How to Allocate Money?

I study a simple equity-efficiency problem: A designer allocates a fixed amount of money to a population of agents differing in privately observed marginal values for money. She can only screen by imposing an “ordeal,” that is, by allocating more money to agents who engage in a socially wasteful activity (such as queuing or filling out forms). I show that giving a lump-sum transfer is outperformed by an ordeal mechanism when agents with the lowest money-denominated cost of engaging in the wasteful activity have an expected value for money that exceeds the average value by more than a factor of two.