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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| 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 |
| 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. |
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