Invited Session Mon.2.H 2051

Monday, 13:15 - 14:45 h, Room: H 2051

Cluster 24: Variational analysis [...]

Variational analysis and economic equilibrium

 

Chair: Alejandro Jofré

 

 

Monday, 13:15 - 13:40 h, Room: H 2051, Talk 1

Abderrahim Jourani
A characterization of the free disposal condition for nonconvex economies on infinite-dimensional commodity spaces

Coauthor: Alejandro Jofré

 

Abstract:
Our aim in this talk is to prove a geometric characterization of the free disposal condition for non convex economies on infinite-dimensional commodity spaces even if the cone and the production set involved in the condition have empty interior such as in l1 with the positive cone l1+. We then use this characterization to prove existence of Pareto and weak Pareto optimum points. We also explore a notion of approximate-Pareto optimum point, called extremal system. We show that the free disposal hypothesis alone assures extremality of the production set with respect to some set.

 

 

Monday, 13:45 - 14:10 h, Room: H 2051, Talk 2

Jean-Marc Bonnisseau
On the rank of payoff matrices with long-term assets

Coauthor: Achis Chery

 

Abstract:
We consider a stochastic financial exchange economy with a finite date-event tree representing time and uncertainty and a nominal financial structure with possibly long-term assets. We exhibit a sufficient condition under which the return matrix and the full return matrix have the same rank. This generalizes previous results of Angeloni-Cornet and Magill-Quinzii involving only short-term assets. We then derive existence results with assumptions only based on the fundamentals of the economy.

 

 

Monday, 14:15 - 14:40 h, Room: H 2051, Talk 3

Alejandro Jofré
The robust stability of every equilibrium in economic models of exchange even under relaxed standard conditions

Coauthors: Terry Rockafellar, Roger Wets

 

Abstract:
In an economic model of exchange of goods, the structure can be specified by utility functions. Under utility conditions identified here, every equilibrium will simultaneously be stable with respect to shifts in the associated holdings of the agents and with respect to the Walrasian tatonnement process of price adjustment. This fact, seemingly contrary to widespread belief, is revealed by paying close attention not only to prices but also to the proximal status of initial holdings. The conditions on the concave utility functions are standard for stability investigations, in that they invoke properties coming from second derivatives, but significantly relaxed in not forcing all goods to be held only in positive amounts. Recent advances in variational analysis provide the support needed for working in that context. The stability results also point the way toward further developments in which an equilibrium might evolve in response to exogenous inputs to the agents’ holdings, or extractions.

 

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