This paper calculates optimal linear income taxes when differences in income are caused by random factors ('luck') rather than by unobserved individual abilities, as assumed in the classical theory of income taxation. As first shown by Varian (1980), in the former case income taxation acts as social insurance. By introducing life uncertainty and precautionary behavior, we find higher optimal marginal tax rates than those found by Varian. We also find that - in the context of a piecewise two-bracket linear tax schedule - the second marginal tax is always higher than the first, and equals 100 percent. This last finding contrasts with results recently obtained in the framework of classical income taxation theory, which show a lower second marginal tax. For the parameters used in the simulation, we find that a Rawlsian social planner chooses a higher first marginal tax rate than a utilitarian planner would.

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