A simple example of complex dynamics

Summary. A discrete tatonnement process is analysed within the context of a two-person, two-good exchange economy where each person has a Cobb-Douglas utility function. This process is shown to exhibit period doubling bifurcation, topological and ergodic chaos. Received: June 22, 1998; revised version: July 15, 1998     

A pitchfork bifurcation in the tatonnement process★

Summary . This note extends the example of Gale (1963) by considering the continuous time tatonnement process for a class of two agent, two commodity exchange economies, parametrized by a number μ∈(0,1). We demonstrate that as the parameter passes a threshold value μ^* the unique, globally stable competitive equilibrium loses local stability while two new locally stable equilibria appear. Intuitively, as μ increases the income effect become increasingly more important relative to substitution effect, and eventually overwhelms the latter. As the parameter μ approaches 1, the economy tends to the example considered by Gale, as does the limiting behavior of the tatonnement. Received: February 28, 1996; revised version August 5, 1996     

Chaotic tatonnement

Summary Debreu's theorem on excess demand functions is used to demonstrate the possibilities of ergodic and topological chaos in a discrete-time tatonnement process with only two goods. The result is in sharp contrast with the well-known result of Arrow and Hurwicz on system stability in a continuous time model of price adjustment with two commodities.We would like to thank Professors Jess Benhabib, Richard Day, John Guckenheimer, Philip Holmes, Nicholas Kiefer and Tapan Mitra.     

A close eye on the invisible hand

The paper shows how, and under what minimal information supply conditions, a market finds its competitive equilibrium price and thus solves the so-called tatonnement process, without sellers and buyers knowing the equilibrium price in advance. The information premises must be understood as a basic first approach, and do not necessarily mimic the real market process. Demonstration of a discovery process under these information handling conditions is an important finding for an evolutionary market theory. Additional information-processing elements should augment the efficiency of the discovery process. The results of the simulated market process set out above raise new questions. The role of institutional elements (such as the relevance of demand flexibility or “certainty” of knowledge in the learning process, etc.) is discussed further outside the context of the simulation model, providing new insight into the market process.     

Walras and Darwin: an odd couple?

General equilibrium theory and the evolutionary branches of economics and game theory take rather opposite positions in the spectrum covered by the economic science. However, we reveal and explore analogies between Darwinian dynamics and Walrasian tatonnement processes for pure exchange economies, as well as further analogies implied by these.     

Global instability in experimental general equilibrium: the Scarf example

Scarf (Int. Econ. Rev. 1 (1960) 157) proposed a model of dynamic adjustment in which the standard tatonnement price adjustment process orbits around, rather than converges to, the competitive equilibrium. Hirota (Int. Econ. Rev. 22 (1981) 461) characterized the price paths. We explore the predictions of Scarf's model in a non-tatonnement experimental double auction. The average transaction prices in each period do follow the path predicted by the Scarf and Hirota models. When the model predicts convergence the data converge; when the model predicts orbits, the data orbit in the direction predicted by the model. Moreover, we observe a weak tendency for prices within a period to follow the path predicted by the model.     

Reconstructing dynamics from intertemporal economic data

Summary This paper is concerned with the relationship between a continuous dynamical system and the trajectory generated by such a system. The main result provides necessary and sufficient conditions for an infinite data stream to be rationalized as the output of a continuous law of motion. The paper develops concepts of informativeness of a given set of intertemporal data and shows that informativeness is maximal when the data is chaotic. It also demonstrates that with probability one the sample paths from a non-trivial independent and identically distributed stochastic process cannot be rationalized as the output of a continuous deterministic system. Two impossibility results are discussed which show that even with an infinite amount of data the hypothesis that the data has been generated by a non-monotonic function cannot be ruled out. An application concerning the recovery of the excess demand function from a sequence of price observations from the tatonnement process is also given.I would like to thank Professors Bent Christensen and Mukul Majumdar for valuable discussions and an anonymous referee for helpful comments. Financial support from SSHRC and Quebec's Fonds FCAR is gratefully acknowledged.     

Equilibrium, Trade, and Capital Accumulation

The paper summarizes the author's principal contributions to economic theory: (1) one of the first rigorous proofs of the existence of competitive equilibrium; (2) existence of competitive equilibrium with weakened assumptions; (3) the minimum income approach to demand theory; (4) tatonnement stability with weak gross substitutes; (5) a general theory of comparative advantage; (6) factor price equalization with attention to factor supplies; and (7) turnpike theory allowing for von Neumann facets and neighbourhood convergence.
JEL Classification Number: B10     

Instability in the implementation of Walrasian allocations

The existence of game forms which implement Walrasian allocations as Cournot (Nash) equilibrium outcomes is well known. However, if the equilibria are also required to be locally dynamically stable, at least for environments with unique Walrasian allocations, this paper shows that the requisite game forms do not exist. Our definition of a game form entails certain regularity conditions, and requires the Cournot equilibrium to be unique when the Walrasian equilibrium is unique. The main result is that for such a game form, there does not exist a continuous-time strategy adjustment process which ensures the local stability of Cournot equilibria throughout a certain class of environments having unique Walrasian equilibria. Each trader adjusts his strategy in response to his own characteristics and the observed current strategies of others; but the direction and magnitude of adjustments are not constrained by any behavioral assumptions. The definitions permit the inclusion of an artificial player, such as an auctioneer, so the well-known tatonnement instability emerges as a special case.     

