Optimal Taxes and Penalties When the Government Cannot Commit to Its Audit Policy

Abstract

This paper presents a two-period model, with a utilitarian government and a continuum of taxpayers. In the first period, the government designs the tax law, which comprises taxes and fines to impose on evaders. Contrary to the previous literature on optimal tax-enforcement policies, the government cannot commit to any future audit policy. In the second period, evasion and costly enforcement take place. Taxpayers report their income to the government. Then, the government decides whether to audit each report or not. If a misreport is detected, evaders are penalized; otherwise, taxpayers pay their due tax.We obtain the optimal tax law by solving the model backwards. In the second period, the dynamic inspection game has, depending on parameter values and first-period choices, either (i) a pure strategy equilibrium, with full evasion; or (ii) a mixed strategy equilibrium, with partial evasion and random auditing. Next, we move back to the first period, where we completely characterize the tax law that maximizes expected social welfare. The main results of the paper are the following. First, the characterization of the optimal tax law crucially depends upon the existence of honest taxpayers. Second, in the partial evasion regime, the tax monotonically decreases with the audit cost whereas, in the full evasion regime, the tax weakly increases with the audit cost. Third, for some parameter values, it may be optimal for the government to impose no fines for evaders as a way to commit not to audit. Finally, we show that, when some individuals are honest, expected social welfare is non-monotonic in the audit cost. We illustrate these results with a numerical example.