Share the Gain, Share the Pain? Almost Transferable Utility, changes in production possibilities, and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions preclude transferable utility (a property we call "Almost TU"). We show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash Bargaining and the utilitarian solutions are special cases). We apply the result to household decision making in the context of the Rotten Kid Theorem and in evaluating a change in family taxation.