We study optimal mechanisms for a utilitarian designer who seeks to assign a finite number of goods to a group of ex ante heterogeneous agents with unit demand. The agents have heterogeneous marginal utilities of money, which may naturally arise in environments where agents have different wealth levels or financing conditions. We show that the utilitarian optimal allocation rule deviates from the ex post efficient allocation rule in two ways, namely by (1) allocating the good to agents with lower willingnesses to pay in certain situations and (2) by potentially keeping some units of the good unallocated. We also highlight how our mechanism can be implemented as an auction with minimum bids and bidding subsidies.
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