Policymakers often intervene in goods markets to effect redistribution -- for example, via price controls, differential taxation, or in-kind transfers. We investigate the optimality of such policies alongside the (optimally-designed) income tax. In our framework, agents possess private information about their ability to generate income and consumption preferences, and a planner maximizes a social welfare function subject to resource constraints. We uncover a generalization of the Atkinson-Stiglitz theorem by showing that goods markets should be undistorted if (i) individual utility functions feature no income effects, (ii) redistributive preferences depend only on agents’ ability, and (iii) there is no statistical correlation between ability and taste for goods. We also show, however, that the conclusion of the Atkinson-Stiglitz theorem fails if any of the three assumptions is relaxed. In a special case of our model with linear utilities, binary ability, and continuous willingness to pay for a single good, we characterize the globally optimal mechanism and show that it may feature means-tested consumption subsidies, in-kind transfers, and differential commodity taxation.

Membership design involves allocating an economic good whose value to any individual depends on who else receives it. We introduce a framework for optimal membership design by combining an otherwise standard mechanism-design model with allocative externalities that depend flexibly on agents’ observable and unobservable characteristics. Our main technical result demonstrates that the optimal mechanism offers distinct membership tiers—differing in prices and level of access—and that the number of membership tiers is increasing in the complexity of the externalities. This insight may help explain a number of mechanisms used in practice to sell membership goods, including musical artists charging below-market-clearing prices for concert tickets, certain admission procedures used by colleges concerned about the diversity of the student body, heterogeneous pricing tiers for access to digital communities, and the use of vesting and free allocation in the distribution of network tokens.

A designer relies on a costly screening device to allocate a set of goods, aiming to maximize a social welfare function. We provide conditions for one screening device to dominate another. We show that the performance of a screening device depends on two channels: (i) targeting effectiveness which measures the alignment between the implemented and desired assignments, and (ii) rent provision which determines the utilities of agents receiving the goods net of the screening costs. We link these two channels to distinct properties of the joint distribution of agents’ characteristics, leading to a number of simple empirical tests for comparing screening devices.