Excess Demand Functions Research Articles

Some issues on the stability of trading based on technical analysis

Some stability effects of technical trading on financial/commodity markets are analyzed in this paper. Technical trading is characterized by using past price information within a time-delay horizon to forecast future price dynamics. By introducing fundamental and technical excess demand functions, the market dynamics is modeled as a time-delayed differential equation, whose (local) stability is determined by means of root-locus techniques. It is proven that the larger the time-delay horizon, the larger the stability margin. This means that short-run technical trading is more likely to induce market instabilities than large-run technical trading. It is also shown that, as expected, the larger the relative weight of technical trading with respect to fundamental trading, the smaller the stability margin of the market dynamics.

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.

Learning to Predict Rationally When Beliefs are Heterogeneous

This paper develops an adaptive learning scheme for an asset market with heterogeneous traders who are characterized by linear mean-variance preferences. We introduce the concept of a perfect forecasting rule which generates rational expectations for fundamentalists in the presence of investors with possibly non-rational beliefs. When these non-rational investors base their decisions on simple technical trading rules, perfect forecasting rules are approximated by successively estimating the excess demand function from historical data. Conditions are given under which trajectories generated by this adaptive learning scheme converge to trajectories with rational expectations for fundamentalists.

Learning to predict rationally when beliefs are heterogeneous

This paper develops an adaptive learning scheme for an asset market with heterogeneous traders who are characterized by linear mean-variance preferences. We introduce the concept of a perfect forecasting rule which generates rational expectations for fundamentalists in the presence of investors with possibly non-rational beliefs. When these non-rational investors base their decisions on simple technical trading rules, perfect forecasting rules are approximated by successively estimating the excess demand function from historical data. Conditions are given under which trajectories generated by this adaptive learning scheme converge to trajectories with rational expectations for fundamentalists.

A stronger criterion for the Weak Weak Axiom

The Weak Weak Axiom (WWA) is a milder version of the Weak Axiom of Revealed Preference (WA) and is equivalent to pseudomonotonicity of the excess demand function. Since the WWA guarantees uniqueness of the equilibrium in a broad class of general equilibrium models, it is important to have criteria to check when the WWA holds. In this paper, a new and more general characterization of pseudomonotonicity for C 1 maps is provided. Using this result, we obtain a stronger criterion for the WWA than those available in the literature. A complete characterization of the WA for excess demand functions is also offered and other important existing results are obtained in a straightforward fashion.

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 discrete fixed point theorem and its applications

This paper proves a fixed point theorem on a discrete set which exploits the “contiguous convexity” of the set and the “direction preserving-ness” of correspondence. Then, applying this result, we study a general equilibrium model with indivisible commodities. A set of sufficient conditions for the existence of a Walrasian equilibrium price is given, in terms of properties of the excess demand function. We also apply it to a non-cooperative game on discrete strategy sets, and show some conditions for the existence of a Nash equilibrium point. A new notion of “contiguity” is proposed as a discrete analog of continuity.

Global Stability Conditions on the Plane

The paper considers price adjustment on the plane and derives global stability conditions for such dynamics. First, we examine the well-known Scarf Example, to obtain and analyze a global stability condition for this case. Next, for a general class of excess demand functions, a set of conditions is identified which guarantee not only convergence to some equilibrium but also robustness of these properties.

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.

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.

Speculative Price Dynamics in a Heterogeneous Agent Model

This paper proposes an agent model of financial markets and analyzes factors leading to speculative bubbles and speculative chaos of the asset price. A financial market is thought to contain two typical types of traders: fundamentalists and chartists who try to maximize their utility. It is shown that the nonlinearity of the excess demand functions, which are derived as a result of the traders' utility maximization, might generate speculative bubbles and speculative chaos of the asset price.

The demand functions that satisfy the weak axiom of revealed preference and generalized monotonicity

We prove that the individual demand function satisfying the Weak Axiom of Revealed Preference and the excess demand function satisfying the Wald’s Axiom are pseudomonotone ∗ + , a new class of generalized monotonicity. With this new concept, we refine the characterization of Zhou for the individual demand function. In particular, a full characterization for the excess demand functions satisfying the Wald’s Axiom is derived.

A first order characterization of generalized monotonicity

It is shown that pseudomonotone and quasimonotone maps can be characterized by a first order property provided they are regular. This result extends the well known characterization of nonvanishing generalized monotone maps to an essentially larger class. The paper supplements a recent contribution by Crouzeix and Ferland (1996) and solves a related open problem concerning homogeneous excess demand functions which occur in general equilibrium theory.

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.

Non-computability of competitive equilibrium

We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]).

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure.

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)).

On the uniqueness of competitive equilibrium

. The paper is concerned with the following question: in addition to local uniqueness, what other conditions must be imposed to ensure global uniqueness of competitive equilibrium? The answer is provided within a standard framework involving excess demand functions. Conditions are identified which have the nice property that they are true close to a regular equilibrium. Uniqueness is established by considering an adjustment process and showing that under the mentioned conditions, every equilibrium is locally asymptotically stable and moreover the process itself is globally stable; uniqueness follows from an Arrow and Hahn (1971) result. Alternatively, the paper may be seen as identifying conditions under which there is a vectorfield satisfying the requirements of an uniqueness result due to Dierker (1974).

Excess demand functions, equilibrium prices, and existence of equilibrium

For continuous excess demand functions, the existing literature (e.g. Sonnenschein (1972, 1973), Mantel (1974), Debreu (1974), Mas-Colell (1977), etc.) achieves a complete characterization only when the functions are defined on special subsets of positive prices. In this paper, we allow the functions to be defined on a larger class of price sets, (allowing, for exam­ ple the closed unit simplex, including its boundary). Besides characterizing excess demands for a larger class of economies, it is also a useful tool for proving other results. It allows us to characterize the equilibrium price set for a larger class of economies. It also permits extending Uzawa's observa­ tion (1962)' by showing that Brouwer's Fixed-Point Theorem is implied by the Arrow-Debreu Equilibrium Existence Theorem ((1954), Thm. I.).