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The Weak Axiom and Comparative Statics

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  • John K.-H. Quah

    (Oxford University)

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 economy's endowment is perturbed, the equilibrium price will move in a direction opposite to that of the perturbation. A distinguishing feature of this paper's 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 where 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 Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0437.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0437

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References

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  1. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 525-43, October.
  2. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  3. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
  4. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
  5. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
  6. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
  7. 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.
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Cited by:
  1. 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.
  2. John Quah, 2001. "Comparative Statics of the Weak Axiom," Economics Series Working Papers 2001-W03, University of Oxford, Department of Economics.
  3. John Quah, 2004. "The existence of equilibrium when excess demand obeys the weak axiom," Economics Series Working Papers 2004-W07, University of Oxford, Department of Economics.
  4. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.
  5. Michael Jerison, 2001. "Demand Dispersion, Metonymy and Ideal Panel Data," Discussion Papers 01-11, University at Albany, SUNY, Department of Economics.
  6. 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.

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