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More on the Fox paradox

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  • Karagiannis, Giannis

Abstract

This paper shows that the compatibility between efficiency measures and the aggregation procedure is not enough to resolve the Fox paradox when different inputs are employed in each activity. We explicitly illustrate this point by considering the additive aggregation of cost efficiency indicators for production and advertising activities, which use different inputs. Then, the overall cost efficiency indicator is given by the weighted (rather than the simple) sum of the production and the advertising cost efficiency indicators. The reason is that the value of the directional vector used to normalize the difference between the minimum and the observed cost in each activity-based efficiency indicator will differ.

Suggested Citation

  • Karagiannis, Giannis, 2012. "More on the Fox paradox," Economics Letters, Elsevier, vol. 116(3), pages 333-334.
    • Handle: RePEc:eee:ecolet:v:116:y:2012:i:3:p:333-334
    DOI: 10.1016/j.econlet.2012.04.002
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    References listed on IDEAS

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    1. Fare, Rolf & Grosskopf, Shawna & Seldon, Barry J. & Tremblay, Victor J., 2004. "Advertising efficiency and the choice of media mix: a case of beer," International Journal of Industrial Organization, Elsevier, vol. 22(4), pages 503-522, April.
    2. Peyrache, Antonio & Coelli, Tim, 2009. "Testing procedures for detection of linear dependencies in efficiency models," European Journal of Operational Research, Elsevier, vol. 198(2), pages 647-654, October.
    3. Seldon, Barry J. & Jewell, R. Todd & O'Brien, Daniel M., 2000. "Media substitution and economies of scale in advertising," International Journal of Industrial Organization, Elsevier, vol. 18(8), pages 1153-1180, December.
    4. Fox, Kevin J., 1999. "Efficiency at different levels of aggregation: public vs. private sector firms," Economics Letters, Elsevier, vol. 65(2), pages 173-176, November.
    5. Fare, Rolf & Grosskopf, Shawna, 2000. "Outfoxing a paradox," Economics Letters, Elsevier, vol. 69(2), pages 159-163, November.
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    Cited by:

    1. Mosnier, Claire & Boukhriss, Sanae & Minviel, Jean-Joseph, 2023. "Does pig production improves cattle farm sustainability in the French massif central? A hierarchical constrained directional benefit-of-the-doubt approach," Agricultural Systems, Elsevier, vol. 210(C).

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    More about this item

    Keywords

    Efficiency measurement; Aggregation; Cost efficiency indicator;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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