In many trading environments, any incentive compatible and individually rational market mechanism will be either inefficient or will run a deficit. We prove that as the market size m gets large, for any fixed surplus (or deficit) x, m times the minimal absolute inefficiency converges to c(x) where c(⋅) is essentially a quadratic function of textitx. We introduce a new mechanism, the double auction with a fixed transaction fee. By choosing the size of the fee appropriately, any level of deficit or surplus can be implemented and the resulting mechanisms achieve the above bound. Corollaries include: an asymptotic version of the Myerson–Satterthwaite Impossibility Theorem; a description of the minimal subsidy required to implement the efficient trading rule; a characterization of the minimal inefficiency obtainable with budget-balanced market mechanisms; recommendations on the optimal organization of trade; and insights on the effects of taxation.

This paper shows how standard arguments supporting the imposition of price caps break down in the presence of demand uncertainty. In particular, though in the deterministic case the introduction or lowering of a price cap (above marginal cost) results in increased production, increased total welfare, decreased prices, and increased consumer welfare, we show that all of the above comparative statics predictions fail for generic uncertain demand functions. For example, for price caps sufficiently close to marginal cost, a decrease in the price cap always leads to a decrease in production and total welfare under certain mild conditions. Under stronger regularity assumptions, all of the monotone comparative statics predictions from the deterministic case also do not hold for a generic uncertain demand if we restrict attention to price caps in an arbitrary fixed interval (as long as the price caps are binding for some values in that interval).