From Catastrophe to Chaos: A General Theory of Economic Discontinuities.

• Author: White, Mark V.

Professor Rosser set out to create a single-volume encyclopedia covering the broad sweep of economic applications for bifurcation theory (the field encompassing the non-linear math specialties of catastrophe and chaos), and to a great extent he has succeeded. For the economist wanting an introduction to this promising new field, Rosser's work is a boon. The research into the non-linear aspects of economics is actually quite extensive, but a paucity of cross-references obscured that range before the emergence of this volume. Rosser studied virtually all the various aspects of this research in economics, then organized them into a consistent presentation that gives linear economists easy access to up-to-date non-linear research in their specialties. Even practicing non-linear economists will find in his volume a useful bibliographic reference in their specialty, a source of inspiration in its scope and perhaps even some useful new ideas. Despite a title that makes our dismal science sound even more dismal, Rosser's book is a great service to the profession.

After a brief introduction motivating the use of bifurcation theory in economics and a mathematical review that nicely balances the non-specialist's needs for both accessibility and rigor, Rosser's book goes on to cover the broad scope of applications. Starting with macroeconomics, he looks at potential routes to bifurcation ranging from preferences to expectations to lags. He then focuses in on speculative bubbles, devoting two chapters to an extensive review of this contentious phenomenon. The first of these chapters examines irrational bubbles, the second looks at rational and semi-rational bubbles. As a student of irrational bubbles, I can highly recommend his discussion as both sensitive and fairly comprehensive within the space constraints.

Turning from microeconomics, Rosser focuses on catastrophe and chaos in macroeconomics models and macroeconomies. He shows how the mathematics of these models can produce bifurcations and chaotic dynamics, and discusses the ongoing econometric search for chaos evidence in macroeconomic variables. After micro ad macro, Rosser illuminates a number of individual topics, including capital theory, urban and regional economics, interfaces between ecology and economy, foreign exchange rates and the world economy. Without the specific focus of bifurcation theory, such a wide array of topics would inevitably lead to a vapid discussion by even the most...