A Theory of Reallocation

Résumé : We consider the problem of reallocation of heterogeneous productive assets between the agents who also differ in intrinsic productivity. While efficient, such reallocation is subject to the « lemons’’ problem, where the owners of low-quality assets wish to imitate the owners of high-quality assets, and the opposite of the « lemons’’ problem, as the owners of the high-quality assets wish to imitate the owners of the low-quality assets. In particular, the latter makes reallocation impossible unless there is some « equal exchange’’ between the owners of low-quality assets. We then analyze this problem as a two dimensional optimal mechanism design. We show that, with equal exchange and no withdrawal of assets, some reallocation occurs if the proportion of the agents with high quality assets is sufficiently high.

A fully incentive efficient mechanism derived in the paper implements reallocation for any proportions of low and high-quality assets in the population, but also requires idling of some owners of low and high-quality assets (production rationing) and a corresponding withdrawal of some low-quality assets. The incentive efficient mechanism cannot be decentralized.