The paper extends the works by Judd [K.L. Judd, Redistributive Taxation in a Simple Perfect Foresight Model, J. Public Econ. 28 (1985), 59–83.] and Chamley [C. Chamley, Optimal taxation of capital income in general equilibrium with infinite lives, Econometrica, 54 (1986), 607–622.], who establish that in the long run the capital income tax should be zero, by considering a discrete time version of the Blanchard–Buiter–Weil perpetual youth model. We show that an independent source of non-zero taxation arises whenever the economy is “disconnected” and this feature is properly taken into account by the policymaker. More precisely, if the weight attached to each cohort in the social welfare function equals the corresponding actual share in the population, there is a force pushing towards positive taxation of capital income, which acts as a Pigouvian intervention. Moreover, room for this intertemporal correction shrinks as the relative weight of a cohort tends to zero: thus, the optimal tax rate decreases with age and tends to zero for the oldest. We also show that our result depends neither on life-cycle behavior, as pointed out by the previous literature on OLG models, nor on population growth.