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A Dual Measure of Economies of Scope

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Abstract
Information on the economies of scope (or cost complementarities) between two or more output variables is traditionally obtained from the second derivative properties of an econometrically estimated multi-output cost function. However, in some instances the econometric estimation of a cost function may not be viable, because cost or input price data are not readily available or because the assumption of cost minimising behaviour is not appropriate in the industry at hand, perhaps due to government ownership or regulatory controls. In this paper we address this issue by utilising the duality between the cost and input distance functions in deriving an expression for a measure of economies of scope in terms of the derivatives of an input distance function. We derive expressions for the special cases of the CES and translog functional forms, and then provide an empirical illustration using sample data on Australian aged care facilities, an industry which is currently undergoing a major pricing and regulatory review. Our empirical results indicate that there is some evidence for existence of economies of scope between high care and low care patients, a result which is of particular interest to policy makers in this industry.

Suggested Citation

  • Gholamreza Hajargasht & Tim Coelli & D. S. Prasada Rao, 2006. "A Dual Measure of Economies of Scope," CEPA Working Papers Series WP032006, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:22
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    File URL: https://economics.uq.edu.au/files/5076/WP032006.pdf
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    1. Maria Olivares & Heike Wetzel, 2014. "Editor's Choice Competing in the Higher Education Market: Empirical Evidence for Economies of Scale and Scope in German Higher Education Institutions," CESifo Economic Studies, CESifo Group, vol. 60(4), pages 653-680.
    2. Jiro Nemoto & Noriko Furumatsu, 2014. "Scale and scope economies of Japanese private universities revisited with an input distance function approach," Journal of Productivity Analysis, Springer, vol. 41(2), pages 213-226, April.
    3. Roberto Mosheim & Robin C. Sickles, 2021. "Spatial effects of nutrient pollution on drinking water production," Empirical Economics, Springer, vol. 60(6), pages 2741-2764, June.
    4. Färe, Rolf & Karagiannis, Giannis, 2018. "Inferring scope economies from the input distance function," Economics Letters, Elsevier, vol. 172(C), pages 40-42.
    5. Swetlana Renner & Thomas Glauben & Heinrich Hockmann, 2014. "Measurement and decomposition of flexibility of multi-output firms," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 41(5), pages 745-773.
    6. Ofori-Bah, Adeline & Asafu-Adjaye, John, 2011. "Scope economies and technical efficiency of cocoa agroforesty systems in Ghana," Ecological Economics, Elsevier, vol. 70(8), pages 1508-1518, June.
    7. Swetlana Renner & Thomas Glauben & Heinrich Hockmann & Pierre Ouellette, 2015. "Primal and dual multi-output flexibility measures," Journal of Productivity Analysis, Springer, vol. 44(2), pages 127-136, October.
    8. Nonthakot, Phanin & Fleming, Euan M. & Villano, Renato A., 2008. "An Assessment of the Impact of Strategic Alliances in Food Processing on the Technical Efficiency of Housewives Groups in Thailand," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44411, European Association of Agricultural Economists.
    9. Villano, Renato & Fleming, Euan & Fleming, Pauline, 2010. "Evidence of farm-level synergies in mixed-farming systems in the Australian Wheat-Sheep Zone," Agricultural Systems, Elsevier, vol. 103(3), pages 146-152, March.
    10. Singbo, Alphonse G. & Emvalomatis, Grigorios & Alfons, Oude Lansink, 2013. "Assessing the impact of crop specialization on farms’ performance in vegetables farming in Benin: a non-neutral stochastic frontier approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149172, Agricultural and Applied Economics Association.
    11. A. Wondemu Kifle, 2016. "Working Paper 237 - Decomposing Sources of Productivity Change in Small-Scale Farming in Ethiopia," Working Paper Series 2332, African Development Bank.
    12. Robertson R.B. Khataza & Atakelty Hailu & Graeme J. Doole & Marit E. Kragt & Arega D. Alene, 2019. "Examining the relationship between farm size and productive efficiency: a Bayesian directional distance function approach," Agricultural Economics, International Association of Agricultural Economists, vol. 50(2), pages 237-246, March.
    13. Karanki, Fecri & Bilotkach, Volodymyr & Gao, Yi & Lu, Chien-Tsung, 2024. "The economic impact of E-commerce on the U.S. airports: Cost savings and productivity growth," Journal of Air Transport Management, Elsevier, vol. 118(C).
    14. Wimmer, Stefan G. & Sauer, Johannes, 2017. "The Economic Benefits of Farm Diversification: An Empirical Analysis of Economies of Scope Using the Dual Approach," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258465, Agricultural and Applied Economics Association.
    15. Renner, Swetlana & Hockmann, Heinrich & Glauben, Thomas, 2011. "Measuring flexibility of multi-output firms: a primal and a dual measure," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114797, European Association of Agricultural Economists.

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