Separable Externalities in Cost and Production Functions

Abstract

The characterization of external effects as "separable" has played an important role in the development of the theory of externalities. The separable case is particularly well behaved when procedures for achieving an optimum allocation of resources in the presence of externalities are examined. Davis and Whinston (1962) find that separability assures the existence of a certain kind of equilibrium in bargaining between firms which create externalities, and that equilibrium does not exist without separability. Kneese and Bower (1968) argue that with separability the computation of Pigovian taxes to remedy externalities is particularly simple. Marchand and Russell (1974) demonstrate that certain liability rules regarding external effects lead to Pareto optimal outcomes if and only if externalities are separable. In each of these cases the problem is posed in terms of two firms related by technological externalities, and separability is defined in terms of a cost function. In this paper, we will characterize that class of production functions which give rise to separable cost functions, and show that the relation between production functions and separable cost functions is by no means as trivial as has been claimed.

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