A Core-equilibrium Convergence in an Economy with Public Goods

This paper deals with a core-equilibrium equivalence in an economy with public goods where preferences of consumers display warm glow effects. We demonstrate that provided that each consumer becomes satiated to other consumers provision, it holds that, for a sufficiently large economy, the set of Edgeworth allocations is non-empty. Moreover, we show that an Edgeworth allocation could be decentralized as a warm glow equilibrium.Competitive equilibrium, Warm glow, Public goods, Edgeworth, Core, Decentralization

Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy

No abstract.

A Competitive Equilibrium for a Warm Glow Economy

Despite a widespread interest in the warm glow model [Andreoni (1989,1990)], surprisingly most attention focused on the voluntary contribution equilibrium of the model, and only very little attention has been devoted to the competitive equilibrium. In this paper, we introduce the notion of competitive equilibrium for a warm glow economy [Henceforth, warm glow equilibrium]. Then, we establish (and prove), in the contest of our model, the three fundamental theorems of general equilibrium: (i) warm glow equilibrium exists; (ii) a warm glow equilibrium is Pareto efficient; and (iii) a Pareto efficient allocation can be decentralized as a warm glow equilibrium). The concept of a warm glow equilibrium may prove to be very useful to the normative and positive theory of public goods provision. First, it is a price based mechanism achieving efficient outcomes. Secondly, not only the warm glow equilibrium outcomes could serve as a point of reference to measure free-riding and welfare loss, but also due to warm glow effects, unlike Lindahl allocations, they are more likely to be achieved.Warm glow, Altruism, Competitive equilibrium, Free riding, Public goods provision

A note on two notions of arbitrage

Since Hart's [5] and Werner's [10] seminal papers, several conditions have been proposed to show the existence of equilibrium in an asset exchange economy with short-selling. In this note, we discuss the relationship between two no-arbitrage conditions. The first condition is the assumption that the individually rational utility set U is compact, as considered by Dana, Le Van and Magnien [1]. The second is inconsequential arbitrage, introduced by Page, Wooders and Monteiro [9]. The main result of this comparison is to show that the inconsequential arbitrage condition is stronger than the assumption that U is compactAsset Market ; Short Selling ; Arbitrage

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

COMPETITIVE PRICING IN SOCIALLY NETWORKED ECONOMIES

In the context of a socially networked economy, this paper demonstrates an Edgeworth equivalence between the set of competitive allocations and the core. Each participant in the economy may have multiple links with other participants and the equilibrium network may be as large as the entire set of participants. A clique is a group of people who are all connected with each other. Large cliques, possibly as large as the entire population, are permitted ; this is important since we wish to include in our analysis large, world-wide organizations such as workers in multi-national firms and members of world-wide environmental organizations, for example, as well as small cliques, such as two person partnerships. A special case of our model is equivalent to a club economy where clubs may be large and individuals may belong to multiple clubs. The features of our model that cliques within a networked economy may be as large as the entire population and individuals may belong to multiple cliques thus allow us to extend the extant decentralisation literature on competitive pricing in economies with clubs and multiple memberships (where club sizes are uniformly bounded, independent of the size of the economy).social networks ; competitive pricing ; cliques ; clubs ; Edgeworth equivalence ; core

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.

Price Taking Equilibrium in Club Economies with Multiple Memberships and Unbounded Club Sizes

This paper develops a model of an economy with clubs where individuals may belong to multiple clubs and where there may be ever increasing returns to club size. Clubs may be large, as large as the total agent set. The main condition required is that sufficient wealth can compensate for memberships in larger and larger clubs. Notions of price taking equilibrium and the core, both with communication costs, are introduced. These notions require that there is a small cost, called a communication cost, of deviating from a given outcome. With some additional standard sorts of assumptions on preferences, we demonstrate that, given communication costs parameterized by ε > 0, for all sufficiently large economies, the core is non-empty and contains states of the economy that are in the core of the replicated economy for all replications (Edgeworth states of the economy). Moreover, for any given economy, every state of the economy that is in the core for all replications of that economy can be supported as a price-taking equilibrium with communication costs. Together these two results imply that, given the communication costs, for all sufficiently large economies there exists Edgeworth states of the economy and every Edgeworth state can be supported as a price-taking equilibrium.Competitive pricing, Clubs, Local public goods, Hedonic coalitions, Edgeworth, Tiebout hypothesis, Core

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