Optimization and Chaos

This collection of essays brings together some articles on dynamic optimization models that exhibit chaotic behavior. Chapters 3, 4, 5, 6, 7, and 9 appeared in a Symposium on Chaotic Dynamical Systems in Economic Theory (Volume 4, Number 5, 1994). Also, Chapters 10,11, and 12 appeared in the Journal of Economic The ory. We would like to thank the authors, and Academic Press for permission to reprint. We are grateful to Professor C.D. Aliprantis for suggesting the idea of a book structured around the Economic Theory Symposium, and without the support and patience of Dr. Mueller this project could not have been completed. We would like to thank Ms. Amy Gowan who cheerfully per formed the arduous task of typing the manuscript. Thanks are also due to Xiao Qing Yu, Tridip Ray and Malabika Majumdar for their help at various stages in the preparation of the manuscript. For a course on dynamic optimization addressed to students with a good background in economic theory and real analysis, one can assign Chapter 2 as a partial introduction to the basic tech niques. Chapters 3 and 4 can be assigned to provide examples of simple optmization models generating complicated behavior.

Edited by three leading researchers Contains an introduction to the fundamental concepts of chaotic dynamical systems

Klappentext

The book begins with an introduction to some of the basic concepts and results on chaotic dynamical systems. Next it turns to a detailed self-contained summary of the literature on discounted dynamic optimization. The first two chapters are of particular pedagogical interest. The volume also brings together a number of outstanding advanced research papers on complex behavior of dynamic economic models. These make it clear that complexity cannot be dismissed as "exceptional" or "pathological" and, for explanation and prediction of economic variables, it is imperative to develop models with special structures suggested by empirical studies. Graduate students in economics will find the book valuable for an introduction to optimization and chaos. Specialists will find new directions to explore themes like robustness of chaotic behavior and the role of discounting in generating cycles and complexity.

Inhalt
1 Dynamical Systems: A Tutorial.- 2 Introduction to Dynamic Optimization Theory.- 3 Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects.- 4 Optimal Chaos, Nonlinearity, and Feasibility Conditions.- 5 The Local Bifurcation of Ramsey Equilibrium.- 6 On the Structure of Ramsey Equilibirum: Cycles, Indeterminacy and Sunspots.- 7 Robust Ergodic Chaos in Discounted Dynamic Optimization Models.- 8 Non-Linear Dynamics and Chaos in Optimal Growth: A Constructive Exposition.- 9 Ergodic Chaos in Optimal Growth Models with Low Discount Rates.- 10 On the Minimum Rate of Impatience for Complicated Optimal Growth Paths.- 11 An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models.- 12 On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles.- 13 On the Relationship between Discounting and Entropy of Dynamic Optimization Models.- References.