Abstract
We investigate the relationship between centralized and decentralized collective demand models applied to consumption within a household with multiple individuals. The centralized program is described by a Bergsonian representation of the household utility function and a household budget constraint, while the decentralized program is described by individual utility maximization subject to an income allocation among individual. The household income allocation among individuals involves an income sharing rule. We show that, in general, income shares are equal to the product of two weights: the Bergsonian weight and a weight reflecting income effects across individuals. We also show that the latter weights play a role in income sharing and in household welfare evaluation when individual preferences depart from quasi-homotheticity. We also examine how individual preferences affect the relationship between centralized and decentralized demand.
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