Economic Theory

, Volume 29, Issue 3, pp 677–699 | Cite as

Weak axiomatic demand theory

  • John K-H. QuahEmail author
Research Article


This paper identifies a class of complete but not necessarily transitive preferences which generate demand functions that obey the weak axiom of revealed preference and within which any function obeying the weak axiom can be rationalized.


Weak axiom of revealed preference Violations of transitivity Rationalizability Demand 

JEL Classification Numbers

C61 D11 D50 


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  1. Al-Najjar N.(1993) Non-transitive smooth preferences. J Econ Theory 60: 14–41CrossRefGoogle Scholar
  2. Aliprantis, C., Border, K.: Infinite dimensional analysis (2nd ed.): Berlin Heidelberg New York Springer 1999Google Scholar
  3. Bandyophadhyay T., Dasgupta I., Pattanaik P.(1999) Stochastics revealed preference and the theory of demand. J Econ Theory 84: 95–110CrossRefGoogle Scholar
  4. Bonnisseau J.-M.(2003) Regular economies with non-ordered preferences. J Math Econ 39: 153–174CrossRefGoogle Scholar
  5. Calvet L., Comon E. (2000) Behavioral heterogeneity and the income effect. Working paper 1892, Harvard Institute of Economic Research. Rev Econ Stat (to appear)Google Scholar
  6. Clark S. (1988). An extension theorem for rational choice functions. Review of Economic Studies, LV: 485–492Google Scholar
  7. Debreu G. (1959) Theory of value. Yale University Press, New Haven LondonGoogle Scholar
  8. Debreu, G.: Existence of competitive equilibrium. In: Arrow, K.J., Intriligator, M.D. (eds.) Handbook of mathematical economics, vol. II. New York: North-Holland 1982Google Scholar
  9. Fishburn P.C. (1991) Nontransitive preferences in decision theory. J Risk Uncertainty 4: 113–134CrossRefGoogle Scholar
  10. Hildenbrand W. (1994) Market demand. Princeton. Princeton University Press, NJGoogle Scholar
  11. Jerison M. (1999). Dispersed excess demands, the weak axiom and uniqueness of equilibrium. J Math Econ 31: 15–48CrossRefGoogle Scholar
  12. Kihlstrom R., Mas-Colell A., Sonnenschein H. (1976). The demand theory of the weak axiom of revealed preference. Econometrica 44: 971–978CrossRefGoogle Scholar
  13. Kim T., Richter M. (1986) Nontransitive-nontotal consumer theory. J Econ Theory 38: 324–363CrossRefGoogle Scholar
  14. Kivetz R., Simonson I. (2000)The effects of incomplete information on consumer choice. J Marketing Res 37: 427–448CrossRefGoogle Scholar
  15. Loomes G., Starmer C., Sugden R. (1991) Observing violations of transitivity by experimental methods. Econometrica 59: 425–439MathSciNetCrossRefGoogle Scholar
  16. Mas-Colell A. (1985). The theory of general economic equilibrium: a differentiable approach. Cambridge University Press, CambridgeGoogle Scholar
  17. Mas-Colell A., Whinston M.D., Green J.R. (1995) Microeconomic theory. Oxford University Press, OxfordGoogle Scholar
  18. Moldau J.H. (1996) A simple existence proof of demand functions without standard transitivity. J Math Econ 25:325–333CrossRefGoogle Scholar
  19. Quah J.K.-H. (1997). The law of demand when income is price dependent. Econometrica 65: 1421–1442MathSciNetCrossRefGoogle Scholar
  20. Quah J.K.-H. (2000). The monotonicity of individual and market demand. Econometrica 68: 911–930CrossRefGoogle Scholar
  21. Quah, J.K.-H.: The existence of equilibrium when excess demand obeys the weak axiom. Nuffield College Working Paper, 2004-W7Google Scholar
  22. Shafer W. (1974). The nontransitive consumer. Econometrica 42: 913–920CrossRefGoogle Scholar
  23. Sonnenschein, H.: Demand theory without transitive preferences, with applications to the theory of competitive equilibrium. In: Chipman, J.S. et al. (eds.) Preferences, utiliity and demand theory. New York: Harcourt Brace Jovanovich 1971Google Scholar
  24. Tversky A. (1969). Intransitivity of preferences. Psychol Rev 76: 31–48CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Economics, Oxford UniversityOxfordUK

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