Identification of the Conditions for Increasing Dimensionality of the Income Expansion Path

This paper determines sufficient conditions for a utility function to be associated with an income expansion path whose dimensionality increases with income i.e. given a finite number of products, the relationship between income and dimensionality of the consumption vector is given by a step function such that successive intervals on the real number line (each real number gives an income level) map on to consumption vectors of increasing dimensionality. This constitutes an important investigation as the rich are observed to exhibit greater consumption variety than the poor and the same household exhibits increasing product variety as its income increases over time.