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Dual Representations Of Strongly Monotonic Utility Functions


  • Sudhir A. Shah

    (Department of Economics, Delhi School of Economics, Delhi, India)


We present theorems that establish dualities, i.e., bijections, be- tween speci¯ed sets of direct utility functions, indirect utility functions and expenditure functions. The substantive properties characterizing the speci¯ed set of direct utility functions are strong monotonicity, upper semicontinuity and quasi-concavity. Our results are strictly in- termediate between two classes of analogous results in the literature. We also provide applications that use all the three classes of duality results.

Suggested Citation

  • Sudhir A. Shah, 2007. "Dual Representations Of Strongly Monotonic Utility Functions," Working papers 161, Centre for Development Economics, Delhi School of Economics.
  • Handle: RePEc:cde:cdewps:161

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    References listed on IDEAS

    1. Jackson, Matthew O., 1986. "Continuous utility functions in consumer theory : A set of duality theorems," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 63-77, February.
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    Cited by:

    1. Alexander Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series Ec-04/16, European University at St. Petersburg, Department of Economics.

    More about this item


    Direct utility function; indirect utility function; ex-penditure function; duality; strong monotonicity;

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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