Back to Fundamentals: Equilibrium in Abstract Economies

Journal of Mathematical Economics, 1979

2009

How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers' preferences. We show in this paper that if consumers' non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: 1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; 2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; 3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; 4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; 5) the pathconnectedness of the sets of stable equilibria.

gradnet.de

The aim of the study is to analyse the equilibrium concept in mainstream economic modelling. In rethinking the equilibrium concept, first we will criticise the thought that economic activities and relations can be explained by the "equilibrium" in the models which are build upon axioms to reach a state of equilibrium. Mainstream economic models are based on and structured according to the focus of equilibrium. According to Roegen (1978:35) in the economic theory there is no concept, which is as fundamental as and as important as the equilibrium. state that the central concept of the static analysis is equilibrium. defines the equilibrium concept in economics as a state in which opposing external forces acting on the system cancel each other out, thereby annulling their respective effects on the system. This understanding of equilibrium is rooted in the first law of Newton; so, in the first part of the study we will cover the boundaries of the equilibrium concept in mainstream economics and in classical mechanics. As physics continued to progress, economics continued to absorb its effects. Thus, the development of quantum mechanics also had an impact on economic modelling. After the Second World War there have been many attempts to incorporate quantum mechanics into economics. These attempts, though successful in modelling equilibrium states, owe their success only to the fact that their underlying axioms are designed to lead to equilibrium. Thus, any criticism of economics from an either a classical or quantum-mechanical point of view is bound to fail because economic models are consistent with classical and quantum mechanics. A good basis for an effective criticism of the equilibrium concept in economics, would be Godel's incompleteness theorem. The reason for this is that it is necessary to confront theorems of economics within the framework of mathematical logic in which they are embedded. The first aim of this study is to demonstrate that economic reality cannot be analysed in a meaningful way using conventional equilibrium-oriented models. Our study suggests that the knowledge generated from economic models is a product of epistemologically flawed knowledge-generation systems. This shows that economic theory of this kind in fact falls far short of its claim to universality. Our study covers alternative models, tries to generate a suggestion for a model that fits more to the social reality. For this aim the study will evolve as below:

Economic Theory, 1996

In the theory of economies with public goods one usually considers the case in which private goods are essential, i.e., each agent receives a fixed minimum level of utility if he consumes no private goods, irrespective of the public goods consumed. This paper develops the second welfare theorem for economies with public projects and possibly inessential private goods. As a corollary we also derive conditions under which valuation equilibria exist. JEL Classification Numbers: H41, D61. * We thank Doll Talman and an anonymous referee for many useful remarks and annotations of a previous draft of this paper.

Games and Economic Behavior, 1999

We focus on axiomatizations of the Pareto equilibrium concept in noncooperative multicriteria games based on consistency. Some axiomatizations of the Nash equilibrium concept have immediate generalizations. For strategic games it was shown that there exist no consistent refinements of the Nash equilibrium concept that satisfy individual rationality and nonemptiness on a reasonably large class of games. We show that such refinements of the Pareto equilibrium concept on multicriteria games do exist. Journal of Economic Literature Classification Number: C72. ᮊ