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On the geometry of luxury


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  • A. Mantovi



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.

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Paper provided by Department of Economics, Parma University (Italy) in its series Economics Department Working Papers with number 2013-EP02.

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Length: 30
Date of creation: 2013
Date of revision:
Handle: RePEc:par:dipeco:2013-ep02

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Keywords: Duality; homotheticity; Cobb-Douglas function; luxury; expansion path; elasticity of substitution; scale effect; substitution effect; income effect; Shephard’s distance;

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  1. Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, Springer, vol. 15(1), pages 31-39, January.
  2. 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, American Economic Association, vol. 79(4), pages 882-88, September.
  3. Andrea Mantovi, 2013. "On the commutativity of expansion and substitution effects," Journal of Economics, Springer, Springer, vol. 110(1), pages 83-105, September.
  4. Bogetoft, Peter & Fare, Rolf, 1999. "Allocative Efficiency of Technically Inefficient Production Units," Unit of Economics Working papers, Royal Veterinary and Agricultural University, Food and Resource Economic Institute 24217, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
  5. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 64, University of Warwick, Department of Economics.
  6. Hicks, John, 1970. "Elasticity of Substitution Again: Substitutes and Complements," Oxford Economic Papers, Oxford University Press, vol. 22(3), pages 289-96, November.
  7. Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, Springer, vol. 109(3), pages 303-313, July.
  8. Hurwicz,Leonid & Reiter,Stanley, 2006. "Designing Economic Mechanisms," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521836418.
  9. Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, Springer, vol. 24(2), pages 183-196, October.
  10. Cornes,Richard, 1992. "Duality and Modern Economics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521336017.
  11. Chipman, John S & Moore, James C, 1980. "Compensating Variation, Consumer's Surplus, and Welfare," American Economic Review, American Economic Association, American Economic Association, vol. 70(5), pages 933-49, December.
  12. Daniel L. McFadden, 2013. "The New Science of Pleasure," NBER Working Papers 18687, National Bureau of Economic Research, Inc.
  13. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521314275.
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