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Economic equilibrium through variational inequalities

Magdalena Nockowska-Rosiak (2009)

Applicationes Mathematicae

The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow-Debreu-McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow-Debreu-McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to...

Économie et théorie des catastrophes

Yves Balasko (1978)

Mathématiques et Sciences Humaines

Les hypothèses de différentiabilité jouent un rôle essentiel dans plusieurs travaux récents consacrés à l'étude des propriétés de l'équilibre économique. Cet article présente une synthèse aussi élémentaire que possible d'une partie de ces travaux et fait aussi le lien avec la théorie des catastrophes de Thom.

El potencial de Hart y Mas-Colell para juegos restringidos por grafos.

J. M. Bilbao Arrese, Jorge López Vázquez (1996)

Qüestiió

This paper analyzes a model of formation of connected coalitions in a cooperative game. This model is a communication situation, and the Shapley value of this graph-restricted game is the Myerson value. The potential function for cooperative games was defined by Hart and Mas-Colell, and Winter showed that the Myerson value admits a potential function. We study a recursive procedure for computing the potential of the Myerson value. In section 3, we use the Myerson value for measuring voting power...

Exponential wealth distribution : a new approach from functional iteration theory*

Ricardo López-Ruiz, José-Luis López, Xavier Calbet (2012)

ESAIM: Proceedings

Different approaches are possible in order to derive the exponential regime in statistical systems. Here, a new functional equation is proposed in an economic context to explain the wealth exponential distribution. Concretely, the new iteration [1] given by f n + 1 ( x ) = ∫ ∫ u + v > x   f n ( u ) f n ( v ) u + v d u d v   . It is found that the exponential distribution is a stable fixed point of this functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions)...

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