On optimal lifetime redistribution policy

In this paper we examine various aspects of the optimal lifetime redistribution policy within a cohort. We characterise optimal redistribution policy when society consists of individuals who do not differ only in productivity, but also in time preference or myopia. We extend Diamond’s (2003) analysis on nonlinear taxation of savings into the three and four type models. Our results provide a rationale for distortions (upward and downward) in savings behaviour in a simple two period model where high skilled and low skilled individuals have different non-observable time preferences beyond their earning capacity. If we interpret our model so that there is no private savings, but public provision of pension in period 2, then in different versions (and different parameterization) of three type model we find the U-shaped pattern of the replacement rates. Our numerical results suggest that the retirement consumption is less dispersed than the first period consumption in a paternalistic case, whereas in a welfarist case the ordering is reversed. Our numerical simulations also show that consumption when old should be less dispersed than consumption when young when some individuals are myopic. Moreover our numerical results suggest that when there are myopic individuals in the economy, a paternalistic government policy increases saving and makes saving larger than with paternalist government policy where there are no myopic individuals.