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Set Valued Dynamical Systems and Economic Flow: Lecture Notes in Economics and Mathematical Systems, cartea 158

Autor L. J. Jr. Cherene
en Limba Engleză Paperback – mai 1978
The purpose of this monograph is to illuminate the central issues of dynamic analysis applied to economic models, using a generally accepted language of the study of dynamical systems at a level of sophistication likely to be understood by an economist versed in elementary topology. Whether an economic system is governed by a first order difference equation or several simultaneous multivalued partial differential equations, its solution is a flow that determines the state of the system given an initial condition and elapsed time. Thus the flow of a system is the central concept from which the theory here expounded develops. The explicit examples and applications herein are discrete time models, but the theoretical re­ sults hold for continuous time models as well. The supplementary bibliography in­ cludes several papers at the frontier of set-valued dynamics which may be viewed using the basic concepts defined in this text; all of these works involve demon­ strating that (almost) all possible trajectories that a system may follow converge to some set of equilibria. The application of set valued dynamical analysis to economic models is pro~ vided to engender in the reader an appreciation for the relevance of these con­ cepts to economic theory.
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Specificații

ISBN-13: 9783540088479
ISBN-10: 3540088474
Pagini: 100
Ilustrații: VIII, 83 p. 1 illus.
Dimensiuni: 170 x 244 x 5 mm
Greutate: 0.17 kg
Ediția:Softcover reprint of the original 1st ed. 1978
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Economics and Mathematical Systems

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

I: Introduction.- II: A General Framework for Dynamic Economic Systems.- 1. Introduction.- 2. The Framework.- 3. Some Numerical Examples.- III: The General Theory of Set Valued Semidynamical Systems.- 1. A Set Valued Flow.- 2. The Space of Subsets.- 3. Semidynamical Systems for Set Valued Flows.- 4. Liapunov Functions.- IV: The Edgeworth Barter Process.- 1. Introduction.- 2. The Model.- 3. The Dynamics.- 4. Ex Post Pareto Optimality.- 5. Concluding Remarks.- V: Comparative Dynamics of Models of Adaptive and Optimal Economic Growth.- I. A Model of Adaptive Behavior.- II. Optimality of Adaptive Behavior.- Conclusion.- VI: The Structure of Optimality in Dynamic Models.- 1. Introduction.- 2. Adaptive and Optimal Programs.- 3. The Space of Trajectories.- 4. Optimal Control as a Set Valued Semidynamical System.- 5. Ex Ante Optimality.- 6. Ex Post Optimality.- 7. Dynamic Pareto Optimality.- 8. Asymptotic Optimality and Attraction.- 9. Concluding Remarks.- Glossary of Notation and Abbreviations.- Supplemental Bibliography.