Optimal Auditing, Insurance, and Redistribution

The objective of this paper is to analyse optimal tax and audit strategies for a principal seeking to redistribute income among a population of taxpayers when the principal can observe the income of an individual at a cost. We show that in very general circumstances, it is optimal for the principal to audit some reports randomly, and reward taxpayers who are audited and found to have reported truthfully. We also investigate whether it is optimal for (post-tax) consumption, taxes, and probabilities of audit to be monotone in income. The same analysis applies to optimal insurance contracts where insurers can observe the ex-post income of insurees at a cost.