IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-00447417.html
   My bibliography  Save this paper

Complementarity and Substitutability: A Dual Approach Based on Luenberger's Benefit Function

Author

Listed:
  • Jean-Michel Courtault

    (CEPN - Centre d'Economie de l'Université Paris Nord (ancienne affiliation) - UP13 - Université Paris 13 - CNRS - Centre National de la Recherche Scientifique)

  • Bertrand Crettez

    (LIBRE - Laboratoire interdisciplinaire bisontin de recherches économiques - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Naïla Hayek

    (Marin Mersenne - Pour les Mathématiques, l'Informatique et l'Interdisciplinarité - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

This paper presents another definition of substitutes and complements. It follows a dual approach using the Luenberger's benefit function. The benefit function measures the amount of a reference bundle that an individual would be willing to give up to move from a given utility level to any bundle. Therefore the benefit function associates to any bundle of goods another bundle that lies on a given indifference curve. This enables one to derive an inverse demand function which is defined as the support price of this associated bundle. The classification of goods between complements and substitutes is then obtained by the comparative static properties of the support price. We present some examples which show that the proposed classification is different from the one obtained with another dual approach based on Deaton's distance function.

Suggested Citation

  • Jean-Michel Courtault & Bertrand Crettez & Naïla Hayek, 2008. "Complementarity and Substitutability: A Dual Approach Based on Luenberger's Benefit Function," Working Papers halshs-00447417, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00447417
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00447417
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00447417/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Keith R. McLaren & K. K. Gary Wong, 2009. "The Benefit Function Approach to Modeling Price-Dependent Demand Systems: An Application of Duality Theory," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(4), pages 1110-1123.
    2. repec:ebl:ecbull:v:4:y:2004:i:5:p:1-6 is not listed on IDEAS
    3. Bertrand Crettez & Naila Hayek & Jean-Michel Courtault, 2004. "On the differentiability of the benefit function," Economics Bulletin, AccessEcon, vol. 4(5), pages 1-6.
    4. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
    5. Färe, Rolf & Grosskopf, Shawna & Hayes, Kathy J. & Margaritis, Dimitris, 2008. "Estimating demand with distance functions: Parameterization in the primal and dual," Journal of Econometrics, Elsevier, vol. 147(2), pages 266-274, December.
    6. Angus Deaton, 1979. "The Distance Function in Consumer Behaviour with Applications to Index Numbers and Optimal Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(3), pages 391-405.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raphaël Giraud, 2012. "Money matters: an axiomatic theory of the endowment effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 303-339, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chavas, Jean-Paul, 2013. "On Demand Analysis and Dynamics: A Benefit Function Approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149683, Agricultural and Applied Economics Association.
    2. Jean-Paul Chavas & Michele Baggio, 2010. "On duality and the benefit function," Journal of Economics, Springer, vol. 99(2), pages 173-184, March.
    3. Di Peng & Haibin Liu, 2023. "Marginal Carbon Dioxide Emission Reduction Cost and Influencing Factors in Chinese Industry Based on Bayes Bootstrap," Sustainability, MDPI, vol. 15(11), pages 1-19, May.
    4. Chambers, Robert & Färe, Rolf & Grosskopf, Shawna & Vardanyan, Michael, 2013. "Generalized quadratic revenue functions," Journal of Econometrics, Elsevier, vol. 173(1), pages 11-21.
    5. Feng, Guohua & Serletis, Apostolos, 2014. "Undesirable outputs and a primal Divisia productivity index based on the directional output distance function," Journal of Econometrics, Elsevier, vol. 183(1), pages 135-146.
    6. Guohua Feng & Chuan Wang & Apostolos Serletis, 2018. "Shadow prices of $$\hbox {CO}_{2}$$ CO 2 emissions at US electric utilities: a random-coefficient, random-directional-vector directional output distance function approach," Empirical Economics, Springer, vol. 54(1), pages 231-258, February.
    7. Valentin Zelenyuk, 2011. "A Scale Elasticity Measure for Directional Distance Function and its Dual," CEPA Working Papers Series WP062011, School of Economics, University of Queensland, Australia.
    8. Bellenger, Moriah J. & Herlihy, Alan T., 2010. "Performance-based environmental index weights: Are all metrics created equal?," Ecological Economics, Elsevier, vol. 69(5), pages 1043-1050, March.
    9. Matsushita, Kyohei & Yamane, Fumihiro, 2012. "Pollution from the electric power sector in Japan and efficient pollution reduction," Energy Economics, Elsevier, vol. 34(4), pages 1124-1130.
    10. Flavius Badau & Nicholas Rada, 2022. "Disequilibrium effects from misallocated markets: An application to agriculture," Agricultural Economics, International Association of Agricultural Economists, vol. 53(4), pages 592-604, July.
    11. Hovhannisyan, Vardges & Stiegert, Kyle W. & Bozic, Marin, 2013. "On Endogeneity Of Retail Market Power In An Equilibrium Analysis: A Control Function Approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149830, Agricultural and Applied Economics Association.
    12. Debdatta Pal & Subrata K. Mitra, 2018. "The efficiency of microfinance institutions with problem loans: A directional distance function approach," Computational and Mathematical Organization Theory, Springer, vol. 24(3), pages 285-307, September.
    13. Badau, Flavius & Färe, Rolf & Gopinath, Munisamy, 2016. "Global resilience to climate change: Examining global economic and environmental performance resulting from a global carbon dioxide market," Resource and Energy Economics, Elsevier, vol. 45(C), pages 46-64.
    14. Yuan, Peng & Pu, Yuran & Liu, Chang, 2021. "Improving electricity supply reliability in China: Cost and incentive regulation," Energy, Elsevier, vol. 237(C).
    15. Zhiqian Yu & Ning Zhu & Tomas Baležentis, 2017. "Impact of Public Education and Regional Economic Growth in China: A Shadow-Price Perspective," Sustainability, MDPI, vol. 9(8), pages 1-10, July.
    16. Quintano, Claudio & Mazzocchi, Paolo & Rocca, Antonella, 2021. "Evaluation of the eco-efficiency of territorial districts with seaport economic activities," Utilities Policy, Elsevier, vol. 71(C).
    17. Tai-Hsin Huang & Yi-Huang Chiu & Chih-Ying Mao, 2021. "Imposing Regularity Conditions to Measure Banks’ Productivity Changes in Taiwan Using a Stochastic Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 273-303, June.
    18. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    19. H Fukuyama & W L Weber, 2009. "Estimating indirect allocative inefficiency and productivity change," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1594-1608, November.
    20. Pei-Ing Wu & Je-Liang Liou & Hung-Yi Chang, 2015. "Alternative exploration of EKC for $$\hbox {CO}_{2}$$ CO 2 emissions: inclusion of meta-technical ratio in quantile regression model," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(1), pages 57-73, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-00447417. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.