Excess Demand Functions Research Articles

AN INTERVIEW WITH HIROFUMI UZAWA

AN INTERVIEW WITH HIROFUMI UZAWA

Excess demand functions when new assets are introduced

We demonstrate that information on the aggregate excess demand function of an incomplete real asset market economy is not helpful toward predicting the equilibrium of a new economy to which unredundant assets are added. An innovation of assets can completely change the aggregate excess demand functions.

Trade and Child Labor: A General Equilibrium Analysis

This paper augments the existing literature on trade and child labor by exploring the effects of terms of trade changes in the context of a three good general equilibrium model, where one of the goods is a non-traded good. We find that under quasi-linear preferences the effect of the terms of trade on child labor depends critically on the pattern of substitutability (or complementarity) in the excess demand functions between the export good and the non-traded good. We extend the analysis to the case of homothetic preferences and find that the basic result is somewhat modified in a context where the marginal utility of income is affected by the terms of trade. We also extend the analysis to the case where factors move freely between the three goods as in a Heckscher-Ohlin type framework. Finally, we show that a balanced budget policy of taxing the education of skilled families and subsidizing the education of unskilled families must reduce child labor without any impact on aggregate welfare.

Quasivariational Inequalities for a Dynamic Competitive Economic Equilibrium Problem

The aim of this paper is to consider a dynamic competitive economic equilibrium problem in terms of maximization of utility functions and of excess demand functions. This equilibrium problem is studied by means of a time-dependent quasivariational inequality which is set in the Lebesgue space . This approach allows us to obtain an existence result of time-dependent equilibrium solutions.

Thom-Boardman Stratification of Aggregate Excess Demand and Finiteness of Equilibria

The paper establishes that the Thom-Boardman stratification result of singularity theory applies generically to the world of aggregate excess demand (AED) functions. In addition, if AED is analytic, then the number of Walrasian equilibria - including non-regular ones - is finite.

Statistical approach to partial equilibrium analysis

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and demand can be derived directly from these distributions. The characteristics of excess demand function are analyzed and the necessary conditions for the existence and uniqueness of equilibrium point of the market are specified. The rationing rates of buyers and sellers are introduced to describe the ratio of realized exchange to willing exchange, and their dependence on the market price is studied in the cases of shortage and surplus. The realized market surplus, which is the criterion of market efficiency, can be written as a function of the distributions of willing exchange and the rationing rates. With this approach we can strictly prove that a market is efficient in the state of equilibrium.

Direct Perturbations of Aggregate Excess Demand

We complement the Sonnenschein-Mantel-Debreu results by establishing that an exchange economy, i.e., preferences and endowments, that generates a given aggregate excess demand (AED) function is close to the economy that generates a perturbation of this AED. As a consequence, genericity and determinacy results obtained by direct perturbation of an AED are as strong as results obtained by perturbing preferences and endowments.

Undecidability of Uzawa equivalence theorem and LLPO (Lesser limited principle of omniscience)

The Uzawa equivalence theorem [H. Uzawa, Walras’s Existence Theorem and Brouwer’s Fixed Point Theorem, Economic Studies Quarterly 8 (1962) 59–62] showed (classically) that the existence of Walrasian equilibrium in an economy with continuous excess demand functions is equivalent to Brouwer’s fixed point theorem, that is, the existence of a fixed point for any continuous function from an n -dimensional simplex to itself. We examine the Uzawa equivalence theorem from the point of view of constructive mathematics, and show that this theorem, properly speaking, the assumption of the existence of a Walrasian equilibrium price vector in this theorem, implies LLPO (Lesser limited principle of omniscience), and so it is non-constructive.

The Dynamics of General Equilibrium

In Walras original description of general equilibrium (Walras, 1954 [1874]), market clearing was effected by a central authority. This authority, which has come to be known as the auctioneer, remains today because no one has succeeded in producing a plausible decentralised dynamic model of producers and consumers engaged in market interaction in which prices and quantities move towards market-clearing levels. Only under implausible assumptions can the continuous auctioneer dynamic be shown to be stable (Fisher, 1983), and in a discrete model, even these assumptions (gross substitutability, for instance) do not preclude instability and chaos in price movements (Saari, 1985; Bala and Majumdar, 1992). 1 Moreover, contemporary analysis of excess demand functions suggests that restrictions on preferences are unlikely to entail the stability of t^ (Sonnenschein, 1972, 1973; Debreu, 1974; Kirman and Koch, 1986). It has been a half century since Debreu (1952) and Arrow and Debreu (1954) provided a satisfactory analysis of the equilibrium properties market economies, yet we know virtually nothing systematic about Walrasian dynamics. This suggests that we lack understanding of one or more fundamental properties of market exchange. This article provides an agent-based model of the Walrasian economy. An agentbased model is a computer simulation of the repeated play of a game in which a large number of agents are endowed with software-encoded strategies governing both how they play the game and how they gather information and update their behaviour. The disequilibrium behaviour of agents in our agent-based models is governed by a replicator dynamic (Taylor and Jonker, 1978) in which, over time, successful agents tend in Darwinian fashion to increase in frequency at the expense of unsuccessful agents. We describe the process of shifting from lower to higher payoff strategies as imitation,

