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Biased quantitative measurement of interval ordered homothetic preferences

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Abstract

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.

Suggested Citation

  • Marc Le Menestrel & Bertrand Lemaire, 2004. "Biased quantitative measurement of interval ordered homothetic preferences," Economics Working Papers 789, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:789
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    1. Dow, James & da Costa Werlang, Sergio Ribeiro, 1992. "Homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 389-394.
    2. Bertrand Lemaire & Marc Le Menestrel, 2004. "Homothetic interval orders," Economics Working Papers 793, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
    4. Bridges, Douglas S., 1986. "Numerical representation of interval orders on a topological space," Journal of Economic Theory, Elsevier, vol. 38(1), pages 160-166, February.
    5. Gianni Bosi, 2002. "Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals," Theory and Decision, Springer, vol. 52(4), pages 303-312, June.
    6. Bosi, Gianni & Candeal, Juan Carlos & Indurain, Esteban, 2000. "Continuous representability of homothetic preferences by means of homogeneous utility functions," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 291-298, April.
    7. Oloriz, Esteban & Candeal, Juan Carlos & Indurain, Esteban, 1998. "Representability of Interval Orders," Journal of Economic Theory, Elsevier, vol. 78(1), pages 219-227, January.
    8. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    9. Candeal, J. C. & Indurain, E., 1995. "Homothetic and weakly homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 147-158.
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    More about this item

    Keywords

    Weak order; semiorder; interval order; intransitive indifference; independence; homothetic; representation; linear utility;

    JEL classification:

    • D00 - Microeconomics - - General - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • O22 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Project Analysis

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