Prices and E cient Assignments Without Transfers

A classic insight of the Walrasian theory of markets, commonly referred to as the Second Welfare Theorem, is that every Pareto e cient assignment can be decentralized through the use of prices. This classic insight is predicated on the assumption that agents are locally non-satiated, an assumption that is readily satisfied in settings with money. However, the non-satiation assumption fails in settings without money such as the assignment of school seats in school choice programs. The assignment of scarce resources in these settings has been intensively studied recently and Pareto e ciency is a commonly accepted goal for such assignments. What assignments are e cient in settings without transfers? Does the insight of the Second Welfare Theorem remain valid in such settings? We address these questions in the ⇤Universitat Autonoma de Barcelona Barcelona Graduate School of Economics, and University of California Los Angeles, respectively. We would like to thank Salvador Barbera, Roland Benabou, Dirk Bergemann, Simon Board, Sergiu Hart, Andrew McLennan, Jordi Masso, Moritz Meyer-ter-Vehn, Michael Richter, William Thomson, Utku Unver, William Zame, Simpson Zhang, and seminar participants at UAB and UCLA for helpful comments. 1This classic insight, also known as the Second Fundamental Theorem of Welfare Economics, was conjectured by Pareto (1909), and subsequently refined and developed by many authors, culminating in the definitive treatment by Arrow (1951) and Debreu (1951). 2Local non-satiation requires that for any agent and any assignment there is a nearby assignment that the agent strictly prefers, for instance because it leaves him with more money. 3See e.g. Abdulkadiroglu and Sonmez (2003).