The effects of population aging on optimal redistributive taxes in an overlapping generations model

The impact of population aging on the steady-state solution to an Ordover and Phelps (J. Public Econ. 12:1–26, 1979) overlapping generations optimal nonlinear income tax problem with two types of worker and quasilinear-in-leisure preferences is investigated. A decrease in the rate of population growth, which leads to an aging population, increases the relative price of consumption per person in retirement, which tends to decrease optimal consumption for retirees of both skill types. Nevertheless, it is also shown that the optimal marginal income tax rates are independent of the rate of population growth. In addition, the steady-state interest rate unambiguously declines when the rate of population growth declines. Resulting adjustments in production plans have an ambiguous effect on the aggregate wage rate. This article identifies factors contributing to an increase in the aggregate wage when the population ages, namely normality of consumption in retirement, complementarity between capital and labor in production, and a large capital deepening effect relative to the increase in dependency owing to demographic change. Depending on the sign of this wage effect, ambiguities may arise in the direction of change in the optimal steady-state consumption and production plans. However, when the dependency effect is sufficiently strong, it is possible to sign the direction of change in all production and consumption plans. Moreover, regardless of the direction of change in optimal consumption plans, the absolute value of the changes in consumption plans are smaller for low-skilled workers than for high-skilled when utility is time-separable and preferences exhibit decreasing absolute risk aversion. Adopting, instead, a quasilinear-in-consumption specification of preferences sharpens the comparative statics of consumption allocations, but introduces ambiguity into the effect of the rate of population growth on the optimal marginal income tax rate.