Title: Cost Based Nonlinear Pricing with Tibor Heumann, Pontificia Universidad Católica de Chile, tibor.heumann@uc.cl.

Stephen Morris, Massachusetts Institute of Technology, semorris@mit.edu

Abstract: How should a monopolist offer quantity or quality differentiated products if they have no information about the distribution of demand and must price based on cost conditions alone? Specifically, we consider a monopolist who cares about the "profit guarantee" of a pricing rule, that is, the minimum ratio value of expected profits to expected surplus for any distribution of demand.

We show that the profit guarantee is maximized by setting the price markup over marginal cost equal to (describe) function of elasticity. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible distributions of willingness to pay and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers.