Pareto Optima and Equilibria: The Finite Dimensional Case

Abstract

We aim at a succint presentation of the finite-dimensional mathematical theory associated with the so-called fundamental theorems of welfare economics. Very roughly these assert that, under some conditions, every price equilibrium is an optimum in the sense of Pareto and, conversely, under other (typically stronger) hypotheses, every optimum is a price equilibrium. This is a classical area of the theory of general economic equilibrium and it has been the object of extensive mathematical economic research. We refer to Debreu (1959, Ch. 7), Arrow and Hahn (1971, Ch. 4) and Mas-Colell (1985, Ch. 4) for systematic accounts.

A first iteration of this paper was presented at the Conference on General Equilibrium Theory celebrated at Indiana University-Purdue University at Indianapolis on February 10–12, 1984. I am indebted to its organizer, C. D. Aliprantis, for the opportunity and to the participants for their comments. Explicit mention to L. Jones is due. Financial support from N. S. F. is gratefully acknowledged.