Market and non-market mechanisms for the optimal allocation of scarce resources

A number of identical objects is allocated to a set of privately informed agents. Agents have linear utility in money. The designer wants to assign objects to agents that possess specific traits, but the allocation can only be conditioned on the willingness to pay and on observable characteristics. I solve for the optimal mechanism. The choice between market or non-market mechanisms depends on the statistical linkage between characteristics valued by the designer and willingness to pay.