Separability and vanishing externalities

In one of the most influential papers written on the subject of externalities, Otto Davis and Andrew Whinston argue that corrective taxes and private bargaining are likely to achieve an optimum in the presence of mutual externalities between two firms only when externalities are separable, in the sense that marginal cost is independent of the level of externality. Further analysis of the concept of separability reveals that even this conclusion is too optimistic. I shall argue below that the assumptions needed to make taxes and negotiations work properly rule out the possibility of having externalities in any observable situation.