Subsistence, saturation and irrelevance in preferences

This paper provides a microeconomic analysis of subsistence consumption in the consumer theory framework. Our key concepts are 'irrelevance' of a good in certain consumption bundles (increasing its amount does not make the consumer better off) and an 'unhappy set' (any bundle outside such a set is preferred to all bundles inside). Using these concepts we axiomatize subsistence and saturation induced irrelevance (SSI) preferences. We also axiomatize a generalized version of Leontief (GL) preferences, for which irrelevance is solely driven by complementarity. Irrelevance in SSI preferences results from the presence of unhappy sets; for GL preferences irrelevance is driven by their absence.