Optimal nonlinear income taxation with a finite population

In the optimal nonlinear income taxation problem of Mirrlees and Stiglitz, the government's tax schedules guarantee consumption-income bundles for each type of consumer regardless of others’ actions. Piketty (Journal of Economic Theory, 1993) allows tax schedules to depend on other consumers' actions. When the government knows the exact distribution of abilities, it can construct more complicated tax schedules which can implement any first-best allocation as the unique outcome of the individuals’ revelation game, in contrast to the secondbest properties of conventional tax schedules. Piketty's mechanism may assign suboptimal or even infeasible allocations to consumers when the distribution of individual reports of types differs from the true distribution of types which the government knows. We consider the effect of requiring either that tax schedules must balance the government budget for every possible vector of revelation by individuals or that after individuals have revealed their types, the government can change its initially announced values subject to constraints that no one who revealed truthfully can be made worse off. Depending on whether individuals reveal their type by simple announcements or by committing to an action, the results differ from those in Mirrlees-Stiglitz and Piketty.