Collective Household Welfare and Intra-household Inequality

We investigate the relationship between the individual and household indirect utility functions in the context of a collective household model. Our analysis pro- duces new results that explain how the rule governing the distribution of resources among household members is related to the measurement of household welfare and intra-household inequality. We show that in a collective model of private consumption, income shares are equal to the product of two weights: the Pareto weight and a distribution weight reflecting income effects across individuals. For a weighted Bergsonian representation of household utility and general assump- tions about individual preferences, we derive the associated household welfare functions and intra-household inequality measures belonging to a family of en- tropy indexes. We illustrate our findings with an empirical application that esti- mates a collective demand system to recover associated individual and household welfare functions along with the measures of intra-household inequality. This is the first application that estimates the Pareto weight and examines its role within a measure of income dispersion among household members.