Mechanism design with financially constrained agents and costly verification

A principal distributes an indivisible good to budget-constrained agents when both valuation and budget are agents' private information. The principal can verify an agent's budget at a cost. The welfare-maximizing mechanism can be implemented via a two-stage scheme. First, agents report their budgets, receive cash transfers, and decide whether to enter a lottery over the good. Second, recipients of the good can sell it on a resale market but must pay a sales tax. Low-budget agents receive a higher cash transfer, pay a lower price to enter the lottery, and face a higher sales tax. They are also randomly inspected.