LECTURE SUPPLEMENT
19–5 The Government Budget Constraint
To better understand the link between government debt and future taxes, it is useful to imagine that the
economy lasts for only two periods. Period one represents the present, period two the future. In period one,
the government collects taxes T1 and makes purchases G1; in period two, it collects taxes T2 and makes
purchases G2. Because the government can run a budget deficit or a budget surplus, taxes and purchases in
the first equation for D into the second equation to obtain
T2 = (1 + r) (G1 – T1) + G2.
This equation relates purchases in the two periods to taxes in the two periods. To make the equation easier
to interpret, we rearrange terms. After a little algebra, we obtain
This equation is the government budget constraint. It states that the present value of government purchases
period two. The consumer’s lifetime income is the same as before the change in fiscal policy. Therefore,
the consumer chooses the same level of consumption as she would have without the tax cut, which implies
that private saving rises by the amount of the tax cut. Hence, by combining the government budget
constraint and Irving Fisher’s model of intertemporal choice, we obtain the Ricardian result that a debt–
financed tax cut does not affect consumption.