Subsistence, saturation and irrelevance in preferences

We present a microeconomic analysis of subsistence consumption in a standard consumer theory setting. We define 'subsistence and saturation induced irrelevance' (SSI) preferences for an individual who makes choices over two goods: a basic good and a non-basic good. The basic good has two key features: subsistence and saturation. We axiomatize SSI preferences using two key concepts: (i) 'irrelevance' of a good in a consumption bundle (increasing its amount does not make the consumer better off) and (ii) an 'unhappy set' (any bundle outside such a set is preferred to all bundles inside). SSI preferences more adequately represent the decision problem of the poor and give certain new insights on consumer behavior that are not captured by widely used utility functions such as Stone-Geary. We also axiomatize a generalized version of Leontief (GL) preferences, for which irrelevance is solely driven by complementarity.