The Demand and Supply of Public Goods
Which Goods Should Be Public?*9
The theory of public goods, as partially sketched out in early chapters of this book, is not a theory of public organization or supply, in either a normative or a positive sense, although it has been interpreted to be such by many scholars. In Samuelson's early and rigorous formulation, goods were classified into two polar categories, purely private and purely public. The allocative norms of modern welfare economics, which were developed in application to private goods, were then extended to public goods, as defined. Given the use that has often been made of these allocative norms with reference to private goods, it is understandable that organizational-institutional implications were read into the theory of public goods from the outset, regardless of the intent of the theory's original proponents. In a sense, and despite the apparent circularity, the implication that "public goods should be public" seemed a natural one. And, of course, linguistic philosophers would suggest that the very usage of the term "public" itself carried substantive overtones for organizational policy.
I have tried to demonstrate in earlier chapters that the formal models of this theory of allocation are considerably more general than the restriction to polar cases might suggest. My emphasis has been placed, not on the manner in which goods are classified in some descriptive sense, but on the manner in which goods are actually supplied. This approach allows us to divorce entirely the allocative theory from the organizational implications. It does not, however, resolve the organizational-institutional question that remains of central importance. What goods and services should a community supply publicly through political-governmental processes rather than privately through market processes?
This is one of the vital questions in any theory of institutional choice, a theory introduced and discussed in Chapter 7 in general terms only. The allocative theory of public goods should surely be of some assistance in answering this question. It should provide a basis for an organizational-institutional theory, whether the latter be framed in normative or positive terms.
The Question Stated
What specific question must this theory ask, and try to answer? Despite the normative "should" in the chapter's title, I want, to the extent possible, to develop a theory that retains positive content. Under what circumstances will individuals as participating members of a politically organized community select collective organization as the means of supplying a particular good or service? The economists' stock response to this question is familiar: "When collective organization is more efficient than its alternatives." This answer says nothing and is tautological. Theory must go considerably beyond such limits if it is to be at all helpful in explanation and prediction.
The question rephrased becomes: Under what circumstances will collective-governmental supply be more efficient than private or noncollective supply? Here the standard response no longer holds, and the economist must answer on the basis of some comparative analysis of alternative institutions. The results that may be predicted to emerge from publicly organized supply must, in each case, be compared with those that may be predicted to emerge from noncollective, voluntarily organized, market supply.
Analysis here can commence with the calculus of an individual who is confronted with a choice as to the preferred organization of supply of a good or service at some conceptual stage of constitutional decision. This calculus reduces to a comparative evaluation of all institutional alternatives in terms of expected benefits and costs, both defined in present values, and both embodying major uncertainties. Alternatives must be compared on a quasi-permanent basis. No remotely relevant theory could be derived on the assumption that the organization of supply changes from one time period to the next.
The Divisibility Spectrum
If the question is one of determining the most desirable form of organization, some means of ranking or classifying goods and services independent of organization must be found. Since the form of organization itself affects the physical characteristics of many goods and services, the development of any such independent criterion will be difficult. We shall proceed here "as if" an independent array can be developed, although some qualifying notes will be made at appropriate points in the discussion.
Initially we may consider arraying all possible goods and services along some divisibility spectrum or scale. At one extreme we include all "purely private" goods and services, those that are perfectly divisible among separate persons (consumers). The total supply of such a good or service is represented by the summation of the supplies available to all persons. If X is the total quantity available to the group, and if x1, x2, ... , are quantities available to individuals, then
At the end of our scale, we include those goods and services that are "purely public," those that are perfectly indivisible as to benefits among the separate persons in the group. Here, if X is the total quantity available to the group, this same quantity is also available to each and every individual in the group,
All other goods and services are then arrayed between these two extremes in accordance with the relative importance of "divisible" and "indivisible" elements. For goods and services along the spectrum between the two extremes, no simple algebraic definition comparable to the familiar ones above is possible. As earlier discussion showed, the problem of defining units becomes important here. For current purposes, it is sufficient to think of all in-between goods as including both divisible and indivisible elements in varying ratios.
