Identical preferences lower bound solution and consistency in economies with indivisible goods

We consider the problem of allocating a finite set of indivisible goods and a single infinitely divisible good among a group of agents, and we study a solution, called the Identical Preferences Lower Bound solution, in the presence of consistency properties. This solution is not consistent. We prove that its maximal consistent subsolution is the No-envy solution. Our main result is that the minimal consistent extension of the intersection of the Identical Preferences Lower Bound solution with the Pareto solution is the Pareto solution. This result remains true in the restricted domain when all the indivisible goods are identical, but not when there is a unique indivisible good.This paper was developed during my stay at Rochester University in the summer of 1992. I would like to express my special thanks to Professor William Thomson for all his help and advice. Iam also grateful to my supervisor Luis Corchón, to Koichi Tadenuma and to the anonymous referees for their helpful comments. The remaining errors are my exclusive responsibility. Financial support from the DGCYT under project PB 91-0756 and the Instituto Valenciano de Investigaciones Económicas are gratefully acknowledged.