When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds

We study the problem of rationing a divisible good among a group of people. Each person’s preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: he finds any amount less than this threshold to be just as good as receiving nothing at all. Further, any amount beyond his ideal quantity has no effect on his welfare. The focus of our study is the existence of Pareto-efficient, strategy-proof, and envy-free rules. While the definitions of these axioms carry through, with minimal changes, from the more commonly studied problem without disposability or acceptance thresholds, we show that these extensions are not compatible in the model that we study. We also adapt the equal-division lower bound axiom and propose another fairness axiom called awardee-envyfreeness. While these are also incompatible with strategy-proofness, we identify the set of all Pareto-efficient rules that satisfy these two properties. We also characterize the class of conditional sequential priority rules as the set of all Pareto-efficient, strategy-proof, and non-bossy rules. JEL classification: C71, D63