Indirect taxation is superfluous under separability and taste homogeneity: a simple proof

Indirect taxation is of no use when nonlinear income taxation is available in an economy where everyone has the same taste for goods: an elementary proof of this result, due to Atkinson and Stiglitz [Atkinson, A., Stiglitz, J., 1976. The design of tax structure: direct versus indirect taxation. Journal of Public Economics 6, 55–75.] is provided