On the Non-existence of Equilibrium: From Thornton to Arrow

Takashi Negishi

Chapter 10 in Arrow and the Ascent of Modern Economic Theory, 1987, pp 361-374 from Palgrave Macmillan

Abstract: Abstract Among the many contributions to economic science made by Arrow, one of the most important is certainly the proof of the existence of an equilibrium for a competitive economy.1 The case where no equilibrium exists even though indifference curves, production functions, and so on, are fairly well behaved is a useful one to show the necessity of proving the existence of equilibrium. Mill (1869) indicates that one of the first examples of the non-existence of equilibrium consists of the counter examples to equilibrium theory given in W. T. Thornton’s On Labour (1869) though Thornton himself was concerned not so much with the non-existence of equilibrium as the possibility of trade at disequilibrium prices. The Thornton-Mill examples of the non-existence of equilibrium are remarkable because they are due to the discontinuity of demand curves; other unsuccessful attempts to show the non-existence of equilibrium failed because of their assumption of continuity. The Thornton-Mill examples, as well as the example of Wald (1951), are, however, not so serious to equilibrium theory, if we consider, not the Walrasian tâtonnement with recontract, but the non-tâtonnement without recontract. From such non-tâtonnement point of view, a truly important example of the non-existence of equilibrium is the one given by Arrow, that is, the case where a Pareto optimal allocation cannot be viewed as a competitive equilibrium.2

Keywords: Demand Curve; Pareto Optimum; Competitive Equilibrium; Supply Curve; Indifference Curve (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations: View citations in EconPapers (1)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-1-349-07239-2_10

Ordering information: This item can be ordered from
http://www.palgrave.com/9781349072392

DOI: 10.1007/978-1-349-07239-2_10

Access Statistics for this chapter

More chapters in Palgrave Macmillan Books from Palgrave Macmillan
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().