This paper finds an optimal mechanism for selling an indivisible good to consumers who may be budget-constrained. Unlike the case where buyers are not budget constrained, a single posted price is not typically optimal. An optimal mechanism generally consists of a continuum of lotteries indexed...

Several recent articles have shown that the efficient outcome for bilateral trade, even in the face of specific investments and incomplete contracting, can be supported with approximately-designed contracts. These studies have, for the most part, restricted attention to specific investments that...