Set Valued Dynamical Systems and Economic Flow

ISBN-13: 9783540088479 / Angielski / Miękka / 1978 / 83 str.

L. J. Jr. Cherene

Opis

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."

Spis treści

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.- 1. The Model.- 2. Some Critical Capital/Labor Ratios.- 3. The Neoclassical Region.- 4. The Malthusian Region.- 5. Capital Accumulation and Population Growth.- II. Optimality of Adaptive Behavior.- 1. A Related Infinite Horizon Planning Problem.- 2. Implications of the Principle of Optimality.- 3. Malthusian Optimality.- 4. Neoclassical Optimality.- 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.