Generalization of the Deaton Theorem: Piecewise Linear Income Taxation and Participation Decisions

Deaton (1979) showed that if preferences are weakly separable in goods and labour quasihomothetic the government imposes an optimal linear progressive tax, commodity taxes redundant. Hellwig (2009) generalized theorem by showing allocation obtained under differential arbitrary income tax is Pareto-dominated one with uniform a reformed tax. We show both extension continue to apply a) implements piecewise b) varies along intensive extensive margins. Some extensions considered.