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 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. However, this mechanism can be suboptimal when narrow preference margins between pure options are sufficiently predictive of higher values. In such cases, the designer can improve welfare by offering mixed bundles, targeting high-value agents through their willingness to accept mixing.