Targeting Without Transfers

I study the welfare-maximizing allocation of heterogeneous goods when monetary transfers are prohibited. Agents have private values, and the designer chooses a mechanism subject to incentive compatibility and aggregate supply constraints. I characterize the optimal mechanism for two kinds of goods, and show that it either offers one pure option per good or adds a bundle that delivers a larger total quantity. Including the bundle is optimal when narrow preference margins between goods are sufficiently predictive of greater need, allowing the designer to target high-value agents through their willingness to accept mixing. I then consider the case with N types of goods and characterize when the optimal mechanism takes the form of a simple menu, where each option offers some amount of one kind of good and none of the others. When this is the case, it can be implemented as a competitive equilibrium with equal incomes or a choice-based lottery.