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On an "important principle" of arrow and Debreu

  • In their seminal 1954 paper on the existence of competitive equilibrium, Arrow and Debreu state what they call an “important principle”, namely that it is necessary for the existence of equilibrium that every consumer has some asset or can supply some labour service which has a positive price at equilibrium. It does not seem to have been noticed that this claim is incorrect. We provide a very simple model of a private ownership economy with three goods where a competitive equilibrium exists, but consumers who have nothing to sell but their labour end up with zero wealth in equilibrium. As zero wealth must be taken to mean non-survival, and the Arrow–Debreu model is frequently interpreted as assuming that all consumers can survive without trade, we also briefly discuss the issue of non-survival in equilibrium. We finally point out that our example illustrates the possibility that technological progress may result in a situation where the value of work becomes negligible.

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Document Type:Article
Author:Arnis VilksORCiD
Chairs and Professorships:Chair of Microeconomics
Parent Title (English):The B.E. Journal of Theoretical Economics
Place of publication:Berlin
Publisher:Walter de Gruyter
Year of Completion:2021
First Page:621
Last Page:627
Tag:Arrow-Debreu model; Competitive equilibrium; Irreducibility; Robots; Survival without trade
Content Focus:Academic Audience
Peer Reviewed:Yes
Rankings:AJG Ranking / 2
Licence (German):License LogoUrheberrechtlich geschützt