Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry?

In this work, we attempt to characterize the main theoretical difficulties to prove the existence of competitive equilibrium in infinite dimensional models. We shall show cases in which it is not possible to prove the existence of equilibrium and some others in which, however the existence of equilibrium can be proved, the equilibrium prices seem not to have natural economic interpretation. Nevertheless in pure exchange economies, most of these difficulties may be avoided by mild restrictions on the model. In productive economies new specifics problem appear, for instance non convexity of the production sets or non boundedness of the feasible allocation sets. To prove the existence and the efficiency of the equilibrium in productive economies we need some strong hypothesis about the technological possibilities of each firm.

Existence and uniqueness of the Competitive Equilibrium for Infinite Dimensional Economies

In this paper, from the excess utility function we obtain a binary relation in the social weights space and then, for an infinite dimensional economy, we prove the existence of equilibrium, in our approach we don’t suppose the existence of a demand function. Finally, we obtain a condition for the uniqueness of equilibrium, and we give some examples of economies that satisfy this condition.

On Uniqueness of Equilibrium for Complete Markets with Infinitely Many Goods and in Finance Models.

Our concern in this work is to obtain conditions for the uniqueness of equilibria, with commodity bundles as consumption patterns which depend on the state of the world. In the first section we consider an economy with complete markets, where consumption spaces are a finite product of measurable function spaces, with separable and proper utility functions and with strictly positive endowments. Using the excess utility function the infinite dimensional problem stated above is reduced to a finite dimensional one. We obtain local uniqueness. The degree theory and specially the Poincar´e-Hopf theorem applied to this excess utility function, allow us to characterize the cardinality of the equilibrium set, and we find conditions for the global uniqueness of this set. On the other hand, we obtain conditions for the uniqueness in economies with incomplete markets and only one good available in each state of the world. When markets are incomplete, equilibrium allocations are typically not Pareto efficient; then the results obtained in section 1, can not be generalized here. Nevertheless we show that for the single consumption good case the first theorem of welfare is satisfied, and then conditions for the uniqueness of equilibrium can be obtained as straightforward extension of our results shown in the first section. This is a particular simple case on incomplete markets but, is a very important one on finance theory.

Structural stability, Morse's lemma and singular economies

In this paper we consider economies whose consumption spaces are subsets of a Hilbert space with non-empty interior, and we introduce the Negishi approach to characterize the social equilibria of these economies. Using Morse's lemma, we analyze the main characteristics of two-agents-economies, and classify them. We show that the characteristics of \similar economies", in the sense introduced in [Debreu,G. (1970)], can be very di®erent from the structural stability point of view. Finally, we show that the useful mathematical de¯nition of structural stability is not enough to characterize structural stability in economics.Structural stability, Morse functions, singular economies

Some remarks about uniquenes of equilibrium for infinite dimensional economies

For economies with infinitely many goods, with two different approaches we obtain sufficient conditions for uniqueness of competitive equilibrium. In the second approach we prove that the Mitjushim-Polterovich conditions is a sufficient condition for uniqueness of equilibrium when the consumption space is a positive cone included in a Banach space. We do not suppose separability of the utility function.

A Characterization of the Singular Economies of the Infinite Dimensional Models in General Equilibrium Theory.

The aim of this paper is to characterize the set of singular economies, when there are a finite set of consumers with infinitely many goods in the sense that goods differ in the time which they are consumed or in the state of the world in which they become available. There exist l available goods in each time or in each state of the world. Employing well know results of the “ Singularity Theory” on differentiable maps, we characterize the structure of the equilibrium set from the so called singular economies. In the last section we introduce a continuous time economy and -although in a limited waywe study the dynamics along the equilibrium path. We show that if there exist singularities then the equilibrium set isn’t a finite set, moreover it may be a continuous set of equilibria. It is important to notice that we will not describe our models in terms of the tˆatonnement. The process of endowments move the price system, we don’t need the demand law to characterize the equilibrium manifold.

To leave or to stay? Uruguay and Paraguay within the Mercosur

The main objective of this paper is to show that when countries conforming a block that makes what some specialists have called: regionalism or integration -- having between them big asymmetries -- the policy to threat to leave the block can be a very efficient policy for those countries more harmed by the presence of such asymmetries. In particular in this article we analyze the current situation inside of the Southern Common Market or at it is better known in Latin America as MERCOSUR.Asymmetries, Integration, Nash Equilibria

A characterization of Walrasian economies of infinity dimension

We consider a pure exchange economy, where agent's consumption spaces are Banach spaces, goods are contingent in time of states of the world, the utility function of each agent is not necessarily a separable function, but increasing, quasiconcave, and twice Frechet differentiable over the consumption space. We characterize the set of walrasian equilibria, by the social weight that support each walrasian equilibria. Using technical of the functional analysis, we characterize this set as a Banach manifold and in the next sections we focuses on singularities.

La teoría de juegos evolutivos, naturaleza y racionalidad

Analiza las soluciones a los conflictos desde la perspectiva de la teoría de juegos. Incluye un análisis de la relación entre los equilibrios de Nash y los equilibrios dinámicos, y su estabilidad. La teoría económica encuentra en la teoría de juegos evolutivos un instrumento válido para analizar aquellas situaciones donde los agentes no se comportan totalmente como individuos racionales o en la que aprenden la racionalidad

The Ramsey model with logistic population growth

In standard economic growth theory it is assumed that labor force follows exponential growth, a not realistic assumption. As described in Maynard Smith (1974), the growth of natural populations is more accurately depicted by a logistic growth law. In this paper we analyze how the Ramsey growth model is affected by logistic growth of population, comparing it with the classic Ramsey model. We show that there is a unique nontrivial steady state of the model and that the parameters of the logistic equation play no role in determining long run equilibrium per worker level of consumption and capital. In addition, we study the stability of the model showing that its nontrivial equilibrium is a saddle point.