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Homotheticity and Non-Radial Changes

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  • Robert Chambers
  • Thomas Mitchell

Abstract

Färe and Mitchell(1992) have shown that cost functions for a multi-output firmobey a particular output-scaling law if and only if the underlyingproduction technology is ray-homothetic. Multi-output firms,however, frequently change their output mix in addition to theirscale. Therefore, it is important to identify technologies thatpossess relatively tractable analytical characteristics whensubjected to non-radial changes in the output vector. This paperconsiders additive and other, more general, changes in the outputvector. One result shows that the cost function obeys an ``output-translationlaw'' if and only if the input correspondence is input homothetic,thus suggesting that ``input homotheticity'' is more than justan ``input-scaling'' property. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, vol. 15(1), pages 31-39, January.
    • Handle: RePEc:kap:jproda:v:15:y:2001:i:1:p:31-39
    DOI: 10.1023/A:1026543822945
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    Cited by:

    1. Tone, Kaoru & Sahoo, Biresh K., 2003. "Scale, indivisibilities and production function in data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 84(2), pages 165-192, May.
    2. 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.
    3. Chen, Po-Chi & Yu, Ming-Miin & Chang, Ching-Cheng & Hsu, Shih-Hsun & Managi, Shunsuke, 2015. "The enhanced Russell-based directional distance measure with undesirable outputs: Numerical example considering CO2 emissions," Omega, Elsevier, vol. 53(C), pages 30-40.
    4. Aparicio, Juan & Cordero, Jose M. & Pastor, Jesus T., 2017. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects," Omega, Elsevier, vol. 71(C), pages 1-10.
    5. 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.
    6. Aparicio, Juan & Zofío, José L., 2021. "Economic cross-efficiency," Omega, Elsevier, vol. 100(C).
      • Aparicio, J. & Zofío, J.L., 2019. "Economic Cross-Efficiency," ERIM Report Series Research in Management ERS-2019-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Sahoo, Biresh K. & Luptacik, Mikulas & Mahlberg, Bernhard, 2011. "Alternative measures of environmental technology structure in DEA: An application," European Journal of Operational Research, Elsevier, vol. 215(3), pages 750-762, December.
    8. Andrea Mantovi, 2013. "On the commutativity of expansion and substitution effects," Journal of Economics, Springer, vol. 110(1), pages 83-105, September.
    9. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2017. "Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration," European Journal of Operational Research, Elsevier, vol. 259(2), pages 576-586.
    10. Aparicio, Juan & Mahlberg, Bernhard & Pastor, Jesus T. & Sahoo, Biresh K., 2014. "Decomposing technical inefficiency using the principle of least action," European Journal of Operational Research, Elsevier, vol. 239(3), pages 776-785.
    11. A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).
    12. King, Robert P. & Park, Timothy A., 2002. "Modeling Scale Economies In Supermarket Operations: Incorporating The Impacts Of Store Characteristics And Information Technologies," 2002 Annual meeting, July 28-31, Long Beach, CA 19881, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    14. Aparicio, Juan & Cordero, Jose M. & Gonzalez, Martin & Lopez-Espin, Jose J., 2018. "Using non-radial DEA to assess school efficiency in a cross-country perspective: An empirical analysis of OECD countries," Omega, Elsevier, vol. 79(C), pages 9-20.
    15. Colin Glass, J. & McCallion, Gillian & McKillop, Donal G. & Rasaratnam, Syamarlah & Stringer, Karl S., 2006. "Implications of variant efficiency measures for policy evaluations in UK higher education," Socio-Economic Planning Sciences, Elsevier, vol. 40(2), pages 119-142, June.
    16. Andrea Mantovi, 2014. "On Luxury and Equilibrium," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 6(2), pages 87-118, December.
    17. Sahoo, Biresh K. & Tone, Kaoru, 2009. "Decomposing capacity utilization in data envelopment analysis: An application to banks in India," European Journal of Operational Research, Elsevier, vol. 195(2), pages 575-594, June.
    18. Aparicio, Juan & Borras, Fernando & Pastor, Jesus T. & Vidal, Fernando, 2013. "Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA," European Journal of Operational Research, Elsevier, vol. 231(2), pages 443-451.
    19. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).

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