Publisher Summary This chapter discusses that the mathematical model of a competitive economy conceived as an attempt to explain the state of equilibrium reached by a large number of small agents interacting through markets. Four distinct, but closely related, approaches to the existence problem are recognized. At first, proofs of existence of an economic equilibrium were uniformly obtained by application of a fixed-point theorem of the Brouwer type or Kakutani type or by analogous arguments. This approach, which has remained of central importance to the present, is the subject of the chapter. Second, in the past decade, efficient algorithms of a combinatorial nature for the computation of an approximate economic equilibrium were developed. Third, recently, the theory of the fixed-point index of a map and the degree theory of maps were used to establish the existence of an economic equilibrium, and finally a differential process was proposed whose generic convergence to an economic equilibrium provides an alternative constructive solution of the existence problem.

Chapter 15 Existence of competitive equilibrium

Publisher Summary Traditional general equilibrium theory has, for a long time, studied an economic model that is essentially static, where the agent's expectations are self-fulfilling and the equilibrium is achieved solely by the price system. The chapter presents the conceptual framework underlying temporary equilibrium models. This chapter discusses the central role played by an agent's expectations in his or her decision-making process. This model is the microeconomic foundation of the whole theory. A few models using the temporary competitive equilibrium method are also studied in the chapter. It is postulated that prices move fast enough in each period to match supply and demand. The first problem studied is the issue of the existence of an equilibrium in asset markets that is very important in any theory of financial markets. In the framework of a simple model, a necessary and sufficient condition for the existence of a competitive equilibrium in asset markets is some partial agreement among economic agents concerning expected future spot prices of these assets. The chapter studies the temporary equilibrium with the quantity rationing method and to the possible contributions of this approach to the theory of employment and inflation. The basic axiom of this approach is that in the short run, quantities adjust infinitely faster than prices. One is thus led to study a model where prices are temporarily fixed in each period and equilibrium is achieved by quantity rationing. The chapter also presents an evaluation of the equilibrium concepts used in this area.

V.K. Chetty

Papers

Temporary competitive equilibrium in a monetary economy with uncertain technology and many planning periods

Efficiency of temporary equilibria