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Identification of individual demands from market data under uncertainty

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Carvajal, Andrés M. and Riascos, Alvaro. (2008) Identification of individual demands from market data under uncertainty. B.E. Journal of Theoretical Economics, Vol.8 (No.1). pp. 1-30. ISSN 1935-1704

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Official URL: http://dx.doi.org/10.2202/1935-1704.1420

Abstract

We show that, even under incomplete markets, the equilibrium manifold identifies individual demands everywhere in their domains. Under partial observation of the manifold, we determine maximal subsets of the domains on which identification holds. For this, we assume conditions of smoothness, interiority and regularity. It is crucial that there be date-zero consumption. As a by-product, we develop some duality theory under incomplete markets.

Item Type: Journal Article
Subjects: H Social Sciences > HB Economic Theory
Divisions: Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH): Consumer economics, Incomplete markets, Equilibrium (Economics)
Journal or Publication Title: B.E. Journal of Theoretical Economics
Publisher: Berkeley Electronic Press
ISSN: 1935-1704
Date: 2008
Volume: Vol.8
Number: No.1
Page Range: pp. 1-30
Identification Number: 10.2202/1935-1704.1420
Status: Not Peer Reviewed
Access rights to Published version: Open Access
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References: Balasko, Y. (2004). The equilibrium manifold keeps the memory of individual demand functions. Economic Theory 24, 493-501. Blanks, J., Blundell, R. and Lewbel, A. (1997). Quadratic Engel Curves and consumer demand. Review of Economics and Statististics 79, 527-539. Brown, D. and Matzkin, R. (1996). Testable restrictions on the equilibrium manifold. Econometrica 64, 1249-1262. Carvajal, A., Ray, I. and Snyder, S. (2004). Equilibrium behavior in markets and games: testable restrictions and identification. Journal of Mathematical Econonomics 40, 1-40. Carvajal, A. and Riascos, A. (2005). Identification of preferences from market data. Advances in Theoretical Economics 5, issue 1, art 3. Carvajal, A. and Polemarchakis, H. (2008). Identification of Pareto-improving policies: information as the real invisible hand, Journal of Mathematical Economics 44, 167-179. Chiappori, P.-A., Ekeland, I., K¨ubler, F. and Polemarchakis, H., 2002. The identification of preferences from equilibrium prices. CORE Discussion Paper 2000/24. Chiappori, P.-A., Ekeland, I., Kübler, F. and Polemarchakis, H., 2004. Testable implications of general equilibrium theory: a differentiable approach. Journal of Mathematical Econonomics 40, 105-120. Donsimoni, M.-P. and Polemarchakis, H. (1994). Redistribution and welfare. Journal of Mathematical Econonomics 23, 235-242. Duffie, D. and Shafer, W. (1985). Equilibrium in incomplete markets: I. A basic model of generic existence. Journal of Mathematical Econonomics 14, 285-300. Geanakoplos, J. and Heal, G. (1983). A geometric explanation of the transfer paradox in a stable economy. Journal of Development Economics 13, 223-226. Geanakoplos, J. and Polemarchakis, H. (1986). Existence, regularity and constrained suboptimality of competitive allocations when assets structure is incomplete, Essays in honor of K.J. Arrow, W. Heller, R. Starr and D. Starret (Eds), Vol 3, 65-95, Cambridge. Geanakoplos, J. and Polemarchakis, H. (1990). Observability and optimality. Journal of Mathematical Econonomics 19, 153-165. Kübler, F. (2003). Observable restrictions of general equilibrium models with financial markets. Journal of Economic Theory 110, 137-153. Kübler, F., Chiappori, P.-A., Ekeland, I., and Polemarchakis, H. (2002). The identification of preferences from equilibrium prices under uncertainty. Journal of Economic Theory 102, 403-420. Lewbel, A. (2003). A rational rank four demand system. Journal of Applied Econometrics 18, 127-135. Magill, M. and Shafer, W. (1991). Incomplete markets. In W. Hildenbrand and H. Sonnenschein (Eds.) Handbook of Mathematical Economics, Vol. 4, 1523-1610. Mas-Colell, A., M. Whinston and J. Green. (1995). Microeconomic theory. Oxford University Press. Matzkin, R. (2005). Identification of consumers’ preferences when their choices are unobservable. Economic Theory 25, 423-443. Michael, E. (1956). Continuous selections, I. Annals of Mathematics 63, 361-382.
URI: http://wrap.warwick.ac.uk/id/eprint/31

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