Do redistributive schemes reduce inequality between individuals?

Redistribution schemes (taxes or benefits) are generally performed at the household level. The issue is to know whether intra-household inequality magnifies or hampers the redistributive effect of the transfers, when the policy-maker focuses on the inequality at the individual level. Depending on the type of the transfer, three properties capturing the idea that the more wealthy the household is, the more unequally it behaves, have been shown to matter. In the moving away approach, the deviation with the equal split make a difference, in the star-shaped approach, the average share counts while the marginal share is relevant for concavity. We complete the analysis by showing how these properties of the intra-household allocation may be recovered through a bargaining model of the household. Then, the DARA and DRRA properties of the utility function emerge as the key conditions for the recovery.