Abstract
This survey paper has three purposes: We first present in finite dimension, different approaches to the problem of uniqueness of Arrow-Debreu equilibrium when agents have additively separable utilities. We then study how, in the specific framework of a two period contingent good economy the results obtained generalize to infinite dimension. We consider economies where agents’ consumption space is L p+ (μ) 1 ≤ p ≤ ∞ and agents’ utilities are additively separable. Lastly, we show that in some restricted settings, some results may be used to prove uniqueness of Arrow-Radner equilibria when there are incomplete financial markets.
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References
Dana, R.A. (1993) Existence and uniqueness of equilibria when preferences are additively separable and gross substitute. Econometrica 61: 953–957
Dana, R.A. (1995) An extension of Milleron, Mitjushin and Polterovich’s result. Journal of Mathematical Economics 24: 259–269
Greenberg, I. (1977) An elementary proof of existence of a competitive equilibrium with weak gross substitute. Quaterly Journal of Economics 91 (4): 513–516
Karatsas, I.; Shreve, S.E. (1998) Methods of Mathematical Finance. Springer, Berlin Heidelberg New York
Kehoe, T.J.; Levine, D.K. (1985) Comparative statics and perfect foresight in infinite horizon economies. Econometrica 53: 433–453
Magill, M.; Quinzii, M. (1996) Theory of Incomplete markets. MIT Press, Cambridge, London
Mas-Colell, A. (1991) On the uniqueness of equilibrium once again. In: Barnet, W.A.; Cornet, B.;d’Aspremont, C.; Gabszewicz, I.; Mas-Colell, A. (eds.) Equilibrium theory and applications.Cambridge University Press, Cambridge
Mas-Colell, A.; Zame, W. (1991) Equilibrium theory in infinite dimensional spaces. Handbook of Mathematical Economics, n°4
Mas-Colell, A. (1985) The theory of general economic equilibrium: a differentiable approach. Econometric Soc.Monograph, Cambridge University Press, Cambridge
Milleron, J.C. (1974) Unicité et stabilité de l’équilibre en économie de distribution. Séminaire d’Econométrie Roy-Malinvaud, mars 1974 (preprint)
Mitjushin, L.G.; Polterovich, V.W (1978) Criteria for monotonicity of demand functions (in Russian). Ekonomika i Matematicheskie Metody 14: 122–128
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Dana, RA. (2003). Uniqueness of Arrow-Debreu and Arrow-Radner equilibrium when utilities are additively separable. In: Ichiishi, T., Marschak, T. (eds) Markets, Games, and Organizations. Studies in Economic Design. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24784-5_3
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DOI: https://doi.org/10.1007/978-3-540-24784-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53465-2
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