Atkinson and Stiglitz show that with weakly separability, differential commodity taxes are unnecessary given an optimal nonlinear income tax. Deaton showed that with an optimal linear progressive income tax, commodity taxes are superfluous under weakly separable and linear Engel curves. Using...

We introduce cross-border shopping and indirect tax competition into a model of optimal taxation. The Atkinson-Stiglitz result that indirect taxation cannot improve the efficiency of information-constrained tax-transfer policies, and that indirect taxes should not be differentiated across goods,...