Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies
Recalling, that the interest for nonconvex economies (arising on the production side as well as on the consumption side) is an old interest in Economics, the authors prove for such economies in the infinite dimensional case (i.e., there are infinitely many commodities) new versions of the second wellfare theorem. To get an equilibrium notion they apply first order optimality conditions written in terms of normal cones (to the preferred and production sets). There are three points, which are especially interesting in this paper: First, the authors use an abstract version of subdifferentials (in Banach spaces) to get different notions of normal cones and discuss the connections to Joffe's, Mordukhovich's and Clarke's subdifferential. Second, they apply a viscous separation theorem [compare \textit{J. M. Borwein} and \textit{A. Jofré}, Math. Methods Oper. Res. 48, 169--179 (1998; Zbl 0935.49008)] which was obtained with help of Ekeland's variational principle. Third, the preferences need not be transitive or complete nor are there monotonicity assumptions. Finally it is worth noticing, that the authors discuss and compare carefully the different assumptions of this paper and show, that -- applied to the convex case -- their results contain the usual second wellfare theorem (when the stated properness assumptions are replaced by interiority conditions).
scientific article; zbMATH DE number 5076542
scientific article