TITLE:
Optimal (Under-)Pricing and Allocation of Publicly Provided Goods
AUTHORS:
David Scrogin
KEYWORDS:
Expected Consumer Surplus, Non-Market Mechanism, Lottery, Hazard Rate, Mean Residual Value
JOURNAL NAME:
Theoretical Economics Letters,
Vol.7 No.4,
May
15,
2017
ABSTRACT: This
paper exploits the links between a private value distribution’s hazard rate,
mean residual value, and eta functions in order to characterize posted-price 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 under-pricing 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.