In this paper, we examine various aspects of the optimal lifetime redistribution policy within a cohort. We characterize the optimal tax policy when society consists of individuals who do not differ only in productivity, but also in time preference. We extend Diamond's analysis on nonlinear taxation of savings into the three-type and four-type models. To gain a better understanding of the lifetime redistribution, the problem is also solved numerically. Our results provide a rationale for distortions (upward and downward) in savings behavior in a simple two-period model where high-skilled and low-skilled individuals have different nonobservable time preferences beyond their earning capacity. If we interpret our model so that instead of private savings there is public provision of pension in the second period, then in the three-type model, we find a nonmonotonic pattern of the replacement rates. The numerical results suggest that retirement consumption is less dispersed than the first-period consumption in a paternalistic case. Paternalistic government policy also increases second-period consumption compared to the welfarist case.