This paper examines the problem of a seller with limited supply selling to a group of agents whose private information is two-dimensional. Each agent has a constant marginal value for the good up to some capacity, thereafter it is zero. Both the marginal value and the capacity are private information. We describe the revenue maximizing Bayesian incentive compatible auction for this environment. A novel feature of the analysis is an interpretation of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice.
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