I study multi-unit auction design when bidders have private values, multi-unit demands, and non-quasilinear preferences. I give conditions under which we can design a mechanism that retains the Vickrey auction’s desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. Instead of assuming that bidders have quasilinear preferences, I assume that bidders have positive wealth effects. My model nests cases where bidders are risk averse, face financial constraints, or have budgets.

With two bidders, I show that there is a mechanism that retains the desired properties of the Vickrey auction if bidders have single-dimensional types. I present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey’s desired properties and weak budget balance when bidders have multi-dimensional types. I also present a second impossibility theorem for the case where there are three or more bidders, even if bidders have single-dimensional types.