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α-Returns to scale and multi-output production technologies

Author

Listed:
  • Jean-Philippe Boussemart

    (LEM - Lille - Economie et Management - 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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Rolf Färe & Giannis Karagiannis, 2022. "Aggregation and decomposition of Farrell efficiencies," Operational Research, Springer, vol. 22(5), pages 5675-5683, November.
    13. 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.
    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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