In a recent issue of this Journal, Alan Williams (1966) presented an analysis of the optimality of public goods supply in a situation in which the public goods are produced by independently operating local governments. By appropriate reference to hitherto neglected income effects, he succeeded in demonstrating that it is possible for too much of the public good to be produced in the aggregate, even though each local government cannot extract payment for the benefits from its public good production which spill out onto other local government areas. The question under discussion is conceptually equivalent to the question of the direction of the distortion resulting under conditions of independent adjustment in a situation of reciprocal externalities of the separable variety,1 and Williams' analysis can be applied equally well to this case. Thus, if A's production of X reduces the total (but not marginal) cost of B's production of X, and B's production of X likewise reduces the total (but not marginal) cost of A's, Williams' result indicates that, where A and B act independently, oversupply of X may result. To those familiar with the work of Buchanan and Kafoglis (1963) and of Baumol (1964), this conclusion may not, in itself, be very surprising. What is perhaps more interesting is Williams' assertion that, although oversupply of public goods can occur in the aggregate, it is not possible for public goods consumption to be overexpanded in every local government area. Or, in the individual case, although too much of X may be produced in toto, simultaneous overproduction by A and B is impossible.2
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