# The Equilibrium Manifold

## Overview

In The Equilibrium Manifold, noted economic scholar and major contributor to the theory of general equilibrium Yves Balasko argues that, contrary to what many textbooks want readers to believe, the study of the general equilibrium model did not end with the existence and welfare theorems of the 1950s. These developments, which characterize the modern phase of the theory of general equilibrium, led to what Balasko calls the postmodern phase, marked by the reintroduction of differentiability assumptions and the application of the methods of differential topology to the study of the equilibrium equation. Balasko’s rigorous study demonstrates the central role played by the equilibrium manifold in understanding the properties of the Arrow-Debreu model and its extensions. Balasko argues that the tools of differential topology articulated around the concept of equilibrium manifold offer powerful methods for studying economically important issues, from existence and uniqueness to business cycles and economic fluctuations. After an examination of the theory of general equilibrium’s evolution in the hundred years between Walras and Arrow-Debreu, Balasko discusses the properties of the equilibrium manifold and the natural projection. He highlights the important role of the set of no-trade equilibria, the structure of which is applied to the global structure of the equilibrium manifold. He also develops a geometric approach to the study of the equilibrium manifold. Applications include stability issues of adjustment dynamics for out-of-equilibrium prices, the introduction of price-dependent preferences, and aspects of time and uncertainty in extensions of the general equilibrium model that account for various forms of market frictions and imperfections. Special effort has been made at reducing the mathematical technicalities without compromising rigor. The Equilibrium Manifold makes clear the ways in which the postmodern” developments of the Arrow-Debreu model improve our understanding of modern market economies.

## About the Author

Yves Balasko is Professor of Economics at the University of York. He is the author of Foundations of the Theory of General Equilibrium and numerous articles on the theory of general equilibrium.

## Endorsements

"Balasko's book is a very clear presentation of some latest results in general equilibrium theory. The notion of equilibrium manifold is introduced in order to examine a wide spectrum of properties of equilibria, not only properties connected to comparative statics. Many important subjects are deeply analyzed, such as price-dependent utility functions, out-of-equilibrium price dynamics, economic fluctuations, and temporary equilibrium."--Aldo Montesano, Department of Economics, Bocconi University, Italy"—**Aldo Montesano**

“The Equilibrium Manifold is a must read -- and a delightful read! -- for anyone interested in contemporary general equilibrium theory, which is essentially the analysis of the equations of supply and demand. Yves Balasko is the master of his subject. No one has contributed more to our current understanding of the equilibrium manifold than Balasko.” --Karl Shell, Thorne Professor of Economics, Cornell University and Editor, Journal of Economic Theory"—**Karl Shell**

“This book will be a ‘must have’ addition to Balasko's earlier book, Foundations of the Theory of General Equilibrium, and for anyone doing research in general equilibrium. The new book extends the smooth economies techniques to the global setting and provides important new results on short-run and long-run general equilibrium dynamics.”--Stephen E. Spear, Professor of Economics, Tepper School of Business, Carnegie Mellon University"—**Stephen Spear**

"Balasko's book is a very clear presentation of some of the latest results in general equilibrium theory. The notion of equilibrium manifold is introduced in order to examine a wide spectrum of properties of equilibria, not only properties connected to comparative statics. Many important subjects are deeply analyzed, such as price-dependent utility functions, out-of-equilibrium price dynamics, economic fluctuations, and temporary equilibrium."**Aldo Montesano **, Department of Economics, Bocconi University, Italy"—

"*The Equilibrium Manifold* is a must read—and a delightful read!—for anyone interested in contemporary general equilibrium theory, which is essentially the analysis of the equations of supply and demand. Yves Balasko is the master of his subject. No one has contributed more to our current understanding of the equilibrium manifold than Balasko." **Karl Shell **, Thorne Professor of Economics, Cornell University, and editor, *Journal of Economic Theory*"—

"This book will be a 'must-have' addition to Balasko's earlier book, *Foundations of the Theory of General Equilibrium,* and for anyone doing research in general equilibrium. The new book extends the smooth economies techniques to the global setting and provides important new results on short-run and long-run general equilibrium dynamics." **Stephen E. Spear **, Professor of Economics, Tepper School of Business, Carnegie Mellon University"—