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Weak Axiomatic Demand Theory

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  • John Quah

Abstract

This paper gives a unified and simple treatment of three related questions in the demand theory of the weak axiom: (i) Is there an elementary, i.e., non-fixed point theoretic, proof of equilibrium existence when the excess demand function of an economy satisfies the weak axiom? (ii) What conditions are sufficient for a non-transitive preference to generate a continuous demand function? Note that such a demand must satisfy the weak, though not necessarily the strong, axiom. This motivates the next question. (iii) Given a function that satisfies the weak axiom, can we find a (non necessarily transitive) preference that generates it? To answer this first question, we give a proof using the separating hyperplane theorem. With the help of this result, we identify a class of non-transitive preferences which generate continuous demand functions, and within which any demand function satisfying the weak axiom can be rationalized.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2000-W12.

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Date of creation: 01 Jan 2000
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Handle: RePEc:oxf:wpaper:2000-w12

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Keywords: weak axiom; representative agent; transitive preferences; rationalizability; demand function;

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References

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  1. 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.
  2. Jerison, Michael, 1999. "Dispersed excess demands, the weak axiom and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 15-48, February.
  3. Bandyopadhyay, Taradas & Dasgupta, Indraneel & Pattanaik, Prasanta K., 1999. "Stochastic Revealed Preference and the Theory of Demand," Journal of Economic Theory, Elsevier, vol. 84(1), pages 95-110, January.
  4. Al-Najjar Nabil, 1993. "Non-transitive Smooth Preferences," Journal of Economic Theory, Elsevier, vol. 60(1), pages 14-41, June.
  5. Loomes, Graham & Starmer, Chris & Sugden, Robert, 1991. "Observing Violations of Transitivity by Experimental Methods," Econometrica, Econometric Society, vol. 59(2), pages 425-39, March.
  6. Laurent Calvet & Etienne Comon, 2003. "Behavioral Heterogeneity and the Income Effect," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 653-669, August.
  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.
  8. Fishburn, Peter C, 1991. " Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-34, April.
  9. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
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Citations

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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. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
  3. Hans Keiding & Mich Tvede, 2013. "Revealed smooth nontransitive preferences," Economic Theory, Springer, vol. 54(3), pages 463-484, November.
  4. Hosoya, Yuhki, 2013. "Measuring utility from demand," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 82-96.
  5. Gerasimou, Georgios, 2009. "Consumer theory with bounded rational preferences," MPRA Paper 18673, University Library of Munich, Germany, revised 16 Nov 2009.
  6. Brighi, Luigi, 2004. "A stronger criterion for the Weak Weak Axiom," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 93-103, February.
  7. Indraneel Dasgupta, . "Revealed Preference with Stochastic Demand Correspondence," Discussion Papers 07/06, University of Nottingham, School of Economics.

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