An Abstract Extremal Principle with Applications to Welfare Economics

In this paper we introduce general prenormal and normal structures in Banach spaces that cover conventional concepts of normals to arbitrary closed sets under minimal requirements. Based on these structures, we establish new abstract versions of the extremal principle in variational analysis, which plays a fundamental role in many applications. The main applications of this paper concern necessary conditions for Pareto optimality in nonconvex models of welfare economics. We obtain new results in this direction that extend approximate and exact versions of the generalized second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations.