Applications of generalized Ky Fan's matching theorem in minimax and variational inequality

We present some application of the generalized Ky Fan's Matching Theorem stated by Chebbi, Gourdel and Hammami in minimax and variational inequalities using a generalized coercivity type condition for correspondences defined in L-space.L-structures, L-spaces, L-KKM correspondences, L-coercing family, minimax and variational inequalities.

Incomplete markets and monetary policy

We consider an extension of a general equilibrium model with incomplete markets that considers cash-in-advance constraints. The total amount of money is supplied by an authority, which produces at no cost and lends money to agents at short term nominal rates of interest, meeting the demand. Agents have initial nominal claims, which in the aggregate, are the counterpart of an initial public debt. The authority covers its expenditures, including initial debt, through public revenues which consists of taxes and seignorage, and distributes its eventual budget surpluses through transfers to individuals, while no further instruments are available to correct eventual budget deficits. We define a concept of equilibrium in this extended model, and prove that there exists a monetary equilibrium with no transfers. Moreover, we show that if the price level is high enough, a monetary equilibrium with transfers exists.Cash-in-advance constraints, incomplete markets, nominal assets, monetary equilibrium, money, nominal interest rate.

Une note sur un théorème de point-fixe

URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSECahiers de la Maison des Sciences Economiques 2006.59 - ISSN 1624-0340We present a theorem on the existence of a maximal element for a correspondence which is upper hemi-continuous in some variables and which satisfies with respect to the other ones one the following conditions: (i) lower semi-continuous if the space has a finite dimension, (ii) lower semi-continuous if the space is complete, (iii) open fibers. This theorem generalizes the result of Gale and Mas-Colell (1975-1979) and the one of Bergstrom (1975) and extend to the infinite dimensional setting the result of Gourdel (1995).Nous présentons ici un théorème d'existence d'éléments maximaux pour une correspondance dont les composantes sont hémi-continues supérieurement par rapport à une partie des variables et qui vérifie par rapport aux autres l'une des conditions suivantes: (i) semi-continues inférieurement si l'espace est de dimension finie, (ii) semi-continues inférieurement et à valeurs fermées si l'espace est complet. (iii) à images inverses ouvertes. Ce théorème généralise les résultats de Gale and Mas-Colell (1975-1979), celui de Bergstrom (1975) et étend à un cadre de dimension infinie celui de Gourdel (1995)

Une note sur un théorème de point-fixe

Nous présentons ici un théorème d'existence d'éléments maximaux pour une correspondance dont les composantes sont hémi-continues supérieurement par rapport à une partie des variables et qui vérifie par rapport aux autres l'une des conditions suivantes : (i) semi-continues inférieurement si l'espace est de dimension finie, (ii) semi-continues inférieurement et à valeurs fermées si l'espace est complet. (iii) à images inverses ouvertes. Ce théorème généralise les résultats de Gale and Mas-Colell (1975-1979), celui de Bergstrom (1975) et étend à un cadre de dimension infinie celui de Gourdel (1995).Point-fixe, élément maximal, hémi-continuité supérieure, théorèmes de sélection.

Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies

In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex economies, a recent result obtained by one of the authors, introduces conditions which, when applied to the convex case, give for Banach commodity spaces the well-known result of decentralization by continuous prices of pareto optimal allocations under an interiority condition. In this paper, in order to prove a different version of the Second Welfare Theorem, we reinforce the conditions on the commodity space, assumed here to be a Banach lattice, and introduce a nonconvex version of the properness assumptions on preferences and the total rpoduction set. Applied to the convex case, our result becomes the usual Second Welfare Theorem when properness assumptions replace the interiority condition. The proof uses a Hahn-Banach Theorem generalization by Borwein-Jofré which allows to separate nonconvex sets in general Banach spaces.Second welfare theorem; nonconvex economies; Banach spaces; subdifferential; Banach lattices; Properness assumptions

New approach of the hairy ball theorem

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2014.51 - ISSN : 1955-611XIn this paper, we establish an equivalent version of the hairy ball theorem in the form of a fixed point theorem. By using a version of Mas-Colell theorem [6] and by applying homotopy and approximation methods, we obtain our main result.Nous présentons dans cet article, une nouvelle version équivalente au théorème de la boule chevelue sous la forme d'un théorème de point fixe. Afin de montrer le résultat principal, on a eu recours au théorème de Mas-Colell theorem [6] ainsi que des techniques d'approximations et d'homotopies

Modelling the effects of nuclear fuel reservoir operation in a competitive electricity market

In many countries, the electricity systems are quitting the vertically integrated monopoly organization for an operation framed by competitive markets. In such a competitive regime one can ask what the optimal management of the nuclear generation set is. We place ourselves in a medium-term horizon of the management in order to take into account the seasonal variation of the demand level between winter (high demand) and summer (low demand). A flexible nuclear set is operated to follow a part of the demand variations. In this context, nuclear fuel stock can be analyzed like a reservoir since nuclear plants stop periodically (every 12 or 18 months) to reload their fuel. The operation of the reservoir allows different profiles of nuclear fuel uses during the different seasons of the year. We analyze it within a general deterministic dynamic framework with two types of generation: nuclear and non-nuclear thermal. We study the optimal management of the production in a perfectly competitive market. Then, we build a very simple numerical model (based on data from the French market) with nuclear plants being not operated strictly as base load power plants but within a flexible dispatch frame (like the French nuclear set). Our simulations explain why we must anticipate future demand to manage the current production of the nuclear set (myopia can not be total). Moreover, it is necessary in order to ensure the equilibrium supply-demand, to take into account the non-nuclear thermal capacities in the management of the nuclear set. They also suggest that non-nuclear thermal could stay marginal during most of the year including the months of low demand.Electricity Market; nuclear generation; optimal reservoir operation; electricity fuel mix; perfect competition with reservoir

Incomplete markets and monetary policy

URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSECahiers de la MSE 2005.24 - Série Bleue - ISSN : 1624-0340We consider an extension of a general equilibrium model with incomplete markets that considers cash-in-advance constraints. The total amount of money is supplied by an authority, which produces at no cost and lends money to agents at short term nominal rates of interest, meeting the demand. Agents have initial nominal claims, which in the aggregate, are the counterpart of an initial public debt. The authority covers its expenditures, including initial debt, through public revenues which consists of taxes and seignorage, and distributes its eventual budget surpluses through transfers to individuals, while no further instruments are available to correct eventual budget deficits. We define a concept of equilibrium in this extended model, and prove that there exists a monetary equilibrium with no transfers. Moreover, we show that if the price level is high enough, a monetary equilibrium with transfers exists.Nous considérons une extension d'équilibre général avec marchés incomplets incluant de la monnaie. Une autorité fait face à une dette publique qu'elle rembourse en produisant de la monnaie sans frais, et en la prêtant aux agents à un taux d'intérêt à court terme. Elle perçoit également des taxes que les agents doivent payer. Les agents reçoivent un transfert de l'autorité si cette dernière accumule un excédent (ou déficit) budgétaire. Nous introduisons la notion d'équilibre monétaire dont nous démontrons l'existence dans ce modèle