Optimal Pricing of Public Lotteries and Comparison of Competing Mechanisms

The negative effects of price controls on consumer surplus in competitive markets are well known. But what of consumer surplus if supply is fixed, as with rival but otherwise non-excludable goods held in public trust? This paper establishes optimal pricing rules for rationing indivisible units of such goods by lottery or mixture of a lottery and auction. The solution to the pricing problem appears in classic inverse elasticity form that may be directly implemented. Analysis of a rich class of private value distributions indicates the optimal lottery yields sizable gains in expected consumer surplus over competitive pricing and zero pricing.