Michael Richter (New York University)
30 January 2012 @ 12:00
This paper studies mechanisms for assigning a divisible good to a population of budget-constrained agents where agents’ private valuations and budgetsare independently distributed. In this setting, I nd the welfare- and revenue-maximizing mechanisms for assigning the good. Both of these optimal mecha-nisms feature a linear price for the good. The welfare-maximizing mechanismadditionally has a uniform lump sum transfer to all agents and a higher linearprice than the revenue-maximizing mechanism. This transfer increases welfarebecause it relaxes the key diculty in the aforementioned setting: agents withhigh valuations cannot purchase an ecient amount of the good because oftheir budget constraints. The welfare-maximizing result can therefore be interpreted as a version of the second welfare theorem. I show that both optimalmechanisms can be implemented using dominant strategies. In addition, I consider extensions where I relax the independence condition, and introduce linearproduction.