Optimal pricing of public lotteries and comparison of competing mechanisms

This article establishes optimal pricing rules for rationing indivisible units of rival and otherwise nonexcludable goods by lottery or a hybrid of a lottery and outright sale by posted price. Given the distributional objective of maximizing expected consumer surplus, the solutions to unconstrained and constrained versions of the pricing problem may be expressed in classic inverse elasticity form, with the lottery price appearing as an entry fee, user fee or a combination of the two. Numerical analysis of a rich class of private value distributions indicates that sizable gains in expected consumer surplus can be realized over competitive pricing and zero pricing.