Existence Of Competitive Equilibrium Research Articles

Existence of equilibria with infinitely many consumers and infinitely many commodities: A theorem based on models of commodity differentiation

This paper presents a general result on the existence of competitive equilibria in exchange economies in which consumers and commodities are both infinite in number. The result shows that — in this framework at least — the added assumptions necessary to handle models with infinitely many agents are remarkably similar to the additional restrictions needed when only finitely many commodities are available for trade. It is shown that the results apply, in a straightforward manner, to two of the common models of consumer choice when commodity differentiation is an important consideration.

Equilibria in markets with a Riesz space of commodities

We present a new proof of the existence of competitive equilibrium for an economy with an infinite dimensional space of commodities.

On the Nonexistence of Market Equilibria in Exhaustible Resource Markets with Decreasing Costs

This paper examines the existence of competitive equilibria in markets for exhaustible resources where there are initial economies of scale in either the extraction of the resource or the utilization of the resource as an input in production. In such instances, which are fairly common, we find that the classic Hotelling rule for competitive extraction does not apply, since competitive price equilibria generally do not exist. This is in marked contrast to static markets where the usual textbook example of firms with U-shaped average cost curves is not inconsistent with the existence of competitive equilibria. Furthermore, oligopolistic market equilibria in which resource firms act as Nash producers may also fail to exist when there are returns to scale in production.

Competitive Equilibria in Markets for Heterogeneous Goods under Imperfect Information: A Theoretical Analysis with Policy Implications

This article characterizes necessary and sufficient conditions for heterogeneous search goods to trade at their competitive prices, and derives policy implications from these conditions. The model differs from earlier search equilibrium models in that it allows the existence of product heterogeneity. Our principal conclusions are that markets for heterogeneous search goods tend rather easily to segment into homogeneous subsets; when they do not, heterogeneity can work against the existence of competitive equilibria because it dilutes the effectiveness of search. Nevertheless, the likelihood of competitive equilibria obtaining in heterogeneous search goods markets can often be increased by

Market power and efficiency

We investigate how price ceilings and floors affect outcomes in continuous time, double auction markets with discrete goods and multiple qualities. When price controls exist, the existence of competitive equilibria is no longer guaranteed; hence, we investigate the nature of non-price competition and how markets might evolve in its presence. We develop a quality competition model based on matching theory. Equilibria of the quality competition model always exist in such price-constrained markets; moreover, they naturally correspond to competitive equilibria when competitive equilibria exist. Additionally, we characterize the set of equilibria of the quality competition model in the presence of price restrictions. In a series of experiments, we find that market outcomes closely conform to the predictions of the model. In particular, price controls induce non-price competition between agents both in theory and in the experimental environment; market behaviors result in allocations close to the predictions of the model.

The Classical Theorem on Existence of Competitive Equilibrium

The Classical Theorem on Existence of Competitive Equilibrium

Diversified Consumption Characteristics and Conditionally Dispersed Endowment Distribution: Regularizing Effect and Existence of Equilibria

The paper introduces the concept of a conditionally endowment distribution (given the consumption set) in the study of regularizing effect of aggregation and existence of equilibria in an exchange economy with an atomless measure space of consumers. It is shown that there is a regularizing effect of aggregation whenever the endowment distribution of an economy is conditionally dispersed. On the basis of this regularizing effect, the existence of a competitive equilibrium is proved in a very general setting where some of the commodities are indivisible and where different consumers may have different consumption sets. GENERAL EQUILIBRIUM THEORY saw, in recent years, explicit formulation of models with indivisible commodities in which existence of competitive equilibria was discussed. (References are Henry [12], E. Dierker [10], Broome [7], and Mas-Colell [19].) A pathbreaking paper by Mas-Colell [19] clearly reconfirmed the power of a continuum of traders model introduced by Aumann [1], and it emphasized, for the first time in the literature of the equilibrium existence problem, the importance of a condition relating to the form of distribution of agents' characteristics. More specifically, a competitive equilibrium was shown to exist in an economy with indivisible commodities where a single perfectly divisible commodity exists and the distribution of its initial holdings among agents is dispersed in the sense that it is absolutely continuous with respect to the Lebesgue measure. (See [19, Theorem 1, p. 446].) This development in the existence literature is of much interest to equilibrium theory and coincides with the way in which the analysis of a certain aggregation problem is being pursued in equilibrium theory. (See, e.g., Sonderman [33], Mas-Colell [20], and Hildenbrand [18].) In both of these problems, elaboration of the concept of dispersedness in the distribution of agents' characteristics is required.3 The work of Mas-Colell [19] was followed by [35] in which the concept of a endowment distribution was introduced in the study of existence of equilibria in an exchange economy with an atomless measure space of consumers where no convexity assumptions on preferences and consumption sets were

