  We consider a nonlinear pricing environment with private information. 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.
