Characterizations of the Free Disposal Condition for Nonconvex Economies on Infinite Dimensional Commodity Spaces

Our aim in this paper is to prove geometric characterizations of the free disposal condition for nonconvex economies on infinite dimensional commodity spaces even if the cone and the production set involved in the condition have an empty interior such as in $L^1$ with the positive cone $L^1_+$. We then use this characterization to prove the existence of Pareto and weak Pareto optimal points. We also explore a notion of extremal systems a la Kruger--Mordukhovich. We show that the free disposal hypothesis alone assures the extremality of the production set with respect to some set.

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