If the government balances the overall budget every period I: the national debt will stay constant forever.II: the debt-to-GDP ratio will fall to zero as long as nominal GDP growth is positive.

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The government budget constraint is:$$B_t + (1+r_t)B_{t-1} = G_t + r_tD_{t-1}$$where:* $B_t$ is the government budget deficit in period t* $r_t$ is the real interest rate in period t* $D_{t-1}$ is the government debt at the end of period t-1* $G_t$ is government spending in period tIf the government balances the overall budget every period, then $B_t = 0$ for all t. This implies that:$$(1+r_t)B_{t-1} = G_t + r_tD_{t-1}$$Rearranging, we get:$$B_{t-1} = \frac{G_t}{1+r_t} + \frac{r_t}{1+r_t}D_{t-1}$$This shows that the government debt will stay constant forever if the government balances the overall budget every period and the real interest rate is constant.If the nominal GDP growth rate is positive, then the debt-to-GDP ratio will fall to zero as long as the government balances the overall budget every period. This is because the debt will stay constant while nominal GDP will grow over time.

If the Government Balances the Overall Budget Every Period I