Consuming your way to efficiency: Public goods provision through non-distortionary tax lotteries

We revisit the classical result that taxation of private consumption is distortionary and therefore precludes the efficient provision of public goods. We introduce a nonlinear consumption tax which we call a ‘tax lottery’. Under this scheme, an ad-valorem consumption tax is supplemented with a lottery in which consumers can win cash prizes. The winning probabilities in this lottery depend on all consumers' private good consumption decisions. We show that for a given ad-valorem tax, an appropriately designed lottery can implement an efficient allocation in pure-strategy Nash equilibrium. The lottery component corrects the distortion in private consumption due to the ad-valorem tax, while the resulting tax revenue is sufficient to efficiently provide the public good and pay out the lottery prize.