A generalization of the Deaton-Hellwig results on uniform commodity taxation

Deaton (1979) showed that with an optimal linear progressive tax, commodity taxes are redundant if preferences are weakly separable between goods and labour and quasi-homothetic in goods. Hellwig (2009) later showed that any allocation with differential commodity taxes and an arbitrary linear progressive income tax is Pareto-dominated by one with uniform commodity taxes and a reformed linear progressive tax. We show that Deaton’s theorem and Hellwig’s extension apply a) with a piecewise linear income tax and tax credits, b) when some individuals earn no income either by choice or involuntarily, and c) when individual preferences for leisure differ.