From Catastrophe to Chaos: A General Theory of Economic Discontinuities
From Catastrophe to Chaos: A General Theory of Economic Discontinuities presents and unusual perspective on economics and economic analysis. Current economic theory largely depends upon assuming that the world is fundamentally continuous. However, an incr
- PDF / 29,504,543 Bytes
- 312 Pages / 439.37 x 666.142 pts Page_size
- 76 Downloads / 213 Views
From Catastrophe to Chaos: A General Theory of Economic Discontinuities (Second Edition) Mathematics, Microeconomics, Macroeconomics, and Finance (Volume I)
J. Barkley Rosser, Jr. Department of Economics James Madison University
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data Rosser, John Barkley, 1948From catastrophe to chaos : a general theory of economic discontinuities I J. Barkley Rosser, Jr.--2nd ed. p. em. Includes bibliographical references and index. Contents: v. I. Mathematics, microeconomics, and finance. ISBN 978-94-017-1615-4 ISBN 978-94-017-1613-0 (eBook) DOI 10.1007/978-94-017-1613-0 1. Economics, Mathematical. 2. Nonlinear theories. 3. Chaotic behavior in systems. I. Title. HB 135 .R66 2000 330'.01 '51--dc21
00-022046
Copyright© 2000 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2000 All rights reserved. No part of this publication may be reproduced, retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC. Printed on acid-free paper.
Dedication The first edition of this book was dedicated to my late father, J. Barkley Rosser, Sr., and my wife, Marina V cherashnaya Rosser. I wish to dedicate this second edition to my daughters, Meagan, Caitlin, and Alexandra (Sasha).
TABLE OF CONTENTS PREFACE
ix
1 1 2 4
1.
Discontinuity in Economic Theory and Economic Discontinuities Some Initial Remarks 1.1 Discontinuity in the Large and the Small 1.2 On Scale and Perspective in Identifying Discontinuities 1.3
2.
The Mathematics of Discontinuity General Overview 2.1 The Founding Fathers 2.2 The Bifurcation of Bifurcation Theory 2.3 The Special Path to Fractal Geometry 2.4 The Complexity of Other Forms of Complexity 2.5
9 9 9 16 52 54
3.
Discontinuities in Microeconomics Systems General Equilibrium Aspects 3.1 Discontinuous Competitive Market Dynamics 3.2 Discontinuities in Imperfectly Competitive Markets 3.3
69 69 75 92
4.
Speculative Bubbles and Crashes 1: Irrational Introduction 4.1 What Is a Speculative Bubble? 4.2 A Classical View of Irrational Bubbles 4.3 Mechanisms of the Speculative Mania 4.4 Mechanisms of the Speculative Panic 4.5 Varieties oflrrational Bubbles 4.6
105 105 107 107 109 114 118
5.
Speculative Bubbles and Crashes II: Rational and Semi-Rational Self-fulfilling Prophecies, Rational Bubbles, and Sunspots 5.1 When Are Rational Bubbles Possible? 5.2 Price Bubbles in Monetary Economies 5.3 Heterogeneous Agents and Semi-rational Bubbles 5.4 The Empirical Observability of Bubbles 5.5
123 123 125 129 135 146
6.
Catastrophe Theory and Hysteresis in Macroeconomics Nonlinear Investment and Business Cycles 6.1 Hysteresis of Stagflation 6.2
161 161 166
Vlll
7.
8.
Chaos Theory and Complex Macroeconomic Dynamics Introduction 7 .I Sunspots and Regular Cycles in Overlapping Generations 7.2 Models Chaotic Cycles in Overlapping Generations Mode
