Regular Economies Research Articles

On the existence and the structure of the pseudo-equilibrium manifold

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1); a robust example of such economies is provided. Theorem 2 establishes that the manifold Ω of global pseudo-equilibria is a fiber bundle with the topological structure of a one- or two-fold covering space of G k, n , the space of k planes in R n , where k is the number of assets in the economy and n the number of states of uncertainty. In particular, the pseudo-equilibrium manifold Ω is not contractible with incomplete markets. This contrasts with the case of complete markets, where the equilibrium manifold is always contractible.

Economies with a Unique Equilibrium: A Simple Proof of Arc-connectedness in the Two-Agent Case

This paper proposes an elementary geometric proof of the arc-connectedness of the set of regular economies with a unique equilibrium in the case of two agents and two goods. Journal of Economic Literature Classification Numbers: C52, D45, D51.

Equilibrio walrasiano en economías de intercambio

Se presentan las funciones de exceso de demanda agregada de una economía de intercambio. Se estudian las propiedades y los vectores de precios de equilibrio de dichas funciones. Se prueba que el equilibrio walrasiano es un óptimo de Pareto. Se estudia el concepto de economía regular y se aprueba la existencia de equilibrio walrasiano, para dicha economía. Por último, estudiamos la unicidad del vector de precios de equilibrio.

Continuity of equilibria in exchange economies

The purpose of this paper is to extend the theory of regular economies to the space of exchange economies with continuous ( C 0) preferences. It is shown that economies with equilibria that are contained in a finite number of arbitrarily small disjoint balls form an open dense set in the space of C 0 economies.

The set of regular equilibria

Debreu has shown that the set of regular economies is open dense. This paper investigates the closely related issue of the size of the set of regular equilibria. It is shown that this set is an open dense subset of the equilibrium manifold. The proof exploits the real algebraic nature of the set of critical equilibria belonging to any given fiber of the equilibrium manifold. This proof yields as by-product an alternative proof of Debreu's theorem, a proof that does not hinge on Sard's theorem.

Regular economies and sets of measure zero in Banach spaces

Using concepts of measure zero in Banach spaces, Debreu result guaranteeing full measure for the economies with stable and finite number of equilibria is generalized. Here, we include utility functions as well as initial endowments in the definition of an economy.

Extension of a theorem of Smale on equilibria for pure exchange economies

The methods used by Smale in his paper Global Analysis and Economics IIa, seem to be heavily dependent on the hypothesis that utility functions have no critical points. In this paper we prove that the no critical point hypothesis can be dropped and the class of regular economies, for which the equilibria are locally continuous functions of the parameters of the economy, can be extended.

The Transfer Problem and the Theory of Regular Economies

The Transfer Problem and the Theory of Regular Economies

Uniqueness of rest points for optimal control models in economics

Optimal control solutions for dynamic multi-sector economic models in general may exhibit multiple rest points having different stability properties, and under such circumstances the qualitative behavior of the system depends crucially upon initial conditions. Both necessary and sufficient conditions for a unique rest point solution are presented, and a class of ‘regular economies’ is defined for which this uniqueness property prevails.

Regular Economies and Conditions for Uniqueness of Steady States in Optimal Multi-Sector Economic Models

Regular Economies and Conditions for Uniqueness of Steady States in Optimal Multi-Sector Economic Models

Equilibria and core of large economies

In this paper we apply results on regular economies to study equilibria and core in a non-differentiable framework. We show that the distributions of agents' characteristics of regular economies form a dense subset of all distributions of agents' characteristics. Therefore ‘most’ economies have equilibria which are contained in finitely many ϵ-balls. And the core of ‘most’ sufficiently large economies is contained in finitely many ϵ-balls centered at equilibrium allocations of these economies.

Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C 1-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.

On the continuity of equilibrium prices in constant-returns production economies

The purpose of this paper is to extend the theory on the local uniqueness of equilibrium prices initiated by Debreu (1970) [and pursued by E. and H. Dierker (1972), Smale (1974a), Hazewinkel(1972), Delbaen (1971), Hildenbrand (1972), Fuchs (1974), and others] to production economies of the constant returns variety. The problem is the familiar one: good theoretical reasons for the uniqueness of equilibria being unavailable, one settles for expecting that, at least, equilibria will be locally unique and will vary continuously with perturbations of the economy, i.e., that economies will be ‘regular’ (as e,, or e,,, not e,, in fig. 1). Still, if multiplicity of equilibria is possible, non-regular economies (as e, in fig. 1) are unavoidable and the best possible result is to establish their exceptionality (that is to say, to justify giving to regular economies its name) by showing, and this is certainly intuitive (see fig. I), that they are associated with degeneracies and constitute a ‘negligible’ subset of economies. The notion of ‘negligibility’ we will use is topological [by contrast to measure theoretical, see E. and H. Dierker (1972)]; namely, the space of economies will be a topological space and negligible sets will be the ones which closures have empty interiors. In a production context, where only a limited number of commodities may be factors of production, initial endowments redistributions (if at all allowable) do not give enough parameter variability and so, consumers’ or producers’ characteristics other than initial endowments have to be regarded as variable; the space of economies becomes then infinite-dimensional and forces the topological definition of negligible. Different approaches to production have been considered by Fuchs (1974) and Smale (1974b). However, constant returns to scale have so far been excluded from the theory in the case of Fuchs (1974), because supply functions are assumed to exist, and, in the case of Smale (1974b), because the class of constant