Aggregate Excess Demand Research Articles

Local disaggregation of negative demand and excess demand functions

The literature on the characterization of aggregate excess and market demand has generated three types of results: global, local, or ‘at a point’. In this note, we study the relationship between the last two approaches. We prove that within the class of functions satisfying standard conditions and whose Jacobian matrix is negative semi-definite, only n / 2 + 1 agents are needed for the ‘at’ decomposition. We ask whether, within the same class, the ‘around’ decomposition also requires only n / 2 + 1 agents.

The Sonnenschein-Mantel-Debreu Results after Thirty Years

The properties of aggregate excess demand or market demand play a key role in the existence, uniqueness, stability, and comparative statics of competitive general equilibrium. They are also important for the theory of imperfectly competitive general equilibrium and the microfoundations of macroeconomics. Because observations of demand are likely to occur at the aggregate level, whereas economic theory has been largely concerned with individual behavior, the properties of aggregate excess or market demand are central to econometric identification. The importance of these projects for the development of general equilibrium theory can be seen in Kenneth Arrow and Frank Hahn’s General Competitive Analysis (1971). Soon after their book was published, though, Hugo Sonnenschein (1973) posed the following problem. Consider a function that maps prices into quantities. What conditions must this function satisfy if it is to be the aggregate excess demand function of a well-behaved exchange economy? The existence theory highlighted the importance of the function’s satisfying continuity, homogeneity of degree zero, and Walras’s law. Were these all of the restrictions on aggregate excess demand implied by the usual

Disequilibrium Dynamics and Aggregate Excess Demand: On a Homunculus Fallacy in Economic Theory

Modern economic theory is predominantly a theory of equilibrium. The question of how such positions of rest, in which all individual plans and expectations match, come about in larger economies is rarely addressed. The discipline has little more to offer on it than the metaphor of the “invisible hand,” the imposed “law of supply and demand,” which says that the prices of goods and services rise when their demand exceeds their supply and fall otherwise until they are equal, or at best formalizations of such price adjustments, carried out by an auctioneer-like central institution with information on aggregate excess demand. The auctioneer model is hardly convincing as an explanation of the majority of market processes in which no such central coordinator is present. By appealing to an outside entity, an “auctioneer,” with no objectives of its own, existing disequilibrium theory is furthermore at odds with the microfoundations of economics. It presupposes a level of coordination, whereas economics’ original research question is whether and how order arises in an unorchestrated society of people making their own individual plans. Moreover, despite this considerable amount of structure, the approach was able to

A note on continuously decomposed evolving exchange economies

It is routine to demonstrate in the exchange economy framework that small changes of individual preferences and endowments always result in small changes of the derived excess demand functions as one should expect. Though being as desirable for reasons of the consistency of the whole approach, however, a precise proof of the converse direction so far is still open to question. The present paper shows that it is actually true. We use a decomposition method for aggregate excess demand functions developed by Mas-Colell which is derived from the well-known decomposition method developed by Sonnenschein and perfected by Debreu and Mantel. Our result fills in a notorious gap in the line of economic justification usually given for this decomposition, or disaggregation, method in that comparative static analysis would be restricted if the decomposition of excess demand functions would not be continuous.

Utility driven dynamic resource allocation using competitive markets in computational grid

This paper presents a utility-based market mechanism for dynamic resource allocation in computational grid. The proposed competitive market economy is described. It consists of three different types of agents: grid request agent, grid resource agents, grid task agents; and a grid market that regulates the prices based on the observed aggregate excess demand. In order to solve the problem of heterogeneous demand in the grid, grid users' preferences are summarized by means of their utility functions. We consider budget and complete times as constraints of optimization problem. The objective of the optimization problem is to determine the amount of resources under different constraints to maximize the users' utilities. This paper proves the existence of a solution of the optimization problem, it also specify an iterative algorithm that is used by the grid market to update the prices, and it leads to an allocation that is close to a solution of the optimization problem in a finite number of iterations. The experiments are made to study characteristics of the utility directed allocation algorithm under budget constraint and under completed time constraint in terms of completion time and resource allocation efficiency.

An Analysis of General Equilibrium with Positive Transaction Costs and Non-Convex Preference

After taking into account positive transaction costs via tackling static nonlinear programming with dynamic programming, this paper reaches three main conclusions: 1) The aggregate excess demand function of each market will be discontinuous at many price points, but the transfiguration of the graph of aggregate excess demand of each commodity will be continuous with respect to prices of other commodities, and at those price points incurring discontinuity, the corresponding traders' utility or profit will be indifferent between different choices. 2) Via a new approach able to tackle the discontinuous aggregate excess demand, it is proved that, there must exist a market equilibrium price vector in a perfectly competitive economy with positive transaction costs even if each consumer's preference isn't convex. 3) Transaction cost probably spoils the satisfaction of those two fundamental theorems of welfare economics, as well as it ruins the social aggregate welfare through three approaches.

Individual excess demands

We characterize the excess demand function in the one-consumer model. We describe the relation between the direct and indirect utility functions. As an application of our result, we derive a short proof of the celebrated Sonnenschein–Mantel–Debreu theorem on the decomposition of aggregate excess demand.

