Continuous Budget Balance

So far we started from the premise that government purchases and the tax rate are given exogenously. In this situation, the government budget constraint equals B = G + rD − t(Y + rD). And the budget deficit adds to public debt $$\dot{D}$$ = B. Now, as an exception, we shall posit that the government continuously adjusts public consumption so as to always balance the budget. Under these circumstances, the government budget constraint simplifies to G = tY. As a corollary, the budget balances B = 0, and there will be no public debt D = 0.