# The Shift of the Burden to Future Generations

## A Two-Overlapping-Generations Model

It takes some time to redeem public debt in reality. The government may impose taxes for redemption in future generations. If we consider multiple generations in the model, the tax burden among generations becomes a crucial point. Considering this point, the Ricardian neutrality theorem does not necessarily hold. Let us explain this conjecture by using the overlapping generations model.

In this regard, we should imagine two overlapping generations, the parent’s generation and the child’s generation, as shown in Fig. 4.1. Both generations live for two periods, and when the parent becomes old in period 2, the child becomes young in period 2. In this sense, two generations overlap in period 2. We call the first generation the parent’s generation, and the second generation the child’s generation.

The government issues public debt in period 1 when the parent is young and redeems it in period 2. Thus, the behavior of the government is the same as in

Fig. 4.1 **Overlapping generations model**

Sect. 1. If the government levies taxes on the parent’s generation to redeem the public debt, the analysis in Sect. 1 holds. We still have Ricardian neutrality.

The only difference is that the government may now levy taxes on the child’s generation instead of the parent’s generation in period 2. Namely, we now consider a situation in which the government imposes a tax for redemption in period 2 on the child and not on the parent.

In other words, the budget constraints are given as

for the parent and

for the child. c_{i}^{p} means the consumption of the parent and c_{i}^{c} means the consumption of the child. Subscript 1 means consumption when young and 2 means consumption when old. Superscript p means parent and superscript c means child.

Note that the parent’s budget constraint in period 1, Eq. (4.2^{0}), is the same as in Sect. 1. The budget constraint in period 2 is rewritten as Eq. (4.9) without taxes for redemption since here the parent’s generation does not pay taxes to redeem the public debt. Equations (4.10) and (4.11) represent the child’s budget constraints. Y_{2 }is the child’s income when young in period 2. The child pays taxes in period 2, T_{2}, for redemption of the public debt.