Equity and efficiency in non-convex economies

The objective of this paper is to consider the following question. Does the presence of increasing returns introduce a fundamental trade-off between equity and efficiency objectives? We show that if the no-envy notion of Foley (1967) is taken as the equity criterion and Pareto optimality as the efficiency criterion, then the answer is yes; there exist economies with increasing returns and well-behaved preferences (and no agent-specific inputs) in which there do not exist any envy-free and Pareto optimal allocations. We also propose a weakening of the no-envy criterion and prove that this weaker equity notion is compatible with Pareto optimality in general non-convex economies.