Continua of Hahn-unsatisfactory equilibria: Some examples

Quantity-constrained fix-price equilibria may occur even at Walrasian equilibrium prices. Structurally stable examples are given to support the claim that there may be a continuum of such equilibria, even in a neighborhood of the Walrasian one.     

On persistent disequilibrium

Consider a standard model of a Walrasian economy where the time derivative of price change is a sign preserving function of excess demand. The only steady states of such a system are the Walrasian equilibria. For if the system is not at a Walrasian equilibrium then there must be excess demands or supplies in some market and thus those prices must be changing. Walras' law implies that all prices cannot change in the same direction, and thus relative prices must change.However, it seems that in real world economies there have been states of persistent disequilibrium. How can this be? How can there be stationary states of an economy that are not Walrasian equilibria?The answer presented in this paper goes something like this: the demands actually presented to the market, i.e., the demands that affect price movements, are not the Walrasian demands. Rather, these demands, the effective demands, are a function of both price and quantity signals. There is no reason why there cannot be equilibria of the effective demand system that are not equilibria of the Walrasian demand system.In this paper, I present a simple abstract model of effective demand systems and given a condition for this system to have non-Walrasian equilibria. I also present a simple example of this phenomena. Finally I discuss the real world implications of this model. Related concepts of effective demand are discussed in [A1H], [2], [3], [L5], and [L6].     

Walrasian General Equilibrium Allocations and Dynamics in Two-Sector Growth Models

This paper analyzes and solves miniature Walrasian general equilibrium systems of momentary and moving equilibria. The Walrasian framework encompasses the fundamental neoclassical and classical two‐sector growth models; the families of solutions of steady‐state and persistent growth per capita in various competitive two‐sector economies are parametrically characterized. Moreover, the endogenous behavior of relative prices and the sectoral allocation of primary factors are analyzed in detail. The technology parameters of the capital good industry are decisive for obtaining long‐run per capita growth in closed (global) economies. A review of the literature complements the theorems on the general equilibrium allocations, dynamic systems, and the time paths of Walrasian two‐sector economies.     

The Second Welfare Theorem in Economies with Non‐Walrasian Markets

The standard version of the second welfare theorem assumes that market operations produce Walrasian outcomes. Therefore, if there are individuals who can manipulate prices, the conclusion of the second welfare theorem is questionable. In this paper, we address the decentralization of a Pareto‐optimal allocation, when markets are non‐Walrasian. Our objective in this paper is to develop a game which can implement Pareto‐optimal allocations as Nash equilibria of strategic exchange in markets. In this way, we develop a version of the second welfare theorem for economies where markets are strategic.     

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.     

Non-marketed options, non-existence of equilibria, and non-linear prices

This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional.The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colell's assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails.Our example has important finite- as well as infinite-dimensional implications. It is also an example of a “well behaved” economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis-Tourky-Yannelis (2001).     

The workings of a commodity money system in an incomplete information macro model

This paper compares the properties of a token money system with that of a commodity money system in an uncertain environment. In an incomplete information world, relative prices are not known with certainty. However, a commodity money system provides some information because the nominal price of the monetary commodity is known. The benefits of this information-enhancing function may be offset, though by distortions in relative prices relative to their full information Walrasian equilibrium values. Because the two systems have vastly different structural parameters, we cannot unambiguously state which system is welfare superior.     

Walrasian bargaining

Given any two-person economy, consider an alternating-offer bargaining game with complete information where the proposers offer prices, and the responders either choose the amount of trade at the offered prices or reject the offer. We provide conditions under which the outcomes of all subgame-perfect equilibria converge to the Walrasian equilibrium (the price and the allocation) as the discount rates approach 1. Therefore, price-taking behavior can be achieved with only two agents.     

Equilibrium prices in a random exchange economy with dependent agents

Summary. This paper presents a model of a Walrasian exchange economy in which the preferences and endowments of the agents are random. Stochastic interaction among the agents is formally described in terms of dependency neighborhoods. The main result is a characterization of the distribution of market-clearing prices in a large economy. Received: April 23, 1999; revised version: May 6, 1999     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

Expectations Heterogeneity and Excessive Price Sensitivity in the Land Market

This paper analyses price behaviour in the land market in which the Walrasian auctioneer is absent. Sellers are informed about the land value and post their asking prices; buyers are uninformed, have different opinions, and decide whether or not to accept the sellers' offers. In this market, sellers are "price-makers" with probabilisitic market power : they can influence the sale probability through their asking price. Price may be excessively sensitive to unexpected changes in market conditions. Moreover, buyer heterogeneity may accentuate the excessive price sensitivity. It has been shown that, the more heterogeneous their opinions, the more sensitive are prices.
JEL Classification Numbers: D40, D43, D82, D84, E44, G12.     

Nash implementation in production economies

Summary This paper provides a general way to incorporate private ownership production economies into the implementation of the Walrasian correspondence. We present two mechanisms, both of which permit agents to behave strategically with respect to their initial endowments, preferences, and production possibility sets. The first mechanism deals with the case of endowment destruction, the second deals with the case of endowment withholding. We show that each mechanism Nash implements the Walrasian correspondence. In addition, both mechanisms are individually feasible, balanced, continuous and only require the transmission of prices and quantities of goods as messages.This paper is based on Chapters 2 and 3 of my dissertation submitted to the University of Minnesota. I want to thank E. Green, J. Jordan, M. Richter, H. Weinberger and especially L. Hurwicz for their many helpful suggestions and comments.     

A market game approach to differential information economies

In this paper we recast a differential information economy as a strategic game in which players propose net trades and prices. Pure strategy Nash equilibria are strong and determine both consumption plans and commodity prices that coincide with the Walrasian Expectations equilibria of the underlying economy. The authors acknowledge support by research grants BEC2003-09067-C04-01 (Ministerio de Educación y Ciencia and FEDER), PGIDT04XIC30001PN (Xunta de Galicia) and SA070A05 (Junta de Castilla y León). JP Torres-Martínez is also grateful to CNPq-Brazil and University of Vigo for financial support. We are indebted to N.C. Yannelis for helpful comments and insights.     

Evolution of Walrasian equilibrium in an exchange economy

We study the stochastic stability of a dynamic trading process in an exchange economy. We use a simplified version of a trading model à la Shapley and Shubik (J Polit Econ 85:937–968, 1977). Two types of agents equipped with Leontief preferences trade goods in markets by offering endowments, and actual trades occur at market clearing prices. Better behavior tends to spread through the same type of agents by imitation, and agents also make mistakes occasionally. We provide a sufficient condition for the perturbed dynamic process to have a unique stochastically stable state that is a Walrasian equilibrium allocation. In this sense, we give a rationale for Walrasian behavior.     

Anticipatory pricing with negligible uncertainty

If firms precommit to output, and price equates either expected excess demand or excess demand when demand takes its expected value to zero, then equilibrium price and output typically do not converge to their Walrasian levels as demand becomes decreasingly risky.     

Walrasian prices in markets with tradable rights

In this paper, we consider an exchange economy where there is an external restriction for the consumption of goods. This restriction is defined by both, a cap on consumption of certain commodities and the requirement of an amount of rights for the consumption of these commodities. The caps for consumption are imposed exogenously due to the negative effects that the consumption may produce. The consumption rights or licenses are distributed among the agents. This fact leads to the possibility of establishing license markets. These licenses do not participate in agents’ preferences, however, the individual’s budgetary constraint may be modified, leading to a reassignment of resources. Our aim is to show the existence of a Walrasian equilibrium price system linking tradable rights prices with commodity prices.     

Equilibrium without prices: A central issue in pareto’smanuale

Pareto in hisManuale asserts that the price concept is inessential for the notion of equilibrium. This view deeply contrasts with the Arrow-Debreu’s dominant approach of Walrasian derivation. This identifies general equilibrium with a system of prices at which the decentralized choices of economic agents match. In this paper the author justifies and gives substance to the Paretian point of view. The differential merit of the Paretian approach is its independence of assumptions of price taking and of convexity in preferences and in production possibility sets. These assumptions are necessary, in the walrasian framework, only to maintain the centrality of prices, but they clash against the request of realism. (JEL:BOO, D51, D60)     

Middle Men: The Visible Market‐Makers

This paper presents a framework in which middlemen emerge to intermediate between ex‐ante homogeneous buyers and sellers in the presence of search frictions. Middlemen announce prices, and hold an inventory to provide more sure services. Middlemen can mitigate trade imbalances with price competition. Using this framework I illustrate how the frictionless limit can emerge and how middlemen can implement the short‐side principle for the market price to be Walrasian. The recent progress in the literature on intermediation will also be discussed.     

Equilibrium and optimality: Some imprints of David Gale

The paper is a review of some of the themes to which David Gale made lasting contributions. It touches upon a number of the fundamental issues in the Walrasian equilibrium theory (existence, uniqueness and stability), the overlapping generations model (non-optimality and indeterminacy of competitive equilibria), the von Neumann equilibrium (as a turnpike), and in the theory of decentralized intertemporal allocation through competitive prices (efficiency and golden rules, duality and existence of optimal programs).     

A simple auctioneerless mechanism with Walrasian properties

A simple mechanism for reallocating holdings is described, in which no auctioneer is required: outcomes are determined solely from traders' actions and without any requirement that the mechanism be in equilibrium. The mechanism is shown to exactly duplicate the performance of the Walrasian auctioneer (both in its equilibria and in its disequilibrium path) if individuals are price takers, and, if the number of individuals is large, to approximately duplicate the auctioneer's performance even when individuals behave strategically, each taking account of his own influence on prices.