Indirect taxes for redistribution: Should necessity goods be favored?

The Atkinson–Stiglitz Theorem shows that with weakly separable preferences, differential commodity taxes are not needed if an optimal nonlinear income tax is imposed. Redistributive objectives can be achieved with the income tax alone even if goods differ considerably in their income elasticities of demand. Deaton showed that if the government is restricted to a linear progressive income tax along with commodity taxes, the latter are superfluous if preferences are not only weakly separable but also yield linear Engel curves whose slopes are common to all households. These have potentially strong policy implications since they suggest that the common practice of giving preferential commodity tax treatment to necessities is not warranted. Assuming the Deaton conditions are satisfied, we derive two results to the contrary, regardless of whether labor supply varies along the intensive or extensive margin. First, if income tax, linear or nonlinear, is less progressive than optimal, necessities should be taxed preferentially relative to luxuries. Second, if a linear income tax is optimal but low-income households are unable to afford any luxury goods, it may still be optimal to tax necessity goods at lower rates than luxuries.