# The Government Budget Constraint

The above arguments suggest that if fiscal management is sustainable, we have the following budget constraint in the long run.

The present value of the net balance (or the primary balance) of tax revenue and government spending = the net public debt outstanding in the initial period.

In the two-period model, the government budget constraints are given by

where B_{0} is the size of bond issued at period 0 and B_{1} is the size of bond issued at period 1. B_{0} is a new variable in the government budget constraint since it is useful to include the initial public bond outstanding to examine the sustainability issue. From these budget constraints, the present value budget constraint becomes

The primary balance or net balance denotes the difference between G_{;} and ^ (i = 1, 2). If G_{;} > T_{;}, the primary balance is in deficit, and if G_{;} < T_{;}, it is in surplus. Equation (6.13) means that the present value of total primary surplus, the left-hand side, should be at least equal to the present value of initial public debt. Otherwise, if we have the following inequality

the government cannot redeem the debt outstanding; hence, the government budget becomes unsustainable.