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The Aggregate Weak Axiom in a Financial Economy through Dominant Substitution Effects

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  • John Quah

Abstract

Consider a two period financial economy with incomplete markets and with agents having von Neumann-Morgenstern utility functions. It is well known that when the economy’s endowments are collinear, its excess demand function will obey the weak axiom when certain mild restrictions are imposed on agents’ coefficient of relative risk aversion. This result is obtained through the application of a theorem on the law of demand (for individual demand) formulated independently by Milleron (1974), and Mitjuschin and Polterovich (1978). In this paper, we develop their arguments further and apply them to economies without collinear endowments. We identify conditions which guarantee that the economy’s excess demand function obeys the weak axiom near an equilibrium price. Keywords: income effects, substitution effects, monotonicity, law of demand, weak axiom.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2004-W18.

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Date of creation: 01 Jul 2004
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Handle: RePEc:oxf:wpaper:2004-w18

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Keywords: income effects; substitution effects; monotonicity; law of demand; weak axiom.;

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  1. Hens, Thorsten & Loeffler, Andras, 1995. "Gross substitution in financial markets," Economics Letters, Elsevier, vol. 49(1), pages 39-43, July.
  2. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
  3. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
  4. Michael Jerison, 1998. "Dispersed Excess Demands, the Weak Axiom and Uniqueness of Equilibrium," Discussion Papers 98-03, University at Albany, SUNY, Department of Economics.
  5. John H. Nachbar, 2002. "General Equilibrium Comparative Statics," Econometrica, Econometric Society, vol. 70(5), pages 2065-2074, September.
  6. John Quah, 2002. "The Law of Demand and Risk Aversion," Economics Series Working Papers 2002-W03, University of Oxford, Department of Economics.
  7. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
  8. Nachbar, John H., 2004. "General equilibrium comparative statics: discrete shocks in production economies," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 153-163, February.
  9. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
  10. repec:rus:hseeco:94360 is not listed on IDEAS
  11. Bettzuge, Marc Oliver, 1998. "An extension of a theorem by Mitjushin and Polterovich to incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 285-300, October.
  12. Quah, John K. -H., 2003. "Market demand and comparative statics when goods are normal," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 317-333, June.
  13. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
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