Subsistence and substitutability in consumer preferences

We propose a formal description of individual preferences that captures a subsistence requirement in consumption in an otherwise standard constant-elasticity-of-substitution (CES) utility specification. We study how substitutability between the subsistence good and another good depends on the subsistence requirement and the level of consumption of the two goods. We find that the Hicksian elasticity of substitution is zero below the subsistence consumption level, and approaches the standard non-subsistence CES value as consumption of the subsistence good goes to infinity. Above the subsistence threshold, it strictly monotonically increases with income. Whether the two goods are market substitutes or complements depends on, besides the CES-substitutability parameter, the level of income and the subsistence requirement. Our result that with a subsistence requirement substitutability between different consumption goods is non-constant but increases with individual income has important implications for growth, development and environmental policy.