# Discounted Present Value

This condition means that the debt outstanding today must be offset by primary budget surpluses in the future. Because we are adding together flows in the future, we have to use the tool of discounted present value. If, for example, the current stock of debt is zero, then the intertemporal budget constraint says that the discounted present value of future primary surpluses must equal zero. Toolkit: Section 16.3 “Discounted Present Value” You can review the meaning and calculation of discounted present value in the toolkit. Linking the Debt and the Deficit The stock of debt is linked directly to the government budget deficit. When the government runs a budget deficit, it finances the deficit by issuing new debt. The deficit is a flow, which is matched by a change in the stock of government debt: change in government debt (in given year) = deficit (in given year). If there is a government surplus, then the change in the debt is a negative number, so the debt decreases. The total government debt is simply the accumulation of all the previous years’ deficits. From this equation, the stock of debt in a given year is equal to the deficit over the previous year plus the stock of debt from the start of the previous year. (In this discussion, we leave aside the fact that the government may finance part of its deficit by issuing new money. In the United States and most other economies, this is a minor source of funding for the government. [9]) To see the interactions between deficits and the stock of debt in action, examine Table 14.5 “Deficit and Debt”, which takes the deficit numbers from Table 14.1 “Calculating the Deficit” and calculates the corresponding debt. We suppose that there is initially zero debt at the beginning of year 1. The deficit of 30 in the first year means that there is outstanding debt of 30 at the end of that year. In the second year, there is a budget surplus of 20. This reduces the debt, but it is not sufficient to bring the debt all the way back to zero. Outstanding debt at the end of the year is 10. In the third year, the deficit of 60 must be added to the existing debt of 10, so the debt at the end of the year is 70.

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