THE FIRST APPEARANCE OF THE ARROW-DEBREU EXISTENCE THEOREM ON COMPETITIVE EQUILIBRIUM

ARROW, Kenneth J. and DEBREU, Gerard. “Existence of an Equilibrium for a Competitive Economy.” IN: Econometrica, Volume 22, Number 3, pp. 265-90. Chicago, Illinois: Econometric Society, University of Chicago, July 1954. Octavo, original gray paper wrappers. Housed in a custom clamshell box. $3500.

First edition of the journal issue containing the first appearance of the groundbreaking article containing one of the first simple proofs of the existence of a competitive equilibrium, the Arrow-Debreu Existence Theorem, a major piece of the work for which Arrow and Debreu were awarded their Nobel Prizes in economics.

This journal contains the paper illustrating one of the first simple proofs of existence of a competitive equilibrium: the Arrow-Debreu Existence Theorem. “Each year, new economics Ph.D. students learn the proof of the existence of a competitive equilibrium as if a rite of passage… While there are a number of proofs that establish the existence of such an equilibrium, the validity of these proofs is indubitable. Indeed, economists with even scant knowledge of the history of economics can identify Kenneth J. Arrow and Gerard Debreu’s Econometrica paper as having provided the proof that settled the issue. That 1954 paper, ‘On the Existence of an Equilibrium for a Competitive Economy’ appeared to bring closure to an argument that was (at least) two centuries old… The Arrow-Debreu model was a major accomplishment; it presented an economy composed of individual self-interested agents—both utility maximizing households and profit equilibrium in which all choices were potentially reconciled. Put briefly, the pursuit of individual self-interest could lead not to social chaos but to a coordinated social order” (Weintraub & Gayer, 421-42). “Debreu and I both started applying Kakutani’s fixed point theorem to the problem of existence. In this case, we exchanged manuscripts in sufficient time to realize our common efforts and also to realize the need for relaxing an excessively severe assumption we had both made” (Arrow, Nobel Lecture 1972). “In our article of 1954, Arrow and I cast a competitive economy in the form of a social system of the preceding type. The agents are the consumers, the producers, and a fictitious price-setter. An appropriate definition of the set of reactions of the price-setter to an excess demand vector makes the concept of equilibrium for that social system equivalent to the concept of competitive equilibrium for the original economy. In this manner a proof of existence, resting ultimately on Kakutani’s theorem, was obtained for an equilibrium of an economy made up of interacting consumers and producers. In the early fifties, the time had undoubtedly come for solutions of the existence problem” (Debreu, Nobel Lecture 1983). The Nobel Prize was ultimately awarded to Hicks and Arrow in 1972 “for their pioneering contributions to general economic equilibrium theory and welfare theory.” It was awarded to Debreu in 1983 “for having incorporated new analytical methods into economic theory and for his rigorous reformulation of the theory of general equilibrium.” Owner stamp on front wrapper of Vanderbilt University economics professor Fred M. Westfield. Westfield did a great deal of work on public utilities and regulatory policy and did consulting work with governments, major organizations, and companies around the world.

Slight crease to corner of journal, only minor rubbing and toning to extremities. A near-fine copy.