A heavily indebted government may end up in a vicious circle, where increasing debt leads to higher interest rates and lower growth, which increases debt even faster with subsequent even higher interest rates and lower growth etc.

a) Derive a formula showing how the change in the government debt ratio depends upon the primary deficit (relative to GDP), the earlier debt ratio, the real interest rate and the growth rate!

b) By how much will the government debt ratio increase in a given year if earlier debt is 100 per cent of GDP, the primary deficit 10 per cent of GDP, the real interest rate 2 per cent and the growth rate 1 per cent? What primary fiscal balance is required to stabilise debt?

c) By how much will the government debt ratio increase in a given year if earlier debt is 170 per cent of GDP, the primary deficit is 2 per cent of GDP, the real interest rate 10 per cent and the growth rate - 4 per cent? What primary fiscal balance is required to stabilise debt?