The Range of the Publicness Interaction
One major flaw in the scalar ranking of goods and services solely by the divisibility-indivisibility characteristic should be apparent. Goods and services will not hold the same rank in the scale as the size of the group changes. It is necessary to supplement the ranking by a second one that describes the range or limit over which the indivisibility characteristic, if it exists, holds. An example will clarify. It is probable that the benefits from mosquito spraying are almost wholly indivisible over the set of families living in one small suburb. It is equally clear that the benefits from mosquito spraying become fully divisible as among residents of suburbs in different outlying areas of the city. As in the case with the degree of divisibility, we may think of a whole scale or spectrum that defines the limits of the interaction. At the one extreme, again, we have the purely private, fully divisible good or service, where this interaction is defined as being limited to the single consuming unit, the person or the family. At the other extreme, we have the good or service that is fully indivisible as to benefits over a group that is, conceptually, of infinite membership.
A Summary Classification
The two independent characteristics, degree of indivisibility and extent or range of indivisibility, may be represented in a single box diagram, Figure 9.1. Along the abscissa we measure the size of the interacting group. Along the ordinate we measure the degree of indivisibility, from zero at the origin to perfect indivisibility at the top. It now becomes possible for us to place any good or service somewhere in the box as it embodies these two characteristics.
The theory of public goods, as it was initially developed, tended to force all goods into the two sets represented at the origin on the one hand and at 0' on the other. Purely private or fully divisible goods and services that may be classified as falling at or near the origin may be put in category (1) for purposes of later analysis. Goods and services classified as falling at or near 0' may be put in category (5).
Three additional categories are noted in Figure 9.1, although no attempt is made to delineate precisely the areas of the figure to which these might refer. Category (2) includes those goods and services that are partially divisible, but which involve indivisibility or "publicness" elements only over a limited number of persons. Category (3) likewise includes goods and services that are only partially divisible. But here the publicness elements extend over a large number of persons. Category (4) covers those goods and services that are fully indivisible, or nearly so, but for which the range of indivisibility extends only over groups of limited size. Whole areas may be empty; few goods and services are likely to be found near the southeast corner of the diagram. It will be helpful to discuss the relevant categories falling between (1) and (5) in more detail.
(2) Partially divisible goods and services, with interactions limited to groups of critically small size For a good or service that may be classified in this way, there must be some substitutability among consumption units, as among separate persons, but this is not one-for-one. If the total supply available to the group is fixed, the increase in consumption by one person will reduce the amount available to some other person, or persons, but not precisely by one unit, as in the purely private-good case, and not by zero, as in the purely public-good case. The "nonprivateness" extends, however, only over a relatively small number of persons. As the group size extends beyond these limits, all publicness elements vanish.
Examples of goods and services falling in this classification are those that involve small-number externalities. Fire extinguishers may be an illustration. A transfer of a fire extinguisher to my neighbor does not reduce my own fire protection from the extinguisher to zero, as would be the case with a purely private or divisible good or service. My neighbor's possession of the extinguisher continues to reduce somewhat the probability of fire damage to my property. However, this interaction is limited in range. The transfer of a fire extinguisher to someone who lives three miles from my house does reduce my own benefits from that extinguisher to zero, in which case the exchange becomes equivalent to that of a purely private good.
(3) Partially divisible goods and services, with interactions extending over groups of critically large size This category includes the large-number externalities, or Pigovian externalities. There are both publicness and privateness elements in a good or service, but the publicness or indivisibility elements extend over a group that is critically large in size. An example is inoculation against communicable disease. The securing of a shot provides me with some privately divisible benefits but, also, it provides some benefits to all other potentially exposed persons in a large group. By comparison with the small-number interaction, in this instance many persons are effectively my neighbors. As we shall demonstrate later, the organizational-institutional differences between goods and services falling in (2) and (3) may be significant.
(4) Fully indivisible goods and services, but with interaction limited to groups of critically small size This includes those goods and services that are characterized by the fact that there can be no increase or decrease in the quantity available for one person independently, so long as we are limited to groups of small size. Outside the common-sharing group, however, this pure publicness does not hold, and among separate small groups there may be no publicness elements at all.
