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Duality Theory of Non-convex Technologies

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  • Timo Kuosmanen

Abstract

Duality Theory of production imposes a number of simplifying assumptions regarding the production technology, including various maintained convexity assumptions. Emphasizing the technological information content of alternative models, this paper challenges some widely held views on the role of convexity. The role of convexity in Duality Theory is asymmetric. While convexity is of importance in recovering technology information from economic models, cost functions are concave and profit functions are convex irrespective of convexity of the underlying technology. For recovering technology information from economic models and data, we discuss two alternative approaches: recovering inexact outer-bound approximations; and enriching standard economic models by additional quantity/financial constraints. The main conclusion is that non-convexities should not stop one from applying the Duality Theory. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Timo Kuosmanen, 2003. "Duality Theory of Non-convex Technologies," Journal of Productivity Analysis, Springer, vol. 20(3), pages 273-304, November.
  • Handle: RePEc:kap:jproda:v:20:y:2003:i:3:p:273-304
    DOI: 10.1023/A:1027399700108
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    9. Timo Kuosmanen & Thierry Post, 2002. "Nonparametric Efficiency Analysis under Price Uncertainty: A First-Order Stochastic Dominance Approach," Journal of Productivity Analysis, Springer, vol. 17(3), pages 183-200, May.
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    Cited by:

    1. Feng, Guohua & Serletis, Apostolos, 2010. "Efficiency, technical change, and returns to scale in large US banks: Panel data evidence from an output distance function satisfying theoretical regularity," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 127-138, January.
    2. Abad, Arnaud & Briec, Walter, 2019. "On the axiomatic of pollution-generating technologies: Non-parametric production analysis," European Journal of Operational Research, Elsevier, vol. 277(1), pages 377-390.
    3. Roberto Esposti, 2003. "Public R&D investment and cost structure in Italian agriculture, 1960--1995," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 30(4), pages 509-537, December.
    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. Vrankić Ilko & Krpan Mira, 2016. "Pseudoproduction, Pseudocost and Profit Functions in Monopoly from the Dual Perspective," Business Systems Research, Sciendo, vol. 7(2), pages 49-64, September.
    6. Sahoo, Biresh K. & Tone, Kaoru, 2013. "Non-parametric measurement of economies of scale and scope in non-competitive environment with price uncertainty," Omega, Elsevier, vol. 41(1), pages 97-111.
    7. Halkos, George & Sundström, Aksel & Tzeremes, Nickolaos, 2013. "Environmental performance and quality of governance: A non-parametric analysis of the NUTS 1-regions in France, Germany and the UK," MPRA Paper 48890, University Library of Munich, Germany.
    8. Ferreira, D.C. & Marques, R.C. & Nunes, A.M., 2018. "Economies of scope in the health sector: The case of Portuguese hospitals," European Journal of Operational Research, Elsevier, vol. 266(2), pages 716-735.
    9. Kuosmanen, Timo, 2006. "Stochastic Nonparametric Envelopment of Data: Combining Virtues of SFA and DEA in a Unified Framework," Discussion Papers 11864, MTT Agrifood Research Finland.
    10. Ehrgott, Matthias & Tind, Jørgen, 2009. "Column generation with free replicability in DEA," Omega, Elsevier, vol. 37(5), pages 943-950, October.
    11. Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, vol. 168(2), pages 340-344, January.
    12. Kuosmanen, Timo & Cherchye, Laurens & Sipilainen, Timo, 2006. "The law of one price in data envelopment analysis: Restricting weight flexibility across firms," European Journal of Operational Research, Elsevier, vol. 170(3), pages 735-757, May.
    13. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2016. "Congestion in production correspondences," Journal of Economics, Springer, vol. 119(1), pages 65-90, September.
    14. Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.
    15. Victor Podinovski, 2004. "Efficiency and Global Scale Characteristics on the “No Free Lunch” Assumption Only," Journal of Productivity Analysis, Springer, vol. 22(3), pages 227-257, November.
    16. Kuosmanen, Timo & Kortelainen, Mika & Sipiläinen, Timo & Cherchye, Laurens, 2010. "Firm and industry level profit efficiency analysis using absolute and uniform shadow prices," European Journal of Operational Research, Elsevier, vol. 202(2), pages 584-594, April.
    17. Kumar, Surender & Managi, Shunsuke, 2016. "Carbon-sensitive productivity, climate and institutions," Environment and Development Economics, Cambridge University Press, vol. 21(1), pages 109-133, February.
    18. Fukuyama, Hirofumi & Shiraz, Rashed Khanjani, 2015. "Cost-effectiveness measures on convex and nonconvex technologies," European Journal of Operational Research, Elsevier, vol. 246(1), pages 307-319.
    19. Timo Kuosmanen & Thierry Post & Timo Sipiläinen, 2004. "Shadow Price Approach to Total Factor Productivity Measurement: With an Application to Finnish Grass-Silage Production," Journal of Productivity Analysis, Springer, vol. 22(1), pages 95-121, July.
    20. Eskelinen, Juha & Kuosmanen, Timo, 2013. "Intertemporal efficiency analysis of sales teams of a bank: Stochastic semi-nonparametric approach," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5163-5175.
    21. Podinovski, Victor V. & Kuosmanen, Timo, 2011. "Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions," European Journal of Operational Research, Elsevier, vol. 211(3), pages 577-585, June.
    22. Barnabé Walheer, 2020. "Output, input, and undesirable output interconnections in data envelopment analysis: convexity and returns-to-scale," Annals of Operations Research, Springer, vol. 284(1), pages 447-467, January.
    23. Timo Kuosmanen & Mika Kortelainen & Timo Sipiläinen & Laurens Cherchye, 2005. "Firm and Industry Level Profit Efficiency Analysis Under Incomplete Price Data: A Nonparametric Approach based on Absolute and Uniform Shadow Prices," Microeconomics 0509011, University Library of Munich, Germany.
    24. Michael L. Polemis & Thanasis Stengos & Nickolaos G. Tzeremes, 2020. "Modeling the effect of competition on US manufacturing sectors’ efficiency: an order-m frontier analysis," Journal of Productivity Analysis, Springer, vol. 54(1), pages 27-41, August.
    25. Frederic Ang & Simon M. Mortimer & Francisco J. Areal & Richard Tiffin, 2018. "On the Opportunity Cost of Crop Diversification," Journal of Agricultural Economics, Wiley Blackwell, vol. 69(3), pages 794-814, September.

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