Nonlinear prices in nonconvex economies with classical Pareto and strong Pareto optimal allocations

The paper is devoted to applications of modern tools of variational analysis to equilibrium models of welfare economics involving generally nonconvex economies with infinite-dimensional commodity spaces. The main results relate to the so-called generalized/extended second welfare theorem ensuring an equilibrium price support at Pareto optimal allocations. Based on advanced tools of variational analysis and generalized differentiation, we establish refined results of this type with the novel usage of nonlinear prices at the three types to optimal allocations: weak Pareto, Pareto, and strong Pareto. We pay a special attention to strong Pareto optimal allocations in economies with ordering commodity spaces showing that enhanced results for them do not require, in contrast to the classical types of weak Pareto and Pareto optimality, any net demand qualification conditions.