Relativity, Inequality and Optimal Nonlinear Income Taxation

How does concern for consumption relative to others (”relativity”) affect the progressivity of the optimal income tax structure? In this paper we revisit this literature and present a more detailed analysis of the solution to the non-linear income tax problem with consumption interdependence than is currently available, generalizing some results and developing other results for cases with special objective functions and special distributions, as well as numerical simulations. Of particular interest for us is the interplay between inequality and relativity in determining the optimal tax schedule. We find support for greater progressivity in the tax structure as relative concern increases. But our numerical calculations show that this incremental impact is less at higher levels of inequality. We also explore what happens when the government does not accept the relative concerns of individuals and maximizes a non-welfarist objective function. 1 We are grateful to Andrew Oswald and participants at the SIRE – Cornell conference on Relativity, Inequality and Public Policy Edinburgh, 2009 for very useful comments and suggestions.