Optimization and Chaos

1. Front Matter

   Pages I-X

   PDF

2. Dynamical Systems: A Tutorial

   • Mukul Majumdar, Tapan Mitra

   Pages 1-30

3. Introduction to Dynamic Optimization Theory

   • Tapan Mitra

   Pages 31-108

4. Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects

   • Mukul Majumdar, Tapan Mitra

   Pages 109-148

5. Optimal Chaos, Nonlinearity and Feasibility Conditions

   • Kazuo Nishimura, Makoto Yano

   Pages 149-172

6. The Local Bifurcation of Ramsey Equilibrium

   • Robert A. Becker, Ciprian Foias

   Pages 173-208

7. On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy and Sunspots

   • Gerhard Sorger

   Pages 209-239

8. Robust Ergodic Chaos in Discounted Dynamic Optimization Models

   • Mukul Majumdar, Tapan Mitra

   Pages 240-257

9. Non-Linear Dynamics and Chaos in Optimal Growth: A Constructive Exposition

   • Kazuo Nishimura, Makoto Yano

   Pages 258-295

10. Ergodic Chaos in Optimal Growth Models with Low Discount Rates

    • Kazuo Nishimura, Gerhard Sorger, Makoto Yano

    Pages 296-314

11. On the Minimum Rate of Impatience for Complicated Optimal Growth Paths

    • Gerhard Sorger

    Pages 315-338

12. An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models

    • Tapan Mitra

    Pages 339-367

13. On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles

    • Kazuo Nishimura, Makoto Yano

    Pages 368-402

14. On the Relationship between Discounting and Entropy of Dynamic Optimization Models

    • Tapan Mitra

    Pages 403-433

15. Back Matter

    Pages 434-454

    PDF

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.

• Chaos
• Chaostheorie
• Dynamical Systems
• Dynamische Systeme
• Non-Linear Systems
• Optimierung
• Optimization Theory
• nicht-lineare Systeme
• optimization

• Department of Economics, Cornell University, Ithaca, USA

  Mukul Majumdar, Tapan Mitra

• Institute for Economic Research, Kyoto University, Kyoto 606, Japan

  Kazuo Nishimura

Policies and ethics