Question

At the end of 2015, the debt-to-GDP ratio is 1.1 (i.e. the debt is 110% of GDP). The government budget deficit was 3% of GDP. By how much should nominal GDP grow to ensure that the debt-to-GDP ratio by the end of 2016 is still 1.1?

Answer 1

To maintain a debt-to-GDP ratio of 1.1 by the end of 2016 with a budget deficit of 3% of GDP, the nominal GDP must grow by 3%.

Step-by-step explanation:

The student has asked about the change in nominal GDP required to maintain the debt-to-GDP ratio at a steady level, despite a budget deficit. To ensure that the debt-to-GDP ratio by the end of 2016 remains at 1.1, we can set up an equation to find the required growth in nominal GDP. This problem requires understanding of ratios and basic algebra to solve.

If the debt-to-GDP ratio is currently 1.1, it means that if the GDP is denoted by 'G' and the debt by 'D,' we have D = 1.1G. After a 3% deficit, the debt increases by 0.03G, making the new debt D + 0.03G. To maintain the ratio at 1.1, the new GDP (let's call it G') must satisfy the condition (D + 0.03G) / G' = 1.1.

By substituting D with 1.1G in the equation, we can find the required growth of GDP. After simplifying, we get G' = (D + 0.03G) / 1.1. Since D = 1.1G, then G' = (1.1G + 0.03G) / 1.1. This simplifies to G' = G(1.13) / 1.1, which further simplifies to G' = 1.03G. Therefore, to maintain the debt-to-GDP ratio at 1.1, the nominal GDP must grow by 3%.