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?
Gross national debt is the total amount outstanding in public and private debt in a country. The new level of the gross national debt would be ($3,300,000,000,000.) three trillion and three billion.
ii. If 100 percent of the deficit is financed 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?
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?
a. The total amount outstanding in public and private debt in a country. The new level of the gross national debt would be ($2,600,000,000,000.) two trillion and six billion.
II. If 100 percent of the deficit is financed 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?

i. The new level of gross national debt would be $3.3 trillion. It's like having $3 trillion and then realizing you left $300 billion in your other pants pocket.

ii. If 100 percent of the deficit is financed by agencies, the amount of debt held by the public would remain the same because the deficit is not financed by the public. The level of gross debt, however, would increase by $300 billion because the government is adding to its overall debt.

iii. If GDP increased by 5 percent, the gross debt as a percentage of GDP would decrease. This is like trying to lose weight but gaining height instead. The level of debt held by the public as a percentage of GDP would also decrease, making it feel like a weight has been lifted off their shoulders.

I. The new level of gross national debt would be $2.6 trillion. It's like starting with $2.5 trillion and then realizing you won $100 billion in the lottery. Party time!

II. If 100 percent of the deficit is financed by agencies, the amount of debt held by the public would remain the same because the deficit is not financed by the public. The level of gross debt, however, would increase by $100 billion because the government is increasing its overall debt.

III. If GDP increased by 5 percent, the gross debt as a percentage of GDP would decrease, just like trying to squeeze into skinny jeans after losing some weight. The level of debt held by the public as a percentage of GDP would also decrease, making it feel like a victory in the battle of financial proportions.

To answer the first set of questions:

i. The new level of gross national debt would be $3.3 trillion. This is calculated by adding the initial debt of $3 trillion with the deficit of $300 billion.

ii. If 100% of the deficit is financed by agencies, it means that the deficit is covered by borrowing from public entities (such as federal agencies). In this case, the amount of debt held by the public remains the same, as the deficit is not financed through public borrowing. The level of gross debt, however, increases by the amount of the deficit, so it would be $3.3 trillion.

iii. If GDP increased by 5%, it means that the overall economic output increased. As a result, the gross debt as a percentage of GDP would decrease. The level of debt held by the public as a percentage of GDP would also decrease.

Now let's move on to the second set of questions:

I. The new level of gross national debt would be $2.6 trillion. This is calculated by adding the initial debt of $2.5 trillion with the deficit of $100 billion.

II. If 100% of the deficit is financed by agencies, it means that the deficit is covered by borrowing from public entities. This results in an increase in the amount of debt held by the public. The level of gross debt, however, increases by the amount of the deficit, so it would be $2.6 trillion.

III. If GDP increased by 5%, it means that the overall economic output increased. As a result, the gross debt as a percentage of GDP would decrease. The level of debt held by the public as a percentage of GDP would also decrease.

It's important to note that these calculations are simplified and do not take into account other factors that can influence the level of debt and its relation to GDP, such as interest rates, government spending, and economic growth rates.