Edgeworth and Walras equilibria of an arbitrage-free exchange economy

In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of the paper, we give conditions under which Edgeworth allocations can be decentralized by continuous prices in a finite dimensional and in an infinite dimensional setting. We then show how these results apply to some finance models.Arbitrage-free asset markets; individually rational utility set; Edgeworth equilibria; fuzzy coalitions; fuzzy core; Walras equilibria; quasiequilibria; properness of preferences

Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy

No abstract.

Edgeworth and Lindahl-Foley equilibria of a general equilibrium model with private provision of pure public goods

In this paper, we propose a definition of Edgeworth equilibrium for a private ownership production economy with (possibly infinitely) many private goods and a finite number of pure public goods. We show that Edgeworth equilibria exist whatever be the dimension of the private goods space, and can be decentralized, in the finite and infinite dimensional cases, as Lindahl-Foley equilibria. Existence theorems for Lindahl-Foley equilibria are a by-product of our results.production economy; public goods; Edgworth equilibrium; Lindahl-Foley equilibrium; proper economy

Satiated economies with unbounded consumption sets : fuzzy core and equilibrium

For an exchange economy, under assumptions which did not bring about the existence of quasiequilibrium with dividends as yet, we prove the nonemptiness of the fuzzy rejective core. Then, via Konovalov (1998, 2005)'s equivalence result, we solve the equilibrium (with dividends) existence problem. In a last section, we show the existence of a Walrasian quasiequilibrium under a weak non-satiation condition which differs from the weak non-satiation assumption introduced by Allouch-Le Van (2009). This result, designed for exchange economies whose consumers' utility functions are not assumed to be upper semicontinuous, complements the one obtained by Martins-da-Rocha and Monteiro (2009).Exchange economy, satiation, equilibrium with dividends, rejective core, fuzzy rejective core, core equivalence.

On the Non-emptiness of the Fuzzy Core

The seminal contribution of Debreu-Scarf (1963) connects the two concepts of core and competitive equilibrium in exchange economies. In effect, their core-equilibrium equivalence result states that, when the set of economic agents is replicated, the set of core allocations of the replica economy shrinks to the set of competitive allocations. Florenzano (1989) defines the fuzzy core as the set of allocations which cannot be blocked by any coalition with an arbitrary rate of participation and then shows the asymptotic limit of cores of replica economics coincides with the fuzzy core. In this note, we provide an elementary proof of the non-emptiness of the fuzzy core for an exchange economy. Unlike the classical Debreu-Scarf limit theorem and its numerous extensions our result does not require any asymptotic intersection -or limit- of the set of core allocations of replica economies.Fuzzy core, Payoff-dependent balancedness, Exchange economies