Stabilizing Consumer Choice: The Role of 'True Dynamic' Stability and Related Concepts in the History of Consumer Choice Theory

It is often argued that the inability of Arrow-Debreu general theory to produce an adequate proof of the of the Walrasian price adjustment mechanism was one of the program's most significant failures (a failure that is directly related to the infamous Sonnenschein-Mantel-Debreu results on aggregate excess demand functions). This paper will not question this standard interpretation of the history of general theory, but makes the case that characterizing the stability question in terms of market - in particular the of the price vector in Walrasian general model - actually helped to stabilize the standard model of consumer choice in general theory and elsewhere within microeconomics. The problem of the of consumer's equilibrium was much discussed early in the twentieth century and it has recently re-emerged in a different guise as the endowment effects and path dependencies of contemporary experimental and behavioral economics, and yet it disappeared from mainstream discussion during the period 1950-1980. This paper argues that shifting the discussion from the intra-agent of the individual consumer to the inter-agent of the competitive market contributed - despite its ultimately negative impact on general theory - to the long period of stable normal science consumer choice theory enjoyed during the middle of the 20th century. The paper ends by considering some of the implications of this interpretation of the history of the literature.

On the non-linear stochastic price adjustment of securities

We introduce a type of Itô process that models the adjustment of the market price of a traded security to new information affecting supply and demand. It is based on supply and demand functions and the Walrasian price adjustment assumption that proportional price increase is driven by excess demand. When supply and demand curves are linearised about the equilibrium point, the process turns out to be a logistic form of Brownian motion with random element of the Wiener type. Keywords: Excess demand function, Walrasian price adjustment process, Logistic Brownian motion. > East African Journal of Statistics Vol. 1 (1) 2005: pp. 109-116

The existence of equilibrium when excess demand obeys the weak axiom

This paper gives a non-fixed point theoretic proof of equilibrium existence when the excess demand function of an exchange economy obeys the weak axiom of revealed preference.

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.

International Financial Linkages of Latin American Banks: The Effects of Political Risk and Deposit Dollarisation

This paper empirically investigates the extent to which the financial linkages of Latin American banks with the exterior are influenced by political risk and deposit dollarisation. We find that the sum of banks' foreign assets and liabilities is a function of risk-return considerations and excess domestic credit demand. An increase in political risk is shown to be associated with a build-up of foreign positions by the banking sector, but this adverse effect on the banking system is mitigated in economies with a high share of dollarised deposits. These relationships largely hold when the determinants of foreign assets and liabilities are estimated separately, with risk-induced capital flight being moderated by a high degree of deposit dollarisation. While changes in overall country risk including the risk of macro collapse drive official capital outflows, for a wider measure of capital flight including informal flows only changes in political risk matter. In each case, deposit dollarisation is shown to possess a risk-mitigating property. The results suggest caution with active dedollarisation strategies in highly dollarised economies where political instability remains an issue.

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

On feedback and stable price adjustment mechanisms

Given an excess demand function of an economy, say Z ( p ) , a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p ( t , p 0 ) to an equilibrium p eq solution of Z ( p ) = 0 . Besides, all equilibrium points of Z ( p ) are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this powerful stability property of SPAMs, their acceptation in the economics community has been limited by a lack of interpretation. This paper focuses on this issue. Specifically, feedback control theory is used to link SPAMs and price dynamics models with control inputs, which match the economically intuitive Walrasian Hypothesis (i.e., prices change with excess demand sign). Under mild conditions, it is shown the existence of a feedback function that transforms the price dynamics into a desired SPAM. Hence, a SPAM is interpreted as a fundamental (e.g., Walrasian) price dynamics under the action of a feedback function aimed to stabilize the equilibrium set of the excess demand function.

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.

On the characterization of excess demand functions

In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras’ law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras’ law and zero homogeneity of Marshallian demand functions.

A New Approach for General Equilibrium with Discontinuous Excess Demand Function

Traditional ways to prove the existence of general equilibrium have to entail a common condition that the excess demand function must be continuous. This paper presents a new approach to change it. The technique used in this paper is that we tackle general equilibrium problem, which in fact is a static nonlinear programming problem, with dynamic programming. By this technique, it is strictly proven that general equilibrium with discontinuous excess demand function still exists.

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.