Optimal income taxation with tax avoidance

We determine the optimal income tax schedule when individuals have the possibility of avoiding paying taxes. Considering a convex concealment cost function, we find that a subset of individuals, located in the interior of the income distribution, should be allowed to avoid taxes, provided that the marginal cost of avoiding the first euro is sufficiently small. This contrasts with the results of Grochulski who shows that, using a subadditive cost function, all individuals should report their true income. We also provide a characterization of the optimal income tax curve.