Metric Distance Function and Profit: Some Duality Results

W. Briec and J. B. Lesourd
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W. Briec: Université de Rennes 1
J. B. Lesourd: Groupement de Recherche en Economis Quantitative d'Aix-Marseille II

Journal of Optimization Theory and Applications, 1999, vol. 101, issue 1, No 2, 15-33

Abstract: Abstract In this paper, we intend to establish relations between the way efficiency is measured in the literature on efficiency analysis and the notion of distance in topology. To this effect, we are interested particularly in the Hölder norm concept, providing a duality result based upon the profit function. Along this line, we prove that the Luenberger shortage function and the directional distance function of Chambers, Chung, and Färe appear as special cases of some l p distance (also called Hölder distance), under the assumption that the production set is convex. Under a weaker assumption (convexity of the input correspondence), we derive a duality result based on the cost function, providing several examples in which the functional form of the production set is specified.

Keywords: Technical efficiency; production microeconomics; metric distance function; profit function; shortage function; efficiency measure; duality (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (31)

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DOI: 10.1023/A:1021762809393

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