非均衡的经济动态模型

本文旨在按现实世界的本来面目建立一个非均衡的内生经济动态模型。在这个模型中 ,源于部门内和部门间关系的内生变量导致资本市场、消费品市场上产量和价格的波动。市场的非均衡过程、存货调节机制以及经济人的最优行为和适应性行为是基于对现实世界的观察进行模拟的。静态性质及其稳定性是作为一般市场动态过程的特例加以讨论的。     

General equilibrium without utility functions: how far to go?

How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers’ preferences. We show in this paper that if consumers’ non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: (1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; (2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; (3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; (4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; (5) the pathconnectedness of the sets of stable equilibria.     

Expectational coordination in simple economic contexts

We consider an economic model that features (1) a continuum of agents and (2) an aggregate state of the world over which agents have an infinitesimal influence. We first review the connections between the ??eductive?? viewpoint on expectational stability and standard game-theoretical rationalizability concepts. The ??eductive?? reasoning selects different plausible beliefs that are a priori, and possibly a posteriori, ??diverse??. Such beliefs are associated with the sets of ??Cobweb tatonnement?? outcomes, ??Rationalizable States?? and ??Point-Rationalizable States?? (the latter two being shown to be convex). In the case where our model displays strategic complementarities, unsurprisingly, all our ??eductive?? criteria support similar conclusions, particularly when the equilibrium is unique. With strategic substitutabilities, the success of expectational coordination, in the case where a unique equilibrium does exists, relates with the absence of cycles of order 2 of the ??Cobweb?? mapping: in this case, full expectational coordination would be achieved. However, when cycles of order 2 do exist, our different criteria predict larger sets of outcomes, although all tied with cycles. Under differentiability assumptions, the Poincaré?CHopf method leads to other global stability results. At the local level, the different criteria under scrutiny can be adapted. They lead to the same expectational stability conclusions, only when there are local strategic complementarities or strategic substitutabilities. However, for the local stability analysis, it is demonstrated that the stochastic character of expectations can most often be forgotten.     

业务流程管理的一般构成模型

流程化和职能化是流程管理研究中的基本矛盾,本文从阐述流程管理与职能环节的关系出发,对制造企业的业务流程进行重新分类并对业务流程管理的一般内容做出概括,在此基础上构建了业务流程管理的构成模型,并阐述模型所包含的理论意义。     

The Political Entrepreneur and the Coordination of the Political Process: A Market Process Perspective of the Political Market

The aim of this article is to apply the Austrian analysis of the entrepreneur to the political process. By distinguishing the political process from the economic process, we will endeavour to show to what extent an analysis in terms of the political market process is both possible and relevant. The existence of an information conveyance which can be assimilated to a price system within the political process, with its resulting profits, are motivating elements for the political entrepreneur. The political entrepreneur is doubly specialised and possesses all the Kirznerian functions of the Austrian entrepreneur as a coordinating agent for the political process.     

论励志自强的内涵

所谓励志,就是在实践中磨砺自己的意志,在坚持志向的前提下,不断增强克服困难的信心和意志。励志的过程就是一个艰苦奋斗、自强不息的过程。＂励志自强＂的过程也是一个＂改过自新＂的过程,＂改过自新＂可以说是在励志自强一个特定方面的表现。     

市场过程内生的垄断:市场权势和自然垄断

作为内生的垄断现象,市场权势实际上是争胜竞争过程的结果,并非垄断的市场结构所决定。如果将竞争理解为一个动态过程,市场权势具有竞争性和暂时性。自然垄断现象也是市场过程演化过程中的自然现象,无论源于规模经济还是范围经济,都表明自然垄断具有动态效率特征。除非政府人为阻碍争胜竞争过程的展开,通常市场过程内生力量能够有效制约非政府垄断现象。     

On managed evaluation processes

Essential step in an evaluation process are descrived. Evaluation projects often follow a somewhat different process because sponsors have considerable incentive to shape the process. The evaluation process can be distorted by altering transactions, by disregarding steps, or by modifying information flowing from a given step in the process. Several types of managed evaluation processes are described to predict evaluations unlikely to provide useful results. To improve the prospects of success for evaluation projects, some essential dialogues between evaluators and sponsors are sketched.     

基于增值流程分布的制造企业分类及其特征

分类是理论研究的基本方法,对制造企业进行分类是流程管理研究的基础。本文从阐述流程管理与职能环节的关系出发,根据业务流程与价值增值的密切程度对制造企业的业务流程进行重新分类,并提出和描述了基于增值流程分布的制造企业分类及其特征,最后阐述这种分类的意义。     

地方财政运行与城镇化机理探讨

中国正进入加速推进城镇化发展时期,城镇化水平的提高可以为经济持续增长提供不竭的动力。城镇化在本质上是一个人口地域集中以及产业聚集的过程。为实现城镇职能而进行的财政分配活动尤其是地方财政的安排尤为重要,地方财政职能发挥将直接影响到城镇化的进程以及水平。     

The effects of transformational leadership,competitive intensity and technological innovation on performance

This study aims to determine the three-way interaction effects of transformational leadership, technological innovation (i.e. product and process innovation) and competitive intensity on firm performance by detecting three-way interactions involving slope differences in moderated multiple regression. Based on a sample of 182 manufacturing enterprises in China, this paper finds that firms under transformational leadership are more likely to conduct process innovation, that the joint effect of the interaction between process innovation and competitive intensity is negatively related to firm performance and that the joint effect of the interaction between transformational leadership and competitive intensity is positively related to firm performance. Accordingly, this paper concludes that a firm should conduct more process innovation in a moderately competitive environment, but it should conduct less process innovation in a fiercely competitive environment, where in stronger transformational leadership should be adopted.