This paper provides necessary and sufficient conditions for the existence of Pareto-improving tax reforms. The conditions can be expressed as sufficient statistics and have a wide range of potential applications in public finance. We discuss one such application in detail: the introduction of...

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...