Chapter 17 Regular economies

Abstract

The theory of regular economies is useful for the studies of the local uniqueness of equilibria, continuity of the equilibrium price correspondence, and possibility of comparative statics. The theory of regular economies also helps give a better understanding of the core correspondence, because core allocations in a large economy is approximately decentralized through prices. There is an intimate relationship between the theory of regular economies and the new methods of computing economic equilibria. The chapter discusses that regularity studies play a role in fields related to economic equilibrium theory. For instance, the general complementarity problem in mathematical programming has been investigated by regularity methods. Another field where regularity methods are applied is game theory. The chapter also focuses on the Arrow–Debreu equilibrium theory. The chapter discusses other problems arising in this context, such as the basic problem of existence of price equilibria or the problem of how equilibrium prices are reached. The investigation of regular equilibria has led to a revival of calculus methods in equilibrium theory. A valuable comprehensive study of many important questions of equilibrium theory is presented in the chapter in a differentiable framework.