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The Weak Axiom and Comparative Statics

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  • John Quah

Abstract

This paper examines conditions which guarantee that the excess demand function of an exchange economy will satisfy the weak axiom in an open neighborhood of a given equilibrium price. This property ensures that the equilibrium is locally stable with respect to Walras tatonnement. A related issue is the possibility of local comparative statics; in particular, the paper examines conditions which guarantee that when an economys endowment is perturbed, the equilibrium price will move in a direction opposite to that of the perturbation. A distinguishing feature of this papers approach is the heavy use of the indirect utility function, though we also provide results that allow for the translation of conditions imposed on indirect utility functions to conditions imposed on direct utility functions. Indeed we apply this to the special case of exchange economies were all agents have directly additive utilities - essentially a complete markets finance model with agents having von Neumann-Morgenstern utility functions. We show that the structural properties of demand near an equilibrium price depend on variations in the coefficient of relative risk aversion.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 1999-W15.

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Date of creation: 01 Jan 1999
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Handle: RePEc:oxf:wpaper:1999-w15

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Keywords: general equilibrium; demand; indirect utility; stability; risk aversion;

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References

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  1. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
  2. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 525-43, October.
  3. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
  4. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
  5. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
  6. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  7. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
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Cited by:
  1. Quah, John K.-H., 2008. "The existence of equilibrium when excess demand obeys the weak axiom," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 337-343, February.
  2. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.
  3. 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.
  4. 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.
  5. John Quah, 2001. "Comparative Statics of the Weak Axiom," Economics Papers 2001-W3, Economics Group, Nuffield College, University of Oxford.
  6. Michael Jerison, 2001. "Demand Dispersion, Metonymy and Ideal Panel Data," Discussion Papers 01-11, University at Albany, SUNY, Department of Economics.

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