Chichilnisky, Graciela (1980): Continuous representation of preference. Published in: Review of Economic Studies , Vol. 47, (1980): pp. 959-963.
Download (1MB) | Preview
In this paper we study a utility representation for preferences, and we price its continuity, using a topology for preferences introduced by Chichilnisky (1977). Such utility representations were constructed under restrictive conditions first by Y. Kannai and S. Reiter (1974, 1975). Our results are related more closely to those of Mount and Reiter (1974 and 1975). Starting from restrictive conditions these works have attempted to enlarge the class of preferences that could be continuously represented. The class of preferences studied here is much larger than those considered earlier, and it therefore applies to a wider class of problems. Our preferences include ones which are not necessarily convex or monotone, and which may be locally satiated; furthermore, no completeness of preferences is required. The assumption made by Mount and Reiter (1975) of the existence of an E-threshold is also not required here. These results are possible due to properties of the order topology introduced in Chichilnisky (1977). As we shall now discuss, this topology has quite desirable features for the study of preferences, and these now make it a natural choice for the problem at hand.
|Item Type:||MPRA Paper|
|Original Title:||Continuous representation of preference|
|Keywords:||preferences utility; utilities; continuity; topology|
|Subjects:||D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles|
|Depositing User:||Graciela Chichilnisky|
|Date Deposited:||03. Apr 2008 04:49|
|Last Modified:||13. Feb 2013 15:27|
CHICHILNISKY, G., (1977), "Spaces of Economic Agents", Journal of Economic Theory, 16 (1), 160-173.
DEBREU, G. (1969), "Neighboring Economic Agents", Las Decision, 85-90 (Paris: Editions du Centre National de la Recherche Scientifique).
HALMOS, P. (1950) Measure theory (Princeton: Van Nostrand, Inc,).
HILDENBRAND, W. (1970), "On Economies with Many Agents", Journal of Economic Theory, 2 (2), 161-187.
HILDENBRAND, W. (1974) Core equilibria of a large economy (princeton: Iniv. Press).
KANNAI, Y. (1970), "Continuous properties of the core of a market", Econometrica, 38 (6), 791-815.
MAS-COLELL, A. (1976), "On the continuous representation of pre-orders" (mimeo).
MICHAEL, E. (1956), "Continuous selections I", Annals of Mathematics, 63 (2), 361-382.
MOUNT, K AND REITER, A. (1974), "Continuous representations of preferences" (discussion paper number 81, Center for Math. Studies in Econ. and Management Sci., Northwestern Univ.).
MOUNT, K. AND REITER, S. (1975), "Construction of a continuous utility function for a class of preferences", Journal of Math. Econ. (forthcoming).
NEUFFEIND, W. (1972), "On continuous utility", Journal of Econ. Theory, 5, 174-176.