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Existence of a Walrasian Equilibrium in Locally Convex Topological Vector Spaces, with Interdependent Utility Functions
Facultad de Economía de la UASLP, San Luis Potosi, Mexico
Facultad de Economía de la UASLP, San Luis Potosi, Mexico
Facultad de Economía de la UASLP, San Luis Potosi, Mexico
- 1 Facultad de Economía de la UASLP, San Luis Potosi, Mexico
- 2 Facultad de Economía de la UASLP, San Luis Potosi, Mexico
- 3 Facultad de Economía de la UASLP, San Luis Potosi, Mexico
Theoretical Economics Letters·Volume 07 (2016)·Pages 35–48·Published 13 December 2016·DOI10.4236/tel.2017.71005
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Abstract
In this paper we extend the well known result of existence of Walrasian equilibrium given in Debreu (1952) to economies modeled over topological vector spaces. Our work is closely related to the previous results of Yannelis-Pranhakar (1983), and Tan and Yuan (1999), but unlike these papers we prove the existence of a Walrasian equilibrium in infinite dimensional economies with interdependent and price-dependent utilities.
KeywordsPseudo GamesGeneralized EconomiesTopological Vector SpacesWalrasian Equilibrium
- Debreu, G. (1952) A Social Equilibrium Existence Theorem. Proceedings of the National Academy of Sciences of the United States of America, 38, 886-893. https://doi.org/10.1073/pnas.38.10.886
- Accinelli, E. (2002) Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry. In: Petri, F. and Hahn, F., Eds., General Equilibrium: Problems and Perspectives, Routledge Siena Studies in Political Economy Ch. 1, 35-57.
- Yannelis, N.C. and Prabhakar, N.D. (1983) Existence of Maximal Elements and Equilibrium in Linear Topological Spaces. Journal of Mathematical Economics, 12, 233-245. https://doi.org/10.1016/0304-4068(83)90041-1
- Shafer, W. and Sonnenschein, H. (1975) Equilibrium in Abstract Economies without Ordered Preferences. Journal of Mathematical Economics, 2, 345-348. https://doi.org/10.1016/0304-4068(75)90002-6
- Tian, G. (1992) Existence of Equilibrium in Abstract Economies with Discontinuous Payoffs and Non-Compact Choice Spaces. Journal of Mathematical Economics, 21, 379- 388. https://doi.org/10.1016/0304-4068(92)90015-Y
- Araujo, A. (1985) Pareto Optimal Allocations in Economies with Infinitely Many Commodities. The Need of Impatient. Econometrica, 53, 455-461. https://doi.org/10.2307/1911245
- Mas-Colell, A. (1974) An Equilibrium Existence Theorem without Complete or Transitive Preferences. Journal of Mathematical Economics, 1, 237-246. https://doi.org/10.1016/0304-4068(74)90015-9
- Chichilnisky, G. (1993) The Cone Condition, Properness, and Extremely Desirable Commodities. Economic Theory, 3, 1177-1182. https://doi.org/10.1007/BF01213700
- Narici, L. and Beckenstein, E. (2011) Topological Vector Spaces. 2nd Edition, CRC Press.
- Berge, C. (1957) Two Theorems in Graph Theory. Proceedings of the National Academy of Sciences of the United States of America, 43, 842-844. https://doi.org/10.1073/pnas.43.9.842
- Kakutani, S. (1941) A Generalization of Brower’s Fixed Point Theorem. Duke Mathematical Journal, 8, 457-459. https://doi.org/10.1215/S0012-7094-41-00838-4
- Aliprantis, C.D., Brown, D.J and Burkinshaw, O. (1990) Existence and Optimality of Competitive Equilibrium. Springer-Verlag. https://doi.org/10.1007/978-3-642-61521-4
- Brown, D.J. and Lewis, L.M. (1989) Myopic Economic Agents. Econometrica, 49, 359-368. https://doi.org/10.2307/1913315