We solve the nonlinear income tax program for rank-dependent social welfare functions, expressing the trade-off between size and inequality using the Gini and related families of positional indices. Absent bunching, ranks in the actual and optimal allocations are invariant. Exploiting this feature, we provide new, simple, and intuitive tax formulas for both the quasilinear and additive cases and new comparative static results. Our approach makes insights from optimal taxation more widely accessible. In some of our simulations the actual US tax policy is close to being optimal—except at the top, where optimal rates are much higher than in actuality.
Simula, Laurent, and Alain Trannoy.
"Gini and Optimal Income Taxation by Rank."
American Economic Journal: Economic Policy,
Personal Income, Wealth, and Their Distributions
Equity, Justice, Inequality, and Other Normative Criteria and Measurement
Taxation and Subsidies: Efficiency; Optimal Taxation
Personal Income and Other Nonbusiness Taxes and Subsidies; includes inheritance and gift taxes