Many scarce public resources are allocated at below-market-clearing prices, and sometimes for free. Such “non-market” mechanisms necessarily sacrifice some surplus, yet they can potentially improve equity. In this paper, we develop a model of mech anism design with redistributive concerns. Agents are characterized by a privately observed social welfare weight and willingness to pay for quality, as well as a publicly observed label. A market designer controls allocation and pricing of a set of objects of heterogeneous quality, and maximizes the expectation of a welfare function defined by the social welfare weights. We derive structural insights about the form of the optimal mechanism, leading to a framework for determining how and when to use non-market mechanisms. The key determinant is the strength of the statistical correlation of the unobserved social welfare weights with the label and the willingness to pay that the designer can, respectively, directly observe or elicit through the mechanism.

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