Excess demand functions with incomplete markets—a global result

The purpose of this paper is to give a global characterization of excess demand functions in a two-period exchange economy with incomplete real asset markets. We show that continuity, homogeneity and Walras’ law characterize the aggregate excess demand functions on any compact price set which maintains the dimension of the budget set.

A Market-Based Approach to Optimal Resource Allocation in Integrated-Services Connection-Oriented Networks

We present an approach to the admission control and resource allocation problem in connection-oriented networks that offer multiple services to users. users' preferences are summarized by means of their utility functions, and each user is allowed to request more than one type of service. Multiple types of resources are allocated at each link along the path of a connection. We assume that the relation between Quality of Service (QoS) and resource allocation is given, and we incorporate it as a constraint into a static optimization problem. The objective of the optimization problem is to determine the amount of and required resources for each type of service to maximize the sum of the users' utilities. We prove the existence of a solution of the optimization problem and describe a competitive market economy that implements the solution and satisfies the informational constraints imposed by the nature of the decentralized resource allocation problem. The economy consists of four different types of agents: resource providers, service providers, users, and an auctioneer that regulates the prices based on the observed aggregate excess demand. The goods that are sold are: (i) the resources at each link of the network, and (ii) services constructed from these resources and then delivered to users. We specify an iterative procedure that is used by the auctioneer to update the prices, and we show that it leads to an allocation that is arbitrarily close to a solution of the optimization problem in a finite number of iterations.

Characterizations of pseudomonotone maps and economic equilibrium

The paper surveys some recent contributions to the analysis of pseudomonotone maps and their application to economics. It is shown that the concept of pseudomonotonicity is strongly related to a notion of rationality of consumer behaviour which is well known in economics as a weak version of the Weak Axiom of Revealed Preference. In economic models of general equilibrium, a pseudomonotone aggregate excess demand function is seen to guarantee convexity of the set of price equilibria and, in the case of so-called regular economies, even the uniqueness of equilibrium. Some general characterizations of differentiable pseudomonotone maps, which reduce to necessary and sufficient first order conditions under the assumption of regularity, are provided. These conditions are employed in order to prove pseudomonotonicity of aggregate excess demand in economies displaying a particular kind of heterogeneous consumer behaviour.

Excess Demand Functions with Incomplete Markets - A Global Result

The purpose of this paper is to give a global characterization of excess demand functions in a two period exchange economy with in-complete real asset markets. We show that continuity, homogeneity and Walras' law characterize the aggregate excess demand functions on any compact price set which maintains the dimension of the budget set.

A Cointegration Analysis of Broad Money Demand in Cameroon

This paper applies cointegration analysis and error-correction modeling to investigate the behavior of broad money demand in Cameroon over 1963/64-1993/94. The cointegrated VAR analysis first describes an open-economy model of money, prices, income, and a vector of rates of return, within which three steady state relations are identified: a stable money demand function, an excess aggregate demand relationship, and the uncovered interest rate relation under fixed exchange rates and perfect capital mobility. Empirical support is thereafter provided for both PPP and the international Fisher parity between Cameroon and France, and the stability of the short-run dynamics of the broad money demand function is confirmed.

Global convergence of the stochastic tâtonnement process

The paper introduces stochastic elements into the Walrasian tâtonnement process, both to make it more realistic and to ensure its global convergence, with probability 1. It is assumed that the aggregate excess demand satisfies standard assumptions but is subject to measurement error. We distinguish two cases. First, the true aggregate excess demand is assumed to satisfy the Weak Axiom of Revealed Preference. This condition will be met if the underlying economy has a single consumer, several consumers with identical homothetic utility functions, or if it maximizes a social welfare function. We prove that after two minor modifications, under a fairly general specification of the measurement error and by imposing a certain consistency property on the estimator of excess demand, the tâtonnement process converges with probability 1 to an equilibrium. Second, we consider the case that the Weak Axiom only holds around some of the equilibria. The procedure proposed imposes a random shock at time intervals of increasing duration. We also discuss how the procedure could be extended to determine all equilibria, to deal with jumps in excess demand including those that do not satisfy the Weak Axiom, and to represent agents who only gradually learn how to find an optimum.

A note on the decomposition (at a point) of aggregate excess demand on the Grassmannian

This paper analyzes the properties of aggregate excess demand functions for economies with an arbitrary finite set of N commodities where agents face trading restrictions of a general, abstract form: their budget set is defined by K-dimensional planes in R N . It is shown that, if there are at least K agents in the economy, the only general property satisfied by the value of aggregate excess demand and its derivative, at any arbitrary point, is Walras Law. The result is established by considering an economy where agents' preferences are of a `generalized Leontief' type.

