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Existence of closed and complete extensions applied to convex, homothetic an monotonic orderings

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T. DEMUYNCK ()

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Abstract

Many theories of consumer demand impose specific properties on the preference relations, e.g. convexity, monotonicity or homotheticity. Existing nonparametric tests which allow us to single out the preference relations that do not satisfy these properties are only valid in very specific contexts. This paper is an attempt to address this lacuna in the literature. We provide a theorem on the existence of complete binary extensions that satisfy properties which are closed under intersection. From this theorem we derive necessary and su_cient conditions for the existence of convex, homothetic and monotonic orderings on general domains.

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Paper provided by Ghent University, Faculty of Economics and Business Administration in its series Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium with number 06/407.

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Length: 25 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:rug:rugwps:06/407

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  1. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Upper Semicontinuous Extensions of Binary Relations," Cahiers de recherche 2002-01, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  2. Bossert, W. & Sprumont, Y., 2000. "Core Retionalizability in Two-Agent Exchange Economies," Cahiers de recherche 2000-09, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  3. Donaldson, David & Weymark, John A., 1998. "A Quasiordering Is the Intersection of Orderings," Journal of Economic Theory, Elsevier, vol. 78(2), pages 382-387, February. [Downloadable!] (restricted)
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  4. Bossert, W. & Sprumont, Y., 2001. "Non-Deteriorating Choice," Cahiers de recherche 2001-01, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  5. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November. [Downloadable!] (restricted)
  6. Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March. [Downloadable!] (restricted)
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