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