# On the stability of dynamic processes in economic theory

@article{dAspremont1979OnTS,
title={On the stability of dynamic processes in economic theory},
author={Claude d'Aspremont and Jacques Dr{\e}ze},
journal={Econometrica},
year={1979},
volume={47},
pages={733-737}
}`
• Published 1979
• Mathematics
• Econometrica
The notion of stability in the sense of Lyapunov is applied to economic dynamic processes of the Champsaur-Dreze-Henry type. Our purpose in this note is to fill a small gap in the literature concerning dynamic processes in economic theory, of the type presented by Champsaur, Dreze, and Henry [3]. Indeed, these authors do not discuss stability in the sense of Lyapunov [7]. However, a recent result of Maschler and Peleg [9] on this kind of stability (presented in a discrete model) can easily be…
9 Citations

## Figures from this paper

Tatonnement Processes with Set-Valued Excess-Demand
• Economics
• 1984
Having solved the problem of existence of equilibria, the central question for the economist is whether there are forces to drive an economy toward an equilibrium. Tatonnement and non-tâtonnement
FROM UNCERTAINTY TO MACROECONOMICS AND BACK: AN INTERVIEW WITH JACQUES DRÈZE
• Economics
Macroeconomic Dynamics
• 2005
Jacques Drèze was born in Verviers, Belgium, in 1929 and completed his Ph.D. in Economics in 1958 at Columbia. His contribution to economics is exceptional, opening up new paths of research in
The MDP Procedure for public goods and local strategy proofness
AbstractThis paper revisits the family of MDP Procedures and analyzes their properties. It also reviews the procedure developed by Sato (Econ Stud Q 34:97–109, 1983) which achieves aggregate correct
Nonmyopia and incentives in the piecewise linearized MDP procedures with variable step-sizes
The paper formulates a piecewise linearized version of the procedure developed by Sato (1983) and analyzes its properties. In so doing, Fujigaki’s (1981) private goods economy is extended to involve
A Customer Management Dilemma: When to Punish or Reward Own Customers
• 2008
Firms routinely use behavior based pricing (BBP), to segment customers by past purchase behavior. This paper answers a dilemma facing such firms – When should the firm reward existing customers as
A Customer Management Dilemma : When Is It Profitable to Reward Existing Customers ?
• 2009
This study attempts to answer a basic customer management dilemma facing firms: When should the firm use behavior-based pricing (BBP) to discriminate between its own and competitors’ customers in a
A Customer Management Dilemma: When Is It Profitable to Reward One's Own Customers?
Mark. Sci.
• 2010
To the best of the knowledge, this study is the first to identify conditions in which it is optimal to reward one's own customers under symmetric competition and BBP can increase profits with fully strategic and forward-looking consumers.
The Invisible Hand in Motion
Proofs of some propositions mentioned in the lecture may be found in Mukherji (2005).

## References

SHOWING 1-10 OF 11 REFERENCES
THE STABILITY OF A COMPETITIVE ECONOMY: A SURVEY ARTICLE
THE THEORY of the general competitive equilibrium, as developed by Leon Walras [64], has recently been reformulated in terms of fairly advanced mathematical methods. The first problem studied
Stable Sets and Stable Points of Set-Valued Dynamic Systems with Applications to Game Theory
• Mathematics
• 1976
Let X be a metric space. A dynamic system on X is a set-valued function $\varphi$ from X to X which satisfies $\varphi (x) \ne \emptyset$ for $x \in X$. It generates $\varphi$-sequences: \[x^{(t +
Neutrality of Planning Procedures in an Economy with Public Goods
Planning procedures for guiding and financing the production of public goods have been proposed by Dreze, de la Vallee Poussin [4] and Malinvaud [8]. Planning procedures are of particular interest in
The Structure of the Equilibrium Points of Heal's Process
For the planning problem of maximizing a given social welfare function subject to technology, resource-availability, and non-negativity constraints, Heal [3, 4, 5, 6] proposed and analysed a
A Tâtonnement Process for Public Goods
• Economics
• 1971
In this paper, we discuss a procedure for choosing efficient output level for public goods. In section 1, we define the concepts of public goods. We introduce three assumptions. We then state the
Planning without Prices
Discussions of decentralized planning procedures are not new in the economic literature: they date back to Lange [6], who seems to have found inspiration in the even earlier writings of Walras [13].
Problème général de la stabilité du mouvement
© Université Paul Sabatier, 1907, tous droits réservés. L’accès aux archives de la revue « Annales de la faculté des sciences de Toulouse » (http://picard.ups-tlse.fr/~annales/) implique l’accord
Problème général de la stabilité du mouvement
The description for this book, Probleme General de la Stabilite du Mouvement. (AM-17), will be forthcoming.