Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context

This paper provides four theorems on the existence of a free-disposal equilibrium in a Walrasian economy: the first with an arbitrary set of agents with compact consumption sets, the next highlighting the trade-offs involved in the relaxation of the compactness assumption, and the last two with a countable set of agents endowed with a weighting structure. The results generalize theorems in the antecedent literature pioneered by Shafer–Sonnenschein in 1975, and currently in the form taken in He–Yannelis 2016. The paper also provides counterexamples to the existence of non-free-disposal equilibrium in cases of both a countable set of agents and an atomless measure space of agents. One of the examples is related to one Chiaki Hara presented in 2005. The examples are of interest because they satisfy all the hypotheses of Shafer’s 1976 result on the existence of a non-free-disposal equilibrium, except for the assumption of a finite set of agents. The work builds on recent work of the authors on abstract economies, and contributes to the ongoing discussion on the modelling of “large” societies.