Knowledge that Transforms

In two recent articles in this Review, James Buchanan and Milton Kafoglis [3] and William Baumol [1] have reexamined the long accepted proposition that activities which exhibit external economies should be expanded in order to achieve a Pareto optimal allocation of resources.' Specifically, Buchanan and Kafoglis, employing the case of immunizations, suggest that where two parties each yield external economies to each other, i.e., the externalities are reciprocal, cooperative purchase of the immunizations may lead to a socially optimum position in which fewer immunizations are purchased than would be the case if each party acted independently. Furthermore, the outputs received by each party may be either lower or higher than in the case of independent adjustment. In attacking the previously held proposition, Buchanan and Kafoglis present a numerical counterexample in the form of a game theoretic matrix. While a counterexample is sufficient to prove their point, it does not indicate the general conditions which must be imposed oln the loss functions in order to achieve their results. The following analysis generalizes the Buchanan-Kafoglis numerical examples, to show when fewer rather than more immunizations should be purchased by the two parties and when less, rather than more, output should be produced. In addition, some comments will be made on Baumol's article which extended and reinterpreted some of their results.2 The main result proved here is that the existence of economies of scale in the production of benefits (outputs) from immunization is a necessary condition for a lower total number of immunizations (inputs) to be purchased at the Pareto optimum, unless rather implausible conditions are placed on the form of the external effects for the examples worked out by Buchanan and Kafoglis and by Baumol. This assumption was not made explicit and appears to have been overlooked in both articles.3 On the output side, it is proved for one of the original Buchanan and Kafoglis examples, that a reduced output level for both parties at the Pareto optimum requires that one party's receipt of immunizations must be a morethan-perfect substitute for the other's receipt of immunizations. The latter strong substitution relationship was explored earlier by Buchanan and Kafoglis but was not used explicitly in their discussion of the reciprocal externalities case. Finally, it is suggested that Buchanan and