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Weak Axiomatic Demand Theory

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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File URL: http://www.nuff.ox.ac.uk/economics/papers/2000/w12/nuffJQ.pdf
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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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Web page: http://www.economics.ox.ac.uk/
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  1. Fishburn, Peter C, 1991. " Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-34, April.
  2. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
  3. Michael Jerison, 1998. "Dispersed Excess Demands, the Weak Axiom and Uniqueness of Equilibrium," Discussion Papers 98-03, University at Albany, SUNY, Department of Economics.
  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. 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.
  7. 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.
  8. Laurent E. Calvet & Etienne Comon, 2000. "Behavioral Heterogeneity and The Income Effect," Harvard Institute of Economic Research Working Papers 1892, Harvard - Institute of Economic Research.
  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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