**"The Optimal Distribution of Income Revisited,"**
August 2017.

pdf file.

This paper revisits the optimal distribution of income model in Fair (1971). This model is the same as in Mirrlees (1971) except that education is also a decision variable and tax rates are restricted to lie on a tax function. In the current paper the tax-rate restriction is relaxed. As in Fair (1971), a numerical method is used. The current method uses the DFP algorithm with numeric derivatives. Because no analytic derivatives have to be taken, it is easy to change assumptions and functional forms and run alternative experiments. The sensitivity of the results to the four main assumptions of the model are examined. Gini coefficients are computed, which provides a metric for comparing the redistributive effects under different assumptions. Ten optimal marginal tax rates are computed per experiment corresponding to ten tax brackets.

This paper also argues that the widely used specification of a
quasi-linear utility function---a utility function with no income
effects---is not realistic. It requires for solution of the overall model
large differences in utility functions across individuals of different
abilities.