The following calculations help you see how the ratio of debt to GDP changes fro

Question

The following calculations help you see how the ratio of debt to GDP changes from one year to the next. Suppose that in a hypothetical country with a currency called the ducat, debt is equal to 140 trillion ducats and GDP is equal to 100 trillion ducats. This means that the ratio of debt to GDP is 1.4, or 140%. Also, suppose that the deficit is 7 trillion ducats, which is 7% of GDP. When the government runs a deficit, it spends more than it collects in tax revenue. To make up the difference, it borrows. So if it runs a deficit of 7 trillion ducats, debt increases by 7 trillion ducats. So debt next year is 147 trillion ducats. Suppose that there is no growth in real GDP and inflation is equal to -2% per year. (Negative inflation is the same as deflation.) Next year's GDP will be equal to trillion ducats. If the ratio of debt to GDP is 1.4 this year, the ratio of debt to GDP next year when inflation is equal to -2% per year will be. Suppose that the deficit remains constant at 7% of GDP and that inflation persists at -2%. The debt to GDP ratio the year after next will be.

Explanation / Answer

98T (100T -0.02(100T))

If the ratio of debt to GDP is 1.4 this year, what will the ratio of debt to GDP be next year when inflation is equal to -2% per year?

147/98 = 1.5


Suppose that the deficit remains constant at 7% of GDP and that inflation persists at -2%. What will the debt to GDP ratio be the year after next?

new debt = 147 + 0.07(98) = 153.86
new GDP = 98 - 0.02(98) = 96.04
new debt/gdp ratio = 153.86/96.04 = 1.6

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