A Proof of the Existence of Competitive Equilibrium in a Generation- Overlapping Exchange Economy with Money

In this paper, we shall prove the existence of a competitive equilibrium in a generalized Arrow-Debreu economy. Instead of the original Arrow-Debreu formulation, we shall assume that the number of economic agents and the number of (dated) commodities are countably infinite. Our model, therefore, is similar to the Samuelson's consumption loan model [1958]. In fact, we shall inherit Samuelson's generational strtucture and the possibility of the existence of money in our model. In an infinite horizon economy, a durable commodity without intrinsic utility may have a positive exchange value, since it may be held as a store of value. Following Samuelson, we shall call this good money; however, in our economy the amount of money in each period will not be treated as an exogenously determined variable. In particular, as a special case, we consider an economy with a government which, at any time, can increase the amount of money in the form of monetary transfer to the living consumers. We consider the following model. In each period, a finite number of consumers are born. All the consumers (except those who exist in period 1) live the same, but finite, number of periods.' The number of consumption goods is (finite and) constant over the time and these goods are completely perishable. There is only one durable good which we call money. Money does not have any intrinsic value at all but it is completely durable. The amount of money stock may not be constant over time, since we allow the government to subsidize consumers in the form of monetary transfers. We assume that all transactions are costless (including those in future markets). Therefore each consumer faces only one life-time budget constraint instead of a sequence of budget constraints.2 We shall give a proof of the existence of a competitive equilibrium in such an economy. The equilibrium we show to exist may be either one of the following two categories: A monetary equilibrium,

The overlapping-generations model. III. The case of log-linear utility functions

Existence of competitive equilibria in the overlapping-generations model has been studied in some detail; see [4-6,9]. We need to know more about the properties of these equilibria. How many are there? How do they depend on the basic parameters of the economy? We also need to compare the set of monetary competitive equilibria with the set of nonmonetary competitive equilibria. Are there “vastly more” monetary equilibria than nonmonetary equilibria? Analysis of the properties of competitive equilibria is for the overlappinggenerations model an important, but difficult, task. In his seminal article [8], Samuelson put it this way: “... if we take any finite stretch of time and write out the equilibrium conditions, we always find them containing discount rates from before the finite period and discount rates from afterward. We never seem to get enough equations; lengthening our time periods turns out always to add as many new unknowns as it supplies equations . ..” Samuelson suggested that, rather than facing this difficulty directly, “We can try to cut the Gordian knot by our special assumption of stationariness . ..”

Existence of competitive equilibrium in a general overlapping-generations model

In the companion paper [2], Balasko and Shell establish existence of competitive equilibrium for a pure-distribution, overlapping-generations economy without money (see, especially, Propositions (3.10) and (3.11) in Section 3). That argument is remarkably simple, but depends critically on some strong hypotheses concerning individual tastes and endowments. In particular, it is assumed that, in any given period, every living consumer has a utility function which is strictly increasing in every available commodity, as well as an endowment which is strictly positive in every available commodity. These two assumptions are especially difficult to rationalize in an intergenerational context. How many teen-agers do you know who are eager viewers of Lawrence Welk? How many “middle-agers” who are likely users of Clearasil? So much for increasing (much less strictly increasing) utility functions! Regarding strictly positive endowments, we invite the reader to dream up his/her own counterexamples. (Another hint: How do you respond to the commonly heard lament, “What I wouldn’t give to be young again!“?) In the present paper, we do away with such unrealistically severe hypotheses. And we do more. Following the Arrow-Debreu tradition, we postulate fairly mild conditions on individual tastes and endowments. Of course, in line with the same tradition, we must then impose some further conditions on the potential economic interrelationships among consumers. This additional structure is an application to the overlapping-generations model of McKenzie’s basic concept of irreducibility.

Indivisible commodities and general equilibrium theory

We identify sufficient conditions for existence of competitive equilibrium with network externalities and indivisibilities. Such combination of externalities and indivisibilities is present in many goods and services with network effects, and it makes existence of equilibrium non-trivial. We provide an existence theorem in a model with a measure space of consumers. Key conditions for existence are anonymity of network effects and dispersion in the economy’s income distribution.

Introduction to Equilibrium Analysis.

Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.

Introduction to Equilibrium Analysis.

Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.

Preferences which have open graphs

Gale and Mas-Collel and Shafer and Sonnenschein introduced powerful new theorems on the existence of competitive equilibrium which used the assumption that the graph of the strict preference relation P is an open set. We show when this condition is satisfied and when it is not.

How to discard ‘free disposability’ - at no cost

This paper shows how to prove the existence of competitive equilibrium without assuming either monotonic preferences or free disposability--and without adding any new assumptions.

Transaction Costs in General Equilibrium Theory-A Survey

It has long been realized that exchange of commodities is a costly activity, and that recognition of such costs will play an important part in explaining certain economic phenomena. Let us consider three examples. The first arises in The Wealth of Nations where Smith argues that division of labour (the economies of scale to be reaped through specialization) is limited by the extent of market, which can in turn be determined by such factors as transportation costs. Thus examination of certain costs of transaction would be part of any explanation of degree of specialization exhibited by an economy. In particular, argument suggests that we ought to be able to use transactions costs to explain existence of competitive equilibrium in presence of certain forms of increasing returns, a task that modern general equilibrium theory cannot claim to have tackled with great success. Our second example can also be found in The Wealth of Nations, where Smith notes that other forms of tralnsaction costs, for example cost of searching for a trading partner, can be reduced by use of a generally acceptable medium of exchange. That some such property provides a door through which can enter economy has been a constant theme in money literature. However, both Clower (1967) and Hahn (1965) have recently argued that only by explicit analysis of transactions costs can we build a monetary theory that is satisfactorily

Some theorems on the existence of competitive equilibrium

The purpose of this paper is to point out a relationship between theorems on the existence of competitive equilibrium in economies with externalities, and recent results (pioneered by A. Mas-Colell) on the existence of equilibrium for economies in which consumer preferences are neither complete nor transitive. This observation leads both to a substantial strengthening of the theorem on the existence of equilibrium with externalities, and at the same time to a revealing perspective on the Mas-Colell theorem.

Competitive equilibria with infinitely many commodities (II)

In this paper we state and prove five theorems concerning the existence of competitive equilibria in production economies with finitely many “agents” and infinitely many commodities. The first theorem is an extension of a theorem of K. Arrow and G. Debreu ([l], Theorem I, p. 272). The second and third are extensions of a theorem of T. Bewley (cf. [2], Theorem 1 and 3, pp. 13 and 19). The last two are extensions of theorems of G. Debreu (cf. [3], Theorems 6.3, 6.4, pp. 94-95). Similar theorems for exchange economies were established in [7]. The need to prove theorems such as Theorems l-5 below arise in the study of resource allocation in economies which operate over infinitely many periods and in economies which operate over finitely many periods in an uncertain world in which one of a denumerable infinity of states of nature might occur. To simlify our notation we will argue as if the economies we consider are faced with the problem of allocating resources over infinitely many periods in a world of perfect certainty with respect to the state of nature. To state our results we must first introduce a lot of symbols. Let R” be the set of all n-dimensional real vectors: let

Satisficing, Selection, and The Innovating Remnant

I. Introduction: Managerialism, behavioralism, and the competitive model, 237. — II. Firm decision processes and the as if argument, 240. — III. Selection, decision rules, and competitive outcomes, 244. — IV. A competitive industry: Orthodox analysis, 248. — V. A competitive industry: Assumptions of the selection model, 249. — VI. Proof of the theorem, 254. — VII. Extensions and generalizations, 257. — VIII. Schumpeterian competition, 259. — IX. Concluding comments, 260. — Appendix: Proof of the existence of competitive equilibrium, 261.

Markets with Countably Many Commodities

Abstract : In this paper, we prove the existence of competitive equilibrium in a market with countably many commodities. By the term 'market' we mean to emphasize that we are dealing with a pure trade model, in which there is no production. Our result generalizes the existing theory of competitive equilibrium in a finite-dimensional commodity space. The significance of this generalization, we feel, is that it opens a door that could lead, eventually, to a theory of decentralized economic growth. (Author)