On the Geometry of Luxury

A class of transcendental preferences is employed as an explicit representation of the luxurynecessity dichotomy which admits a smooth Cobb- Douglas limit. The analytical tractability of the model enables us to represent explicitly Marshallian demand and income elasticity of demand. The noncommutativity of scale and substitution effects, and measured by Lie brackets of the corresponding vector fields, is employed in order to define a measure of deviation from scale symmetry which is profoundly connected with Shephard’s distance.