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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 function; (iii) that mergers may be able to internalize “weak” externalities but not “strong” ones; and (iv) that “parallelism” of indifference curves (quasi-linear utilities, absence of income effects) is necessary, and not merely sufficient, for the validity of the Coase Invariance Theorem (asserting that alternative institutional arrangements do not change the level of externality). The paper builds on the seminal contributions of Starrett, Calsamiglia, Baumol, Bradford, Oates, Boyd, and Conley.