Optimal (Under-)Pricing and Allocation of Publicly Provided Goods

Abstract

This paper exploits the links between a private value distribution's hazard rate, mean residual value, and eta functions in order to characterize postedprice rules for a public agency to allocate scarce units of an indivisible good under the utilitarian distributional objective of maximizing expected consumer surplus. Sufficient conditions on the monotonic and non-monotonic classes of the functions are established that identify either market assignment at the clearing price or lottery assignment with partial or complete underpricing as the optimal allocation mechanism. The results are summarized across a wide range of parametric value distributions, and selected non-monotonic cases are evaluated numerically to determine the relative scarcity or abundance of the good necessary for market or non-market assignment to dominate.