We derive the optimal incentive compatible and individually rational mechanisms to reallocate arbitrary given ownership shares among a set of agents. These mechanisms are optimal in the sense that they maximize social surplus of the final allocation subject to the aforementioned constraints and a revenue constraint. We allow for the agents' types to be drawn from non-identical distributions and for interdependent values. Because outside options are type dependent, the critical types for which individual rationality binds must be determined simultaneously with the allocation rule. We show that optimality uniquely pins down the set of critical types, which allows us to fully characterize the optimal mechanisms. Moreover, we find that the value function is Schur-concave in ownership shares when types are identically distributed, so that more symmetric shares are better irrespective of size of the revenue constraint.
