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Public Goods (and Federalism)*

Published online by Cambridge University Press:  07 November 2014

J. C. Weldon
J. C. Weldon*
Affiliation:
McGill University
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Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 32 , Issue 2 , May 1966 , pp. 230 - 238
Copyright
Copyright © Canadian Political Science Association 1966

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Footnotes

*

I must mention helpful written comments from A. Asimakopulos, A. Deutsch, and an unknown referee. As this goes to press, A. Breton has been good enough to send me his “Reply.” The temptation to reply to the reply must be resisted, but perhaps I can use the rest of this (extended!) sentence to say that the point of my equations (7) is that they follow from specialforms of equations (1), and that “intermediate” goods should surely lie between the “polar” cases.

References

1 This Journal, XXXI, no. 2 (May 1965), 175–87. See also Breton's, recent “The Economics of Nationalism,” Journal of Political Economy, 08 1964, 376–86.CrossRefGoogle Scholar

2 “A Theory of Government Grants,” 178.

3 Ibid., 177. Breton speaks of “goods which are not pure public goods and which I call non-private goods.”

4 Ibid., 176. “The ‘ideal type’ or polar case of a non-private good is the pure public good … the objective benefits of such a good accruing to a given individual are independent of the benefits accruing to others. Let me stress that this is a technological property of public goods; it is independent of the subjective valuation which individuals attach to the objective benefits derived from the goods … the property of being available in equal quantity to everyone is inherent in the good itself.” All of this, I think, is quite mistaken, as is the extension of the theme to non-private goods in general in the next stage of Breton's argument.

5 The basic references are Samuelson's, P. A. “The Pure Theory of Public Expenditure,” Review of Economics and Statistics, 11 1954, 387–9Google Scholar, and his “A Diagrammatic Exposition of a Pure Theory of Public Expenditure,” ibid., Nov. 1955, 350–6. For later contributions, see the further sources Breton cites, and for earlier contributions see the attribution Samuelson makes to Wicksell and others.

6 The scope of the game (or game within a game) is difficult to define, since what is given in the situation and what is to be determined are not to be distinguished in any obvious way. But to ask about an optimum constitution does not take very much as given.

7 “A Theory of Government Grants,” 178.

8 Ibid., 180.

9 Ibid.

10 Ibid.

11 Ibid., 187. Earlier (pp. 180–1) Breton remarks that if “non-private goods are paid for by benefit taxes and if the prices of private goods are set by a mechanism which correctly reflects the preferences of society and the scarcities of resources in that society, then an optimum constitution yields an allocation of resources which is Pareto optimal.” But what-ever can be done in a federation to attain Pareto optimality can be done at least as easily in the unitary state, always given the idealized conditions under which Breton's economy operates. Needless to say this tells us little about the real value of the unitary state.

12 There is the optimizing effect of consumers moving from community to community to consider, as in Tiebout's, Charles M. “A Pure Theory of Local Expenditure,” Journal of Political Economy, 10 1956, 416–24.CrossRefGoogle Scholar While from one point of view this effect might be regarded as taking place within a fixed pattern of government, here it is better seen as part of the choice of coalitions that produce a pattern of governments.

13 Most of Breton's commentary is directed to the last of these questions. If it is not a commentary that points to solutions better than the existing formalisms, it is most instructive as to what the problems are.

14 Minor notational changes aside, the argument expressed by equations (1) to (5) follows J. de V. Graaff's compact and elegant exposition in the appendices to chap, II and III of Theoretical Welfare Economics (Cambridge, 1957), 28–32 and 53–4.Google Scholar But Graaff later (in the appendix to chap, IV, 72) follows the Samuelson convention in dealing with pure public or “collective” goods.

15 Defining a γκ ≡ 1, we have from equations (2) the relations

15.1 . (i = 1, …, m; j = 1, …, n).

Noting from equation (1) that

15.2 , (i = 1, …, m; j, s = 1, …, n),

so that on substituting (15.1) in (15.2) and adding over j we have

15.3,

we can then go from 15.1 to equations (3), merely taking care to take a named individual's marginal utilities from under the summations.

16 Samuelson, , “A Diagrammatic Exposition,” 354.Google Scholar Here and elsewhere I carry the discussion back only to the Scitovsky frontier. The usual complications need to be added in a full account, particularly on the production side.

17 Ibid., 353–4.

18 “A Theory of Government Grants,” 176.

19 Ibid. In identifying the argument he rejects, Breton cites Tiebout, C. M. and Houston, D. B., “Metropolitan Finance Reconsidered: Budget Functions and Multi-Level Governments,” Review of Economics and Statistics, 11 1962, 412.Google Scholar The “argument,” though, is little more than an assertion! “It should be recognized that the presence of externalities, say the authors, “as well as the degree to which they exist, are part of a consumer's utility function. Some individuals may perceive large externalities where others perceive none at all.” I think Tiebout and Houston are undoubtedly correct, but they are interested in other things, and take this issue as settled.

20 ”A Theory of Government Grants,” 177. Where Breton does point to objective qualities of these goods—their location, for example—he is not in fact cataloguing non-private goods, but only showing us categories that in the usual treatment would be divided into separate goods.

21 Here again marginal conditions in terms of inequalities are neglected, although in the nature of things the condition “not greater than” would often be required in equations (11). Apparently a fair majority of the Canadian public is satiated with CBC programmes at zero levels of use.

22 When speaking of national defence as a close approximation to a pure public good, Breton says (“A Theory of Government Grants,” 176) “the level and degree of security and protection (i.e., objective benefits) afforded by the existing arms are, in principle at least, equal for everyone.” I do not see how this matters, how we would decide whether it was true or not, how we measure these things, what the relationship of the equal benefits is to Samuelson's conception of the pure public good, and what the significance of the weakening phrase “in principle at least” may be.

23 Ibid., 177.

24 Ibid., 176 (and see again my footnote 19).

25 If the numeraire does not keep its simple properties, then equations (9) have to be widened in that respect too. Equations (8) contain all the possibilities that have been discussed, but may well be pointlessly inclusive. In any case something as wide as equations (9) is needed, and cannot be constructed as a special form of equations (1).

26 Samuelson, , “A Diagrammatic Exposition,” 350.Google Scholar As I remarked before, J. de V. Graaff accepts the same convention—as do others, including A. Asimakopulos and the unknown referee (if I read their comments correctly). But if they also accept that some of Breton's “intermediate” cases fall outside the range of Samuelson's “polar” cases, differences seem merely semantic.

27 Here X 2 1 + X 2 2 ≠ X 2, so the distinction exists.

28 Samuelson, “A Diagrammatic Exposition,” 350.

29 This leaves aside ways in which the public good is made to share properties with the pure private good, thus the independence of the numeraire (an assumption, incidentally, that has a silent place in many parts of the literature). The question that matters is what is special vis à vis the private good.