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 t runs a deficit of 7 trillion ducats, debt increase 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% 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
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