Abstract
The purpose of this paper is to study the continuity and uniqueness properties of equilibria for linear exchange economies. We characterize the sets of utility vectors and initial endowments for which the equilibrium price is unique and respectively the set for which the equilibrium allocation is unique. We show that the equilibrium allocation correspondence is continuous with respect to the initial endowments and we characterize the set of full measure where the equilibrium allocation correspondence with respect to the initial endowments and utility vectors is continuous.
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References
Gale, D., Price Equilibrium for Linear Models of Exchange, Technical Report P-1156, The Rand Corporation, Santa Monica, California, 1957.
Gale, D., The Theory of Linear Economic Models, Academic Press, New York, NY, 1960.
Gale, D., The Linear Exchange Model, Journal of Mathematical Economics, Vol. 3, pp. 205–209, 1976.
Eaves, B. C., A Finite Algorithm for the Linear Exchange Model, Journal of Mathematical Economics, Vol. 3, pp. 197–203, 1976.
Cornet, B., Linear Exchange Economies, Cahier Eco-Math, CERMSEM, Université de Paris 1, Paris, France, 1989.
Mertens, J. F., The Limit Price Mechanism, CORE DP9650, Université Catholique Louvain-la-Neuve, 1996; Essays in Honour of Martin Shubik, Edited by P. Dubey and J. Geanakoplos (to appear).
Bonnisseau, J. M., and Florig, M., Oligopoly Equilibria in Large but Finite Linear Exchange Economies, Cahier Eco-Math, CERMSEM, Université de Paris 1, Paris, France, 1996.
Bonnisseau, J. M., Florig, M., and JofrÉ, A., Differentiability of Equilibria for Linear Exchange Economies, Journal of Optimization Theory and Applications, Vol. 109, pp. 265–288, 2001.
Champsaur, P., and Cornet, B., Walrasian Exchange Processes, Economic Decision-Making: Games, Econometrics, and Optimization, Edited by J. J. Gabszewicz, J. F. Richard, and L. A. Wolsey, Elsevier Science Publishers, New York, NY, 1990.
Bottazzi, J. M., Accessibility of Pareto Optima by Walrasian Exchange Processes, Journal of Mathematical Economics, Vol. 23, pp. 585–603, 1994.
Debreu, G., Smooth Preferences, Econometrica, Vol. 40, pp. 603–615, 1972.
Balasko, Y., Foundation of the Theory of General Equilibrium, Academic Press, New York, NY, 1988.
Jouini, E., Structure de l'Ensemble des Equilibres d'une Economie Non Convèxe, Annales de l'Institut Henri Poincaré, Analyse Non-Linéaire, Vol. 9, pp. 321–336, 1992.
Jouini, E., The Graph of the Walras Correspondence, Journal of Mathematical Economics, Vol. 22, pp. 139–147, 1993.
Mas-colell, A., The Theory of General Economic Equilibrium: A Differential Approach, Cambridge University Press, Cambridge, England, 1985.
Smale, S., Global Analysis and Economics, Chapter 8, Handbook of Mathematical Economics, Edited by K. Arrow and M. Intriligator, North-Holland, New York, NY, Vol. 2, pp. 331–370, 1981.
Cheng, H. C., Linear Economies Are “Gross Substitute” Systems, Journal of Economic Theory, Vol. 20, pp. 110–117, 1979.
Graham, R. L., Grotschel, M., and LovÁsz, L., Editors, Handbook of Combinatorics, Vol. 1, North-Holland_Elsevier, Amsterdam, Holland, 1995.
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BONNISSEAU, J.M., FLORIG, M. & JOFRÉ, A. Continuity and Uniqueness of Equilibria for Linear Exchange Economies. Journal of Optimization Theory and Applications 109, 237–263 (2001). https://doi.org/10.1023/A:1017517020329
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DOI: https://doi.org/10.1023/A:1017517020329