the sales of securities to the public, what happens to the level of debt held by the public? What happens to the the level of gross debt?
3. 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?
1. The new level of gross national debt is $2.5 trillion (the initial amount) + $100 billion (the deficit) = $2.6 trillion.
2. If 100 percent of the deficit is financed by the sales of securities to the public, the level of debt held by the public increases by $100 billion. The gross debt also increases, but it already increased in question 1. So, the level of debt held by the public becomes $100 billion higher, and the level of gross debt remains at $2.6 trillion.
3. Assuming the initial GDP was $10 trillion (just an example, the question did not provide the initial GDP):
- Gross debt as a percentage of GDP is (($10 trillion * 1.06) / $2.6 trillion) * 100.
- Debt held by the public as a percentage of GDP is (($10 trillion * 1.06) / $100 billion) * 100.
Calculating the above expressions:
- Gross debt as a percentage of GDP is 25.96%.
- Debt held by the public as a percentage of GDP is 6.60%.
Note that these values might be different if the given initial GDP was different. The formulas remain the same.
To answer these questions, we need to understand the concepts involved and the calculations required. Let's break it down step by step:
1. What is the new level of gross national debt?
To find the new level of gross national debt, we need to add the deficit to the initial debt. In this case, the deficit is $100 billion, and the initial debt is $2.5 trillion.
New Gross National Debt = Initial Debt + Deficit
New Gross National Debt = $2.5 trillion + $100 billion
Before proceeding, we need to convert the units to match. Since the initial debt is given in trillions and the deficit is given in billions, we need to convert billions to trillions.
$100 billion = $0.1 trillion
Now we can continue with the calculation:
New Gross National Debt = $2.5 trillion + $0.1 trillion
New Gross National Debt = $2.6 trillion
Therefore, the new level of gross national debt is $2.6 trillion.
2. If 100 percent of this deficit is financed by the sales of securities to the public, what happens to the level of debt held by the public? What happens to the level of gross debt?
If 100 percent of the deficit is financed by the sales of securities to the public, there will be an increase in the level of debt held by the public. This is because the government sells securities (such as Treasury bonds) to the public to borrow money, increasing the debt held by the public.
The level of gross debt will also increase because the deficit is added to the existing debt, regardless of who holds it. So both the debt held by the public and the gross debt will increase.
3. If GDP increases by 6 percent in the same year as the deficit is run, what happens to the gross debt as a percentage of GDP? What happens to the level of debt held by the public as a percentage of GDP?
To determine the impact on the gross debt as a percentage of GDP and the level of debt held by the public as a percentage of GDP, we need to do the following calculations:
Percentage of Gross Debt to GDP = (Gross Debt / GDP) * 100
Percentage of Debt Held by the Public to GDP = (Debt Held by the Public / GDP) * 100
Assuming the gross debt and the debt held by the public remain the same, we can calculate the percentages using the given information.
Let's say the GDP before the 6 percent increase is represented as "GDP_0," and after the increase, it becomes "GDP_1."
Percentage of Gross Debt to GDP = (Gross Debt / GDP_1) * 100
Percentage of Debt Held by the Public to GDP = (Debt Held by the Public / GDP_1) * 100
Since the gross debt and the debt held by the public didn't change in this scenario, we can assume the same values for each.
Now let's calculate the percentages:
Percentage of Gross Debt to GDP = (2.6 trillion / GDP_1) * 100
Percentage of Debt Held by the Public to GDP = (2.6 trillion / GDP_1) * 100
Remember that GDP increased by 6 percent, so we can represent the new GDP as:
GDP_1 = GDP_0 * (1 + 0.06)
GDP_1 = 1.06 * GDP_0
Now we can substitute GDP_1 in the percentage calculations:
Percentage of Gross Debt to GDP = (2.6 trillion / (1.06 * GDP_0)) * 100
Percentage of Debt Held by the Public to GDP = (2.6 trillion / (1.06 * GDP_0)) * 100
Simplifying the expressions further may not be possible without the exact value of the initial GDP, but you can now calculate the percentages by substituting the appropriate values for GDP_0 in the above equations.
Note: It's important to have the specific GDP value to calculate the exact percentages.
1. The new level of gross national debt can be calculated by adding the deficit to the initial debt:
New Gross National Debt = Initial Debt + Deficit
New Gross National Debt = $2.5 trillion + $100 billion
To simplify the calculations, it's important to convert the deficit from billion to trillion:
$1 billion = $0.001 trillion
New Gross National Debt = $2.5 trillion + ($100 billion * $0.001 trillion)
New Gross National Debt = $2.5 trillion + $0.1 trillion
New Gross National Debt = $2.6 trillion
Therefore, the new level of gross national debt is $2.6 trillion.
2. If 100 percent of the deficit is financed by the sales of securities to the public, the level of debt held by the public increases. The level of gross debt also increases because the debt held by the public is part of the total gross debt.
In this case, the level of debt held by the public increases by the same amount as the deficit:
Level of Debt Held by the Public = Deficit
Level of Debt Held by the Public = $100 billion
Therefore, the level of debt held by the public increases by $100 billion. The level of gross debt also increases by this same amount.
3. If GDP increases by 6 percent in the same year as the deficit is run, the ratio of gross debt to GDP and the ratio of debt held by the public to GDP could change.
To calculate the new ratios, divide the new level of debt by the new GDP:
Gross Debt as a Percentage of GDP = (New Gross National Debt / New GDP) * 100
Debt Held by the Public as a Percentage of GDP = (Level of Debt Held by the Public / New GDP) * 100
Assuming that GDP was initially $100 trillion:
Gross Debt as a Percentage of GDP = ($2.6 trillion / $106 trillion) * 100
Gross Debt as a Percentage of GDP ≈ 2.45%
Debt Held by the Public as a Percentage of GDP = ($100 billion / $106 trillion) * 100
Debt Held by the Public as a Percentage of GDP ≈ 0.094%
Therefore, the gross debt as a percentage of GDP would be approximately 2.45%, and the level of debt held by the public as a percentage of GDP would be approximately 0.094%.