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On the geometry of luxury

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  • A. Mantovi

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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
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    References listed on IDEAS

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    1. Daniel L. McFadden, 2013. "The New Science of Pleasure," NBER Working Papers 18687, National Bureau of Economic Research, Inc.
    2. Hurwicz,Leonid & Reiter,Stanley, 2008. "Designing Economic Mechanisms," Cambridge Books, Cambridge University Press, number 9780521724104.
    3. 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.
    4. 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.
    5. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    6. Cornes,Richard, 1992. "Duality and Modern Economics," Cambridge Books, Cambridge University Press, number 9780521336017.
    7. Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, vol. 15(1), pages 31-39, January.
    8. Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, vol. 109(3), pages 303-313, July.
    9. 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.
    10. Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
    11. Andrea Mantovi, 2013. "On the commutativity of expansion and substitution effects," Journal of Economics, Springer, vol. 110(1), pages 83-105, September.
    12. Hicks, John, 1970. "Elasticity of Substitution Again: Substitutes and Complements," Oxford Economic Papers, Oxford University Press, vol. 22(3), pages 289-296, November.
    13. 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.
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    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;

    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

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