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Generalized benefit functions and measurement of utility

Author

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  • Walter Briec
  • Philippe Gardères

Abstract

Luenberger [8] introduced the so-called benefit function that converts preferences into a numerical function that has some cardinal meaning. This measure has a number of remarkable properties and is a powerful tool in analyzing welfare issues ([10], [12], [13], [14]). This paper studies the conditions for a general function to make it a relevant welfare measure. Therefore, we introduce a large class of measures, called generalized benefit functions. The generalized benefit function is derived from the minimization of a convex function over the complement of a convex set. We show this class encompases as a special case the benefit function and is suitable to provide an alternative characterization of preferences. We also make a connection to the expenditure function through Fenchel duality theory and derive a duality result from Lemaire [7] for reverse convex optimization. Finally, we study the relationship between our class of functions and Hicksian compensated demand and we establish a link to the Slutsky matrix. Copyright Springer-Verlag 2004

Suggested Citation

  • Walter Briec & Philippe Gardères, 2004. "Generalized benefit functions and measurement of utility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(1), pages 101-123, September.
    • Handle: RePEc:spr:mathme:v:60:y:2004:i:1:p:101-123
    DOI: 10.1007/s001860200231
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    Citations

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    Cited by:

    1. Aparicio, Juan & Pastor, Jesus T. & Zofio, Jose L., 2015. "How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies," European Journal of Operational Research, Elsevier, vol. 240(3), pages 882-891.
    2. Juan Aparicio & Fernando Borras & Jesus T. Pastor & Jose L. Zofio, 2016. "Loss Distance Functions and Profit Function: General Duality Results," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor (ed.), Advances in Efficiency and Productivity, chapter 0, pages 71-96, Springer.
    3. Chavas, Jean-Paul, 2013. "On Demand Analysis and Dynamics: A Benefit Function Approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149683, Agricultural and Applied Economics Association.
    4. R. Russell & William Schworm, 2011. "Properties of inefficiency indexes on 〈input, output〉 space," Journal of Productivity Analysis, Springer, vol. 36(2), pages 143-156, October.
    5. Jean-Paul Chavas & Michele Baggio, 2010. "On duality and the benefit function," Journal of Economics, Springer, vol. 99(2), pages 173-184, March.
    6. Jean-Paul Chavas & Zohra Mechemache, 2006. "Efficiency measurements and the gains from trade under transaction costs," Journal of Productivity Analysis, Springer, vol. 26(1), pages 67-85, August.

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