Tax avoidance and commodity tax differentiation

We examine the optimal combination of direct and indirect taxes in the presence of tax avoidance. Our findings indicate that linear commodity taxes should be included in the optimal tax mix, even when they are subject to avoidance and when the conditions of the Atkinson-Stiglitz theorem hold. This is because taxing consumption—despite the possibility of avoidance—enhances the ability to screen true income, whereas income taxation alone depends solely on reported income. Additionally, we show that when utility is weakly separable, tax rates should be positive and uniform across goods if the subutility function is homothetic, leading to linear Engel curves. However, when Engel curves are nonlinear, commodity taxes need not be uniform. Furthermore, the optimal taxation of luxuries versus necessities depends on the distribution of productivity levels.