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On the geometry of luxury

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  • 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
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    References listed on IDEAS

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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;
    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

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