The geometry of optimal taxation: a primal approach

We characterize zero tax results geometrically as a condition on indifference curves and the implementability constraint. The condition can also be expressed as a generalized homotheticity condition on the utility function and also extends older results on uniform taxation that use the duality approach. Many zero taxation results in dynamic macroeconomics can be derived from our characterization; thus it provides a unified framework for a systematic study of these phenomena. Our geometric method also allows to study the sign of deviations from zero tax results in more complicated frameworks such as taxation without commitment.