IDEAS home Printed from https://ideas.repec.org/p/par/dipeco/2013-ep02.html
   My bibliography  Save this paper

On the geometry of luxury

Author

Listed:
  • A. Mantovi

Abstract

A 2-parameter class of ordinal utility functions over a pair of goods is discussed with respect to general traits of preferences for luxury. The class contains Cobb-Douglas functions as no-luxury limit; its analytical tractability is probed by simple closed form solutions for Marshallian demand functions, expansion paths, Engel curves, income elasticity of demand, saturation levels, elasticity of substitution. Following Mantovi (2013), scale and substitution effects can be represented in terms of flows on bundle space; departure from homotheticity can thereby be represented by an index of luxury which measures the noncommutativity of such effects. On conceptual grounds, our index is intimately connected with Shephard’s distance. Decompositions of productive efficiency as tailored by Bogetoft et al. (2006) represent a natural setting for the application of our approach.

Suggested Citation

  • A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).
  • Handle: RePEc:par:dipeco:2013-ep02
    as

    Download full text from publisher

    File URL: http://www.swrwebeco.unipr.it/RePEc/pdf/I_2013-02.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Daniel L. McFadden, 2013. "The New Science of Pleasure," NBER Working Papers 18687, National Bureau of Economic Research, Inc.
    2. Bogetoft, Peter & Fare, Rolf & Obel, Borge, 2006. "Allocative efficiency of technically inefficient production units," European Journal of Operational Research, Elsevier, vol. 168(2), pages 450-462, January.
    3. Hurwicz,Leonid & Reiter,Stanley, 2008. "Designing Economic Mechanisms," Cambridge Books, Cambridge University Press, number 9780521724104, September.
    4. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    5. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    6. Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, vol. 109(3), pages 303-313, July.
    7. Andrea Mantovi, 2013. "On the commutativity of expansion and substitution effects," Journal of Economics, Springer, vol. 110(1), pages 83-105, September.
    8. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, September.
    9. Hicks, John, 1970. "Elasticity of Substitution Again: Substitutes and Complements," Oxford Economic Papers, Oxford University Press, vol. 22(3), pages 289-296, November.
    10. Peter Moffatt & Keith Moffatt, 2011. "Mirror utility functions and reflexion properties of various classes of goods," University of East Anglia Applied and Financial Economics Working Paper Series 031, School of Economics, University of East Anglia, Norwich, UK..
    11. Chipman, John S & Moore, James C, 1980. "Compensating Variation, Consumer's Surplus, and Welfare," American Economic Review, American Economic Association, vol. 70(5), pages 933-949, December.
    12. Cornes,Richard, 1992. "Duality and Modern Economics," Cambridge Books, Cambridge University Press, number 9780521336017, September.
    13. Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, vol. 15(1), pages 31-39, January.
    14. Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
    Full references (including those not matched with items on IDEAS)

    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. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).
    2. Andrea Mantovi, 2016. "Smooth preferences, symmetries and expansion vector fields," Journal of Economics, Springer, vol. 119(2), pages 147-169, October.
    3. 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.
    4. Andrea Mantovi, 2013. "On the commutativity of expansion and substitution effects," Journal of Economics, Springer, vol. 110(1), pages 83-105, September.
    5. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, vol. 36(1), pages 79-89, August.
    6. Stern, David I., 2010. "Derivation of the Hicks, or direct, elasticity of substitution using the input distance function," Economics Letters, Elsevier, vol. 108(3), pages 349-351, September.
    7. Paul, Saumik, 2019. "A Decline in Labor's Share with Capital Accumulation and Complementary Factor Inputs: An Application of the Morishima Elasticity of Substitution," IZA Discussion Papers 12219, Institute of Labor Economics (IZA).
    8. Frédéric Reynès, 2011. "The cobb-douglas function as an approximation of other functions," SciencePo Working papers Main hal-01069515, HAL.
    9. Paolo Bertoletti & Giorgio Rampa, 2011. "On Marginal Returns and Inferior Inputs," Quaderni di Dipartimento 145, University of Pavia, Department of Economics and Quantitative Methods.
    10. Giulia BETTIN & Alessia LO TURCO & Daniela MAGGIONI, 2011. "A firm level perspective on migration," Working Papers 360, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    11. Ma, Chunbo & Stern, David I., 2016. "Long-run estimates of interfuel and interfactor elasticities," Resource and Energy Economics, Elsevier, vol. 46(C), pages 114-130.
    12. Javier Calatrava & Alberto Garrido, 2005. "Spot water markets and risk in water supply," Agricultural Economics, International Association of Agricultural Economists, vol. 33(2), pages 131-143, September.
    13. repec:spo:wpmain:info:hdl:2441/1cpd872l2j8lb968d53pu5f30q is not listed on IDEAS
    14. Fuller, Frank H., 1999. "Farm-Level Feed Demand In Turkey," 1999 Annual meeting, August 8-11, Nashville, TN 21534, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Ariu, Andrea & Müller, Tobias & Nguyen, Tuan, 2023. "Immigration and the Slope of the Labor Demand Curve: The Role of Firm Heterogeneity in a Model of Regional Labor Markets," CEPR Discussion Papers 18091, C.E.P.R. Discussion Papers.
    16. Farsi, Mehdi & Filippini, Massimo, 2009. "An analysis of cost efficiency in Swiss multi-utilities," Energy Economics, Elsevier, vol. 31(2), pages 306-315, March.
    17. Frédéric Reynès, 2017. "The Cobb-Douglas function as a flexible function. Analysing the substitution between capital, labor and energy," Documents de Travail de l'OFCE 2017-12, Observatoire Francais des Conjonctures Economiques (OFCE).
    18. Dawei Zhang & Zhuo (June) Cheng & Hasan A. Qurban H. Mohammad & Barrie R. Nault, 2015. "Research Commentary—Information Technology Substitution Revisited," Information Systems Research, INFORMS, vol. 26(3), pages 480-495, September.
    19. Lundmark, Robert & Olsson, Anna, 2015. "Factor substitution and procurement competition for forest resources in Sweden," International Journal of Production Economics, Elsevier, vol. 169(C), pages 99-109.
    20. Alarcón, Silverio, 2005. "Input Substitution in the Spanish Food Industry," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24487, European Association of Agricultural Economists.
    21. Parenti, Mathieu & Ushchev, Philip & Thisse, Jacques-François, 2017. "Toward a theory of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 167(C), pages 86-115.

    More about this item

    Keywords

    Duality; homotheticity; Cobb-Douglas function; luxury; expansion path; elasticity of substitution; scale effect; substitution effect; income effect; Shephard’s distance;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:par:dipeco:2013-ep02. 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: Andrea Lasagni (email available below). General contact details of provider: https://edirc.repec.org/data/feparit.html .

    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.