Consider an economy that exists for three periods: period 1, period 2, and period 3. In each period, the government must satisfy the budget constraint Bt+1 = (1 + i)Bt + Gt - Tt.
(a) Write this budget constraint for each period.
(b) What must be true about B4?
(c) Using the result from part (b), solve the period 3 budget constraint for B3, and substitute this back into the period 2 budget constraint.
(d) Solve this new version of the period 2 budget constraint for B2, and substitute the result back into the period 1 budget constraint.
(e) At this point, you should have the intertemporal budget constraint for the three-period economy. Interpret this equation.