Black Markets and Optimal Evadable Taxation

A simple model of indirect taxation, evasion, and enforcement is presented in which some surprising results emerge. Because of a "˜market-thinning' effect of high prices, high taxes lead to multiple equilibria (low-price black markets and high-price legal markets), and black-market comparative statics tend to give the "˜wrong' sign. Further, the incentive compatibility constraint for tax compliance is shown to confer a kind of concavity on enforcement costs. As a result, enforcement costs may be minimized by tax rates that vary dramatically between sectors. This consideration is dominant for relatively ineffective tax administrations, so for them the optimal tax system follows a "˜cash cow' pattern, with one sector bearing all of the tax; but for relatively effective administrations, the optimum follows a slightly modified Ramsey rule. This bifurcation of the parameter space provides one approach to a positive theory of tax systems