What money can't buy: Efficient mechanism design with costly signals

I study the ex-ante efficient allocation of a set of quality-heterogeneous objects to a number of heterogeneous risk-neutral agents. Agents have independent private values, which represent the maximum cost they are willing to sustain to obtain an object of unitary quality. The designer faces a trade-off between allocative efficiency and cost of screening, because the cost sustained is wasted. The optimal mechanism ranks agents based on their marginal contribution to social surplus and distributes objects to higher-ranked agents. The ranking is independent of the scarcity of objects or the extent of their heterogeneity. If the hazard rates of the distributions of values are increasing, agents are ranked according to their expected values. If hazard rates are decreasing and agents are symmetric, the objects are allocated to the agents that sustain the highest costs. In general, optimal mechanisms combine both pooling and screening of values.

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