Trade-off between equity and efficiency in a general economy with indivisible goods

In most of the recent literature on fair allocation in economies with indivisible goods and a single infinitely divisible good, it is assumed that each agent can consume at most one indivisible good. In this paper, we show that if this assumption is dropped, there do not necessarily exist envy-free and Pareto efficient allocations. However, envy-free allocations still exist and so do Pareto efficient allocations. Hence, a trade-off between equity and efficiency arises. <!--ID="" Acknowledgements. This paper was written while I was visiting the Department of Economics at the University of Rochester. I would like to thank the faculty and staff members of the Department, especially William Thomson, for their hospitality. Useful comments of William Thomson, Tomoichi Shinotsuka. Carmen Bevia, and a referee are also gratefully acknowledged.-->