Disaggregation of excess demand functions in incomplete markets

AbstractWe are interested in general equilibrium incomplete markets, where the number ofconsumers is N, the number of goods is L, and the dimension of the space of admissibletrades is K..the case of complete markets being then s Ly1 . We prove that, ifNGK, any non-vanishing analytic function satisfying the natural extension of the Walraslaw is, locally at least, the excess demand function of such a market. To be precise,consider a map u“Fu.associating with a T-dimensional parameteru a K-dimensionallinear subspace Fu.of R L , representing the set of market transactions allowed by u.Given parameter values u 1 , ...,u T , and a non-vanishing analytic function Z defined onsome neighbourhood of u with values in R L , with X. .ugFu; , then there existconcave utility functions U n ,1FnFN and individual endowments v 1 ,...,v N , such thatthe corresponding aggregate excess demand function coincides with Z on a possiblysmaller neighbourhood of. u.IfZ vanishes at u, the disaggregation is still possible, butrequires .Kq1 agents. q1999 Elsevier Science S.A. All rights reserved.

Characterizing C 2 aggregate excess demand functions

We integrate and sharpen two characterizations of aggregate excess demand functions: we obtain Mas-Colell's (1977) equilibrium invariance, and strengthen Geanakoplos' (1984) weakly concave utility functions to strictly concave ones. Our proofs modify and extend Geanakoplos' utility-construction. We note two applications: a sharper characterization of equilibrium price sets (cf. Mas-Colell (1977)), and a basis for the studies of computable economies (Richter and Wong (1996)).

Conditions for the Existence of Market Equilibrium

most remarkable achievements of modern microeconomic theory are the proof of the existence of an equilibrium and the First and Second Theorems of Welfare Economics. . . . Understandably, therefore, much attention has been devoted to various interpretations, alternative proofs, and extensions of these basic results (Luenberger 1994, 147). In an earlier article (Bryant 1994), I discussed a common misinterpretation of the second theorem of welfare economics. This article complements that one in that I discuss here a defect in the standard graduate textbook treatment of the existence problem for market equilibrium. In particular, I draw attention to assumptions that appear, one way or another, in all known existence theorems and that play a central role in those theorems by ensuring that an economy's aggregate excess demand function never behaves discontinuously. Although these assumptions are crucial in establishing the existence of market equilibrium and often turn out to be quite restrictive, their role is not generally discussed in the literature and is almost never acknowledged in the major graduate textbooks in microeconomics. As a consequence, graduate students are often given little insight into the potentially limited range of circumstances under which market equilibrium can be expected to exist. The impression (in some cases, the explicit instruction) may be that existence theorems for market equilibrium rest on quite general foundations when the opposite is arguably the case.

Computer Simulation for Supply-Demand Interaction

The most basic result in economics is that, for perfect competition, equilibrium price and quantity are determined by the intersection of aggregate demand and supply curves. How this equilibrium is achieved and the adjustment process have received less attention. The adjustment process may be based on aggregate demand and supply curves only, via the imaginary actions of an auctioneer or a tatonnement process or on modeling of price and excess aggregate demand interaction. Such models are less plausible because they assume agents have perfect information about a unique price at which all transactions are concluded. Alternative assumptions necessitate explicit modeling of individual agents and their search behaviour, which increases greatly the level of complication of the model. Though it is possible to deal with such models analytically (Stigler 1961, Rothschild 1973, Fisher 1973, McAfee and McMillan 1988), special assumptions are needed to obtain desired results. Lesourne (1992) studies many of these models mostly in a descriptive manner in the framework of self-organizing systems. Dynamic models which explicitly include multiple interacting agents contain many details that are difficult to handle without computers. Computer simulation makes it possible to include almost any assumption about individual agents and their interactions and to find out the consequences of these assumptions on the path toward equilibrium. One of the few examples of such simulation is the work by Albin and Foley (1992) which deals with geographically dispersed agents with costs of communication. Applications of computer simulation to other areas of economics can be found in Forrester (1961), Witt (1986) and Orcutt (1990). The current paper describes a computer simulation system that has been organized to enable simulation of interaction using a wide range of assumptions regarding agents, search, and samples, so that the consequences

Distribution of Income and Aggregation of Demand

We show that, under certain regularity conditions, if the distribution of income is price independent and satisfies a condition on the shape of its graph, then total market demand, F(p), is monotone; i.e., given two positive prices, p and q, one has (p−q) (F(p)−F(q)) < 0. These results allow for density functions increasing on some intervals, like unimodal distributions or even densities with more than one peak. Similar assumptions on the distribution of endowments, yield a restricted monotonicity property on aggregate excess demand, where, now, wealth is determined by market prices. This property guarantees uniqueness and stability of equilibrium of the Walrasian pure exchange economy.

An Elementary Approach to Approximate Equilibria with Infinitely Many Commodities

We prove the existence of approximate equilibria in a finite exchange economy with a countably infinite number of commodities and nonconvex preferences, when every trader has an excess demand set that is finitely spannable, i.e., that could be covered by a union of its convex subsets in finitely many steps. We show that the bound on the norm of the per capita aggregate excess demand is reciprocally related to the square root of the population. Extensions are also made to the case where countably many commodities are indivisible. The proofs are elementary. Journal of Economic Literature Classification Numbers: D50, C62, D52.