A Fresh Look at the Rotten Kid Theorem
Gary Becker's ``Rotten Kid Theorem'' asserts that if all family members receive gifts of money income from a benevolent household member, then even if the household head does not precommit to an incentive plan for family members, it will be in the interest of selfish family members to maximize total family income. We show by examples that the Rotten Kid theorem is not true without assuming transferable utility. We find a simple condition on utility functions that is necessary and sufficient for there to be the kind of transferable utility needed for a Rotten Kid Theorem. While restrictive, these conditions still allow one to apply the strong conclusions of the Rotten Kid Theorem in an interesting class of examples.
Ted Bergstrom. "A Fresh Look at the Rotten Kid Theorem" Journal of Political Economy 97.5 (1989): 1138-1159.