We study the sustainability of pension systems using a life-cycle model with distortionary taxation that sets an upper limit to the real value of tax revenues. This limit implies an endogenous threshold dependency ratio, i.e. a point in the cross-section distribution of the population beyond which tax revenues can no longer sustain the planned level of transfers to retirees. We quantify the threshold using a computable life-cycle model calibrated on the United States and on 14 European countries which have dependency ratios among the highest in the world. We examine the effects on the threshold and welfare of a number of policies often advocated to improve the sustainability of pension systems. New tax data on dynamic Laffer effects are provided.