A nonconvex separation property and some consequences
Since G. Debreu`s work on the general equilibrium theory, a great effort has been made to generalize the economics models as well as to weak the hypotheses made in the original model. Two main problems have been studied. The equilibrium price existence and the relation between a Pareto optimum and an equilibrium price whose study is also an aim of this work. Indeed, from the Economics point of view we establish a result which allow us to associate for each Pareto Optimum of a general nonconvex nontransitive economy a non-zero price such that each consumer and producer satisfied for this price {open_quotes}first-order conditions{close_quotes} involving subgradients of the distance function to the preferences and production sets. The most important difference between the obtained results in this topic is the geometrical concepts associated with the {open_quotes}first-order conditions{close_quotes}. Guesnerie (1975) used the normal cone associated with Dubovickii-Miljutin`s tangent cone concept, whereas Yu (1984), Quinzii (1986), Cornet (1986), Kahn and Vohra (1987) and Bonnisseau and Cornet (1988, 1990) used Clarke`s normal cone. Also, Kahn (1987) established a similar result that Cornet by using the approximate normal cone which is always contained in Clarke`s normal cone. Thus, his formulation gives sharper results. The demonstration of afore mentioned results are based on Hahn-Banach separation theorem or on a nonsmooth version of Karush-Kuhn-Tucker`s theorem. Recently, the authors Jofre and Rivera established in finite dimension this result by using the set-valued map of {open_quotes}approximate subgradients of the distance function{close_quotes} which is smaller than approximate normal cone and it is compact, moreover this set-valued map is always upper semicontinuous.
- OSTI ID:
- 36169
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0449
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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