Working Paper: CEPR ID: DP17897
Authors: Dirk Bergemann; Tibor Heumann; Stephen Morris
Abstract: 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.
Keywords: nonlinear pricing; second degree price discrimination; profit guarantees; competitive ratio
JEL Codes: D44; D47; D83; D84
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| constant markup pricing (D49) | optimal revenue guarantee (H21) |
| constant markup pricing (D49) | seller profits (L85) |
| distribution of values (C46) | profits and consumer surplus (D26) |
| convexity of cost function (D24) | revenue guarantee (H27) |
| cost elasticities (D12) | profit guarantees (L21) |