Examples for this category are drawn from club-like arrangements, which provide the organizational norm for this set of goods and services. Swimming pools may be mentioned. The single pool may be equally available to all members of the swimming club, provided only that the size of the membership is limited.
Political-Group Size and the Structure of Property Rights
Before proceeding to use the classification scheme for purposes of trying to answer the organizational question posed in the chapter's title, two important additional qualifications must be introduced. Any actual classification of goods and services on the two-dimensional surface represented by Figure 9.1, along with the five numbered categories, must presume that the size of the overall political group is fixed exogenously and, also, that there is some existing structure of property rights.
The importance of the size of the political group can be shown easily. Suppose, initially, that the political group is of size P, that shown by the limits of interaction on Figure 9.1. Assume, now, that we classify a good as falling at point T, at or near the interaction limits. Suppose that the political unit is then incorporated into a larger jurisdiction of size 100 P. Clearly, the good falling at T no longer falls within category (5) or even nearly so. The extension in the size of the group has, in effect, shifted the classification from (5) to (4).
The relevance of some existing structure of property rights for any such classification scheme is also evident, but this is not so readily demonstrable. We may introduce an example. If the existing property laws do not allow landowners to prosecute poachers, then all wooded areas are indivisible among many potential users. "Hunting land" would be classified as falling, say, at R, high on the indivisibility spectrum. On the other hand, if landowners can prosecute poachers, hunting land may be shifted to R', much lower on the divisibility scale.
For our purposes, we may specify simply that the size of the political group as well as the structure of property rights are fixed exogenously. This allows the two-dimensional classification of Figure 9.1 to be made without major inconsistencies or contradictions.
The Functions of Organization
Before we proceed to utilize this classification in answering the basic organizational question, it is helpful to recall the functions that any organization of supply must perform. Varying somewhat the familiar listing in Chapter 2 of almost every elementary economics textbook, these functions may be listed as follows:
1. determination of how much to produce—the allocation function
We shall, for simplicity, refer to these three functions as those of allocation, financing and distribution. The institutional-organizational structure selected, whether this be public, private or in-between, must perform all of these functions, jointly or separately.
A Pure Distribution Model
In order to simplify our analysis and to get somewhere with our two-dimensional classification, let us isolate only one of these three functions, that of distributing the benefits among persons. To do this, we resort to a highly unreal model that involves only the distributive function. Assume that goods and services falling anywhere on the classification matrix of Figure 9.1 are provided externally to the choosing group in fixed quantities. By this manna-from-heaven assumption, we rule out both the allocation and the financing problems.
What does the classification tell us about the problem of distributing supplies of goods and services among separate persons in the group?
Look first at goods and services classified in category (1). Unless the total amount supplied is sufficient to satiate the demands of all members of the group, there will arise some problem of distributing the scarce quantity among the separate users. If property rights are initially assigned to individuals in some fashion not related to their own evaluations, and if utility functions differ, efficiency criteria dictate that some transfers take place among separate persons. If a fully divisible numeraire good exists, trades among persons can be expected to emerge almost automatically. A pricing structure will arise out of the ordinary utility-maximizing behavior of individuals.
For goods and services that are roughly classified in category (2), there will exist some problem of distribution, both within the limits of the indivisibility interaction (which here is only partial) and among the separate small groups. A pricing-exchange system can be predicted to emerge to insure the resolution of the second of these problems in a manner equivalent to that for goods in (1). Within the limits of the small group itself, the partial indivisibility or publicness of the good or service requires that some bargained solution to the distribution problem be reached. Strategic behavior along with negotiating costs may prevent this in-group function being efficiently performed, but pressures toward efficiency will always be present. This case may be illustrated by the fire extinguisher. Suppose that the fixed quantity made available for distribution to the inclusive group, of size N, is N/5 . How will this quantity come to be distributed both among and within small subgroups? Initially, we may presume that individuals will give consideration to the privately divisible elements inherent in the good. A market structure will emerge that will distribute the fire extinguishers to those consumers who place the highest evaluations on these, as privately divisible commodities. Such a distribution will not, however, take into account any of the spillover elements in benefits. All residents in some areas may possess fire extinguishers, and no residents in other areas. Faced with this prospect, we should expect cooperative small groups to form and to bid among themselves and among individuals for the scarce quantity. This will take place until some distribution is achieved that does take the benefit spillovers into account. Within the limits of each cooperating group, however, there remains a distribution problem. In whose residence shall the fire extinguisher be located? This must be the subject of negotiations within the group, and exchanges or compensations can be expected to resolve the issues. But significant negotiation costs are likely to arise.
