  Adverse selection is a version of the principal-agent problem that includes
monopolist nonlinear pricing, where a monopolist with known costs seeks a
profit-maximizing price menu facing a population of potential consumers whose
preferences are known only in the aggregate. For multidimensional spaces of
agents and products, Rochet and Chon\'e (1998) reformulated this problem to a
concave maximization over the set of convex functions, by assuming agent
preferences combine bilinearity in the product and agent parameters with a
quasilinear sensitivity to prices. We characterize solutions to this problem by
identifying a dual minimization problem. This duality allows us to reduce the
solution of the square example of Rochet-Chon\'e to a novel free boundary
problem, giving the first analytical description of an overlooked market
segment.
