Rationalizing allocation data—a nonparametric Walrasian theory when prices are absent or non-Walrasian

Abstract

In this paper we develop a nonparametric Walrasian theory for allocation data. We show, using the Tarski–Seidenberg Theorem, that for each such data set or social plan, there exist necessary and sufficient conditions on this data set to decide, whether it can be supported by prices. This demonstrates that the cooperative foundation of the Walrasian theory and the decentralization theory for social plans can be formulated independently of theoretical, unobservable notions. We state and prove these conditions for a Walrasian equilibrium of a two-agent, n-good economy with two observations on individual endowments and final consumptions. In doing so, we develop a general framework for deriving conditions on data sets in terms of linear programs that characterize utility-based solution concepts. Applying this framework, we extend the analysis to more agents and specialize to quasi-linearity.