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A budget deficit occurs when a government's expenditures are greater than its revenues. A budget surplus is the opposite, occurring when the government's revenues exceed its expenditures. The debt/GDP ratio is a measurement that compares a country's debt to its GDP. It is calculated by dividing the country's total debt by its GDP.

Yes, it is possible for a nation to run budget deficits and still have its debt/GDP ratio fall. One reason is that the GDP of the country could grow faster than the growth of the national debt. For example, consider the following hypothetical scenario: Year 1: Debt: $1,000,000 GDP: $10,000,000 Debt/GDP Ratio: 1,000,000/10,000,000 = 0.1 or 10% Year 2: (The government runs a budget deficit) Debt: $1,100,000 (10% increase) GDP: $12,000,000 (20% increase) Debt/GDP Ratio: 1,100,000/12,000,000 = 0.0917 or 9.17% Even though the government ran a budget deficit and increased the national debt, the debt/GDP ratio still fell because the GDP grew at a faster rate than the debt.

Yes, it is possible for a nation to run budget surpluses and still have its debt/GDP ratio rise. This could happen if the GDP of the country does not grow as fast as the reduction of the national debt. For example, consider the following hypothetical scenario: Year 1: Debt: $1,000,000 GDP: $10,000,000 Debt/GDP Ratio: 1,000,000/10,000,000 = 0.1 or 10% Year 2: (The government runs a budget surplus) Debt: $900,000 (10% reduction) GDP: $9,500,000 (5% reduction) Debt/GDP Ratio: 900,000/9,500,000 = 0.0947 or 9.47% While the government ran a budget surplus and decreased the national debt, the debt/GDP ratio still rose because the GDP did not grow or even contracted at a faster rate than the debt reduction. In conclusion, it is possible for a nation to run budget deficits and still have its debt/GDP ratio fall, as well as for a nation to run budget surpluses and still have its debt/GDP ratio rise. The key factors in these situations are the growth rate of the GDP and the change in the national debt.