Rolf Mantel and the Computability of General Equilibria: On the Origins of the Sonnenschein-Mantel-Debreu Theorem

In this brief paper we revise the original motivations of Rolf Mantel to pursue a proof of Sonnenschein´s conjecture. We contend that his work on computational models of general equilibrium lead him to seek an alternative to the usual fixed point theorems used in proofs of existence. Confronted with...

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Detalhes bibliográficos
Autor: Tohmé, Fernando Abel
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/96997
Acesso em linha:http://hdl.handle.net/11336/96997
Access Level:acceso abierto
Palavra-chave:General Equilibrium
Smd Theorem
Rolf Mantel
https://purl.org/becyt/ford/5.2
https://purl.org/becyt/ford/5
Descrição
Resumo:In this brief paper we revise the original motivations of Rolf Mantel to pursue a proof of Sonnenschein´s conjecture. We contend that his work on computational models of general equilibrium lead him to seek an alternative to the usual fixed point theorems used in proofs of existence. Confronted with a paper of Uzawa and his own experience in programming a national planning system he found that the use of theorems like Brouwer´s and Kakutani´s was unavoidable. To check out whether Uzawa was right he sought to find out whether the only properties required of excess demand functions to ensure the existence of equilibria in competitive markets were continuity, homogeneity and Walras´ law. In 1974, he found that this was actually the case. We will see that this result and his interpretation were informed by Mantel´s interest in economic development and planning.