Optimally constraining a bidder using a simple budget

I study a principal's optimal choice of constraint for an agent participating in an auction (or auction-like allocation mechanism). I give necessary and sufficient conditions on the principal's beliefs about the value of the item for a simple budget constraint to be the optimal contract. The results link the observed use of budget constraints to their use in models incorporating budget-constrained bidders. Other implications of the model are that a general revenue equivalence result applies and that the optimal auction with budget-constrained bidders has a standard solution analogous to the one for classic models.