Set Valued Dynamical Systems and Economic Flow. Questo articolo non è disponibile.Set Valued Dynamical Systems and Economic Flow

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.

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.