Optimal design for redistributions among endogenous buyers and sellers

Given a large market of individuals entitled to equal shares of a limited resource, each allowed to buy or sell the shares, we characterize the interim incentive-constrained Pareto frontier subject to market clearance and budget balance. At most two prices—partitioning the type space into at most three tiers and using rations only on the middle tier—are needed to attain any interim Pareto optimum. When the virtual surplus function satisfies a single crossing condition without having to be monotone, the optimal mechanism reduces to a single, posted price and requires neither rationing nor lump sum transfers. We find which types gain, and which types lose, when the social planner chooses a rationing mechanism over the single-price solution, as well as the welfare weight of which type is crucial to the choice. The finding suggests a market-like mechanism to distribute Covid vaccines optimally within the same priority group.