Public Provision of Scarce Resources when Preferences are Non-Linear

In most of the literature considering assignment problems it is assumed that agents’ preferences are linear in money. In contrast, I study the problem of assigning an indivisible good of limited availability to a continuum of agents that exhibit decreasing marginal utility in money. I assume that two types of agents exist - rich and poor agents. I find that randomly assigning the good without monetary transfers can be ex-post efficient and might even ex-ante Pareto-dominate selling the good for a market clearing price and redistributing the revenues. I furthermore study optimal assignments of consumption probabilities and transfers in an incomplete information setting under the objective of welfare maximization. If both agents benefit equally from consuming the good, the consumption probabilities of the poor agents are distorted downwards compared to first-best where both types consume the good with equal probabilities. However, if the poor agents benefit more from consuming the good than the rich agents, randomly assigning the good can be optimal despite the richer agents having a higher willingness to pay for the object. Whenever income differences are large enough, the optimal assignment might not distribute all resources of the good in order to incentivize higher redistribution of income.