We consider a package assignment problem with multiple units of indivisible items. The seller can specify preferences over partitions of their supply between buyers as packaging costs. We propose incremental costs together with a graph that defines cost interdependence to express these preferences. This facilitates the use of linear programming to characterize Walrasian equilibrium prices. Firstly, we show that equilibrium prices are uniform, anonymous, and linear in packages. Prices and marginal gains exhibit a nested structure, which we characterize in closed form for complete graphs. Secondly, we provide sufficient conditions for the existence of package-linear competitive prices using an ascending auction implementation. Our framework of partition preferences ensures fair and transparent dual pricing and admits preferences over the concentration of allocated bundles in the market. The full paper is available at https://arxiv.org/abs/2306.14247.

We initiate the study of how auction design affects the division of surplus among bidders. We propose a parsimonious measure for equity and apply it to standard auctions for homogeneous goods. Our surplus-equitable mechanism is efficient, Bayesian-Nash incentive compatible, and achieves surplus parity among winners ex-post. The uniform-price auction is equity-optimal if and only if bidders have a common value. Against intuition, the pay-as-bid auction is not always equity-preferred if bidders have private values. In auctions with price mixing between pay-as-bid and uniform prices, we provide prior-free bounds on the equity-preferred pricing under a common regularity condition on signals. The full paper is available at https://arxiv.org/abs/2403.07799.

In an epidemic, how should an organization with limited testing resources safely return to in-person activities after a lockdown? We study this question in a setting where the population is heterogeneous in both utility for in-person activities and probability of infection. During a period of re-integration, tests can be used as a certificate of non-infection, whereby those in negative tests are permitted to return to in-person activities for a designated amount of time. Under the assumption that samples can be pooled, the question of how to allocate a limited testing budget in the population to maximize the aggregate utility (i.e. welfare) of negatively-tested individuals who return to in-person activities is non-trivial, with a large space of potential testing allocations.