Let us now examine goods and services that are classified in (4), leaving aside for the moment those in (3). For (4), the degree of indivisibility is great, but the range of the interaction is small. These goods are purely public but only for a small group of sharers. These are club-type goods and services, and we should expect sharing clubs to emerge as the appropriate organizational arrangements. Consider this in the context of our pure distribution model. Suppose that the quantity of a good made available to the all-inclusive political group is again N/5 . Although a bit far-fetched here, let us remain consistent and use the swimming-pool example.
As with (2), we should expect prospective swimming clubs to be formed and to bid against each other, in units of a numeraire, until some distribution of the available pools is achieved. Within each sharing group, however, there will be no problem of distribution. This sharply distinguishes category (4) from (2). If, by classification, the goods fall in (4), there are no privately divisible elements present within the common sharing group, and, hence, the individual's utility cannot be affected by in-group distributional variations.
Remaining within the pure distribution model, we must now examine goods and services falling in category (3). Some problem of distributing any scarce quantity of a good will arise here because, by definition, there are privately divisible elements along with publicness elements. Given any fixed total quantity available to the inclusive group, along with some structure of property rights in this quantity, we should expect that an exchange system would emerge. Individuals would trade among themselves, in units of a numeraire, until the scarce quantity is distributed in accordance with the relative evaluations placed on the privately divisible elements.
As distinct from goods in category (2), however, no further voluntary behavior on the part of individuals could be expected to emerge. Somewhat paradoxically, the distribution in accordance with the relative evaluations placed on the privately divisible elements alone will be efficient, at least in the limiting model. Consider an example of inoculations for a communicable disease. The scarce supply comes to be distributed in accordance with the private-goods aspects alone; spillover benefits are wholly neglected. However, because the publicness elements extend over the whole of the large group, and because every person secures a spillover benefit equal to every other person no matter who gets an inoculation, no distributional change will modify the utility secured from the spillover benefits. This seemingly paradoxical conclusion holds only to the extent that a change in the distribution does not, in itself, modify the basic characteristics of the good itself.*10
There remain only those goods and services that are found in category (5) in our two-dimensional classification. These are the polar public goods in which there are no privately divisible elements and for which the range of indivisibility is sufficiently large to include the whole of the membership of the political community. A useful statement can be made about such goods and services in this pure distribution model. The distribution problem wholly disappears. In fact, one means of defining a purely public good is to say that distribution costs are zero. Since, by definition and classification, the benefits are wholly indivisible among all members of the group, there will arise no problem of distributing the quantity that is available. The purely public good in this polar sense becomes equivalent to a "free good." This does not imply that individual demands for the good are satiated. Individual marginal evaluations may all be positive, but, so long as the benefits are wholly indivisible, no in-group pricing structure will emerge.
This approach emphasizes the inefficiency that must arise if any attempt is made to impose user prices on such a good or service. Since no problem of distributing scarce supplies among separate persons arises, any attempt at user pricing would be equivalent to converting such a good into one that falls within one of our other categories. However, this is only one of the sorts of inefficiencies that must be considered in any organizational comparison. We shall refer to this as distributional inefficiency.
Allocation and Financing
The pure-distribution or manna-from-heaven model has been discussed in some detail because it provides a helpful preliminary stage in using the two-dimensional classification scheme developed. It is only a preliminary stage, however, and the assumptions must be abandoned before serious organizational comparisons can be made.
