The optimal income tax problem, since it requires self-selection
constraints which define nonconvex feasible sets, is one of the many problems
in economics for which randomization in the solution may be desirable. For a
two-class economy. we characterize the optimal random tax schedules and we
present necessary and sufficient conditions for the desirability of local
randomization. The standard single-crossing restriction on preferences is not
required for these results. We also show that randomization can be beneficial
without violating (ex post as well as ex ante) horizontal equity. Lastly, we
give an example to demonstrate that the gains from randomization may be large.
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