We consider a budget-constrained mechanism designer who selects an optimal set
of projects to maximize her utility. A project's cost is private information and its
value for the designer may vary. In this allocation problem, the selection of projects
- both which and how many - is endogenously determined by the mechanism. The
designer faces ex-post constraints: The participation and budget constraints must
hold for each possible outcome while the mechanism must be implementable in
dominant strategies. We derive the class of optimal mechanisms and show that
it has a deferred acceptance auction representation. This feature guarantees an
implementation with a descending clock auction. Only in the case of symmetric
projects do price clocks descend synchronously such that the cheapest projects are
executed. The case in which values or costs are asymmetrically distributed features
a novel tradeoff between quantity and quality. Interestingly, this tradeoff mitigates
the distortion due to the informational asymmetry compared to environments where
quantity is exogenous.
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