For economies with one-sided externalities between firms, four types of results are presented and discussed: (i) the impossibility of decentralized finite-dimensional mechanisms guaranteeing Pareto optimality; (ii) the possibilities for Pigou taxes in situations where Arrovian markets cannot...

A transversal generated by a system of distinct representatives (SDR) for a collection of sets consists of an element from each set (its representative) such that the representative uniquely identifies the set it belongs to. Theorem 1 gives a necessary and sufficient condition that an arbitrary...