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The existence of equilibrium when excess demand obeys the weak axiom

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  • John Quah

Abstract

This paper gives a non-fixed point theoretic proof of equilibrium existence when the excess demand function of an exchange economy obeys the weak axiom. The proof is simple and geometrically intuitive, and it also permits a weakening of the continuity assumption on the excess demand function. (This paper is a more developed and (one hopes) improved version of an earlier working paper entitled An Elementary Equilibrium Existence Theorem, Working Paper W6 (2000), Nuffield College, Oxford.)

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2004/w7/demandobeys.pdf
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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2004-W07.

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Date of creation: 01 Feb 2004
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Handle: RePEc:oxf:wpaper:2004-w07

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Keywords: weak axiom; Gale-Nikaido-Debreu Lemma; existence of equilibrium; violations of transitivity;

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References

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  1. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers 06-07, University at Albany, SUNY, Department of Economics.
  2. John K.-H. Quah, 2000. "The Weak Axiom and Comparative Statics," Econometric Society World Congress 2000 Contributed Papers 0437, Econometric Society.
  3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  4. John Quah, 2006. "Weak axiomatic demand theory," Economic Theory, Springer, vol. 29(3), pages 677-699, November.
  5. 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.
  6. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
  7. Michael Jerison, 1998. "Dispersed Excess Demands, the Weak Axiom and Uniqueness of Equilibrium," Discussion Papers 98-03, University at Albany, SUNY, Department of Economics.
  8. John H. Nachbar, 2002. "General Equilibrium Comparative Statics," Econometrica, Econometric Society, vol. 70(5), pages 2065-2074, September.
  9. Reinhard John, 1999. "Abraham Wald's equilibrium existence proof reconsidered," Economic Theory, Springer, vol. 13(2), pages 417-428.
  10. Barbolla, Rosa & Corchon, Luis C, 1989. "An Elementary Proof of the Existence of a Competitive Equilibrium in a Special Case," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 385-89, May.
  11. 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.
  12. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September.
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Citations

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Cited by:
  1. Frayssé, Jean, 2009. "A simple proof of the existence of an equilibrium when the weak axiom holds," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 767-769, December.
  2. John Quah, 2000. "Weak Axiomatic Demand Theory," Economics Series Working Papers 2000-W12, University of Oxford, Department of Economics.
  3. Mackowiak, Piotr, 2010. "The existence of equilibrium without fixed-point arguments," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1194-1199, November.
  4. Ruscitti, Francesco, 2012. "On the boundary behavior of the excess demand function," Research in Economics, Elsevier, vol. 66(4), pages 371-374.

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