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α-Returns to scale and multi-output production technologies

Author

Listed:
  • Jean-Philippe Boussemart

    (UMR CNRS 8179 - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

  • Walter Briec

    (LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations - UPVD - Université de Perpignan Via Domitia)

  • Nicolas Peypoch

    (LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations - UPVD - Université de Perpignan Via Domitia)

  • Christophe Tavéra

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

Abstract

This contribution proposes a specification of strictly increasing and decreasing returns to scale in multioutput technologies. Along this line a notion of a-returns to scale is derived from that of homogeneous multi-output technology. For a large class of technologies we establish necessary and sufficient conditions characterizing strictly increasing and strictly decreasing returns to scale to scale. Furthermore, a relationship between input, output and graph distance functions is established. These connections lead naturally to a link between the various Malmquist indexes and the Chavas–Cox productivity index. Finally, we show that these concepts can be implemented in a DEA context using a piecewise homogeneous constant elasticity substitution–transformation model due to [Färe, R., Grosskopf, S., Njinkeu, D., 1988b. On piecewise reference technologies. Management Science 34, 1507–1511].

Suggested Citation

  • Jean-Philippe Boussemart & Walter Briec & Nicolas Peypoch & Christophe Tavéra, 2009. "α-Returns to scale and multi-output production technologies," Post-Print halshs-00418883, HAL.
    • Handle: RePEc:hal:journl:halshs-00418883
    DOI: 10.1016/j.ejor.2008.05.028
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    Citations

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    Cited by:

    1. Juan Aparicio & José L. Zofío, 2017. "Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 133-146, December.
    2. Hideyuki Mizobuchi, 2016. "A Superlative Index Number Formula for the Hicks-Moorsteen Productivity Index," CEPA Working Papers Series WP032016, School of Economics, University of Queensland, Australia.
    3. J-P Boussemart & W Briec & H Leleu, 2010. "Linear programming solutions and distance functions under α-returns to scale," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1297-1301, August.
    4. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    5. Laurens Cherchye & Timo Kuosmanen & Hervé Leleu, 2010. "Technical and Economic Efficiency Measures Under Short Run Profit Maximizing Behavior," Recherches économiques de Louvain, De Boeck Université, vol. 76(2), pages 163-173.
    6. Briec, Walter & Liang, Qi Bin, 2011. "On some semilattice structures for production technologies," European Journal of Operational Research, Elsevier, vol. 215(3), pages 740-749, December.
    7. Élisé Wendlassida Miningou & Medjy Pierre‐Louis & Jean‐Marc Bernard, 2022. "Improving learning outcomes in francophone Africa: More resources or improved efficiency?," African Development Review, African Development Bank, vol. 34(1), pages 127-141, March.
    8. Élisé Wendlassida Miningou, 2020. "Matching the Education System to the Needs of the Economy: Evidence from Burkina Faso," Cahiers de recherche 20-04, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    9. Sahoo, Biresh K & Khoveyni, Mohammad & Eslami, Robabeh & Chaudhury, Pradipta, 2016. "Returns to scale and most productive scale size in DEA with negative data," European Journal of Operational Research, Elsevier, vol. 255(2), pages 545-558.
    10. Rolf Färe & Giannis Karagiannis, 2022. "Aggregation and decomposition of Farrell efficiencies," Operational Research, Springer, vol. 22(5), pages 5675-5683, November.
    11. Sheng, Yu & Zhao, Shiji & Nossal, Katarina & Zhang, Dandan, 2015. "Productivity and farm size in Australian agriculture: reinvestigating the returns to scale," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 59(1), January.
    12. Hideyuki Mizobuchi, 2017. "A superlative index number formula for the Hicks-Moorsteen productivity index," Journal of Productivity Analysis, Springer, vol. 48(2), pages 167-178, December.
    13. Wanke, Peter & Barros, Carlos P. & Faria, João R., 2015. "Financial distress drivers in Brazilian banks: A dynamic slacks approach," European Journal of Operational Research, Elsevier, vol. 240(1), pages 258-268.
    14. Peter Wanke & Carlos Barros & Nkanga Pedro João Macanda, 2016. "Predicting Efficiency in Angolan Banks: A Two-Stage TOPSIS and Neural Networks Approach," South African Journal of Economics, Economic Society of South Africa, vol. 84(3), pages 461-483, September.

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