Abstract
Continuity of the mapping from initial endowments and utilities to equilibria is an essential property for a desirable model of an economy – without continuity, small errors in the observation of parameters of the economy may lead to entirely different predicted equilibria.
We show that for the linear case of Fisher’s market model, the (unique) vector of equilibrium prices, is a continuous function of the initial amounts of money held by the agents, , and their utility functions, . Furthermore, the correspondence , giving the set of equilibrium allocations for any specified and , is upper hemicontinuous, but not lower hemicontinuous. However, for a fixed , this correspondence is lower hemicontinuous in .
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References
Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)
Brainard, W.C., Scarf, H.E.: How to compute equilibrium prices in 1891. Cowles Foundation Discussion Paper 1270 (2000)
Debreu, G.: Mathematical Economics: Twenty papers of Gerard Debreu. Cambridge University Press, Cambridge (1986)
Eisenberg, E., Gale, D.: Consensus of subjective probabilities: the Pari-Mutuel method. The Annals of Mathematical Statistics 30, 165–168 (1959)
Gale, D.: Theory of Linear Economic Models. McGraw-Hill, New York (1960)
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© 2007 Springer-Verlag Berlin Heidelberg
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Megiddo, N., Vazirani, V.V. (2007). Continuity Properties of Equilibrium Prices and Allocations in Linear Fisher Markets. In: Deng, X., Graham, F.C. (eds) Internet and Network Economics. WINE 2007. Lecture Notes in Computer Science, vol 4858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77105-0_39
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DOI: https://doi.org/10.1007/978-3-540-77105-0_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77104-3
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