This book 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 this book 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. This study demonstrates the central role played by the equilibrium manifold in understanding the proper ... More

This book 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 this book 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. This study demonstrates the central role played by the equilibrium manifold in understanding the properties of the Arrow–Debreu model and its extensions. It 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, the book discusses the properties of the equilibrium manifold and the natural projection. It 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. The book 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.