On the geometry of luxury
AbstractA 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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Bibliographic InfoPaper provided by Department of Economics, Parma University (Italy) in its series Economics Department Working Papers with number 2013-EP02.
Date of creation: 2013
Date of revision:
Duality; homotheticity; Cobb-Douglas function; luxury; expansion path; elasticity of substitution; scale effect; substitution effect; income effect; Shephard’s distance;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-24 (All new papers)
- NEP-MIC-2013-06-24 (Microeconomics)
- NEP-UPT-2013-06-24 (Utility Models & Prospect Theory)
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