Priority Rules and Other Inequitable Rationing Methods
Herv‚ Moulin
Department of Economics, Duke University, Box 90097, Durham NC 27708, Phone: 919-660-1816; Fax: 919-684-8974; Email: moulin@econ.duke.edu

Abstract
	In a rationing problem, each agent demands a quantity of a certain commodity and the available resources fall short of total demand.  A rationing method solves this problem at every level of resources and individual demands.  	We impose three axioms: Consistency(with respect to variations of the set of agents(, Distributivity, and Distributivity*(with respect to variations of the available resources.
	In the model where the commodity comes in indivisible units, the three axioms characterize the family of priority rules, where individual demands are met lexicographically according to an exogeneous ordering of the agents.
	In the (more familiar) model where the commodity is divisible, these three axioms plus Scale Invariance(independence of the measurement unit(characterize a rich family of methods.  It contains exactly three equitable methods, giving equal shares to equal demands: these are the familiar proportional, uniform gains and uniform losses methods.  The inequitable methods in the family partition the agents into priority classes; within each class, they use either the proportional method or an asymmetric weighted version of the uniform gains or uniform losses methods.

Key words: rationing, priority rule, consistency, distributivity, scale invariance.
JEL classification:	D63, D70

Acknowledgment: Many stimulating conversations with Scott Shenker have been very helpful.  This paper was born during a visit at the Universitat Autonoma de Barcelona, May(June, 1997; financial support by the Foundacion BBV is gratefully acknowledged.