Assume now that units of any good or service, falling anywhere in our classification, can be secured, from either domestic or foreign sources, at constant cost. (Our theory of public goods is sufficiently complex as it stands without introducing the additional problems that arise when decreasing or increasing costs on the production or supply side are present.) Assume further that this cost per unit is invariant over the separate organizational alternatives that are to be examined.
In this modified model, the organizational arrangement that is finally chosen for any good or service must perform the other two functions in addition to the limited distributional task isolated in the previous section. Some means must be found for determining how much of the good is to be provided; some allocation of resources to this good must be made. The securing of resources involves costs, and some means must be found for covering these; the financing function must be performed.
In the model which isolated the distribution function, it was shown that some market or pricing system would tend to emerge even in the performance of this limited task, at least for all goods save those in category (5). To the trained economist, orthodox micro-economic theory suggests that market or pricing structures can perform the other two functions simultaneously.
With goods and services that fall either in category (1), (2) or (4), collective or public activity in the strict sense may be limited to some establishment and enforcement of property rights, including contracts, and some policing of market structures against fraud and monopolistic combination. To an individual who tries to make the appropriate institutional-organizational comparison at some conceptual constitutional stage of decision, it seems unlikely that collective supply in the standard sense would be appealing for goods and services so classified. And if, for any reason, governmental organization is selected, efficiency criteria would dictate a structure that would closely parallel the working of a market.
Serious consideration for explicit collectivization of supply seems likely to be limited to goods and services that are descriptively classified in categories (3) and (5). Goods and services in (3) contain both privately divisible and indivisible elements. An efficient organizational structure may embody some direct user pricing to facilitate the distributional task. To the extent that user pricing is employed, all three functions are simultaneously performed. Revenues are collected from consumers, and the total of these provides some indication as to the total quantity to be purchased by the community. However, precisely because of the publicness or spillover effects simple efficiency criteria dictate that exclusive reliance on direct user pricing may be undesirable. In a broad institutional setting, more complex efficiency criteria may still suggest exclusive reliance on direct user pricing. This would be the case when the commonality or publicness features are relatively insignificant. In such situations, organizational arrangements will not be different from those for goods in the categories (1), (2) and (4). These arrangements can be predicted to emerge from the voluntary interactions of individuals in trading processes.
But when the commonality elements are considered to be significant, direct user pricing may be supplemented by tax-pricing. This combination necessarily implies that the organization of supply be collectivized, at least in the financing sense. The activity now lies within the domain of "public finance." Examples have already been mentioned, but these can be recalled here. Inoculations against communicable diseases may be provided at nominal fees to the individuals getting the shots, but the main share of the costs of financing the program of immunization may be tax financed. Other examples may be public park facilities, garbage collection services, soil erosion for farmers, college education.
There remain the goods and services classified in category (5). These are purely public with the interaction extending all over members of the politically organized community. In some in-group behavioral sense, these goods are "free." No problem arises in distributing any given supply among individual consumers, since, by definition, each consumer has available to him the full quantity provided. No allocation of shares is necessary.
Concentration on the divisibility characteristic and on the distributional problem alone might suggest that collective organization of supply is strongly implied for such goods and services. A priori, no such implication can be derived. No presumption can be established for either of the two broad institutional alternatives. The necessity that any organization perform the allocative and financing functions, along with the distributive one, removes any apparent presumption that collective organization is necessarily more efficient.
As we have previously shown, any attempt to charge prices for goods classified under (5) must involve distributional inefficiency. The marginal cost of allowing users access to the good is zero; efficiency criteria at this level dictate that the supply should be collectivized and "given away" to all potential users. But let us suppose that attention to these criteria of efficiency causes a good or service to be collectively organized. A decision is made to provide the good free to all users. Somehow the community must also determine how much to supply, and how to finance this quantity. If no user prices are to be charged, resort to the taxing mechanism is necessary. Any real-world taxing scheme must involve its own inefficiencies. The economist's benchmark of the lump-sum tax remains just that, an economist's benchmark. Any tax financing must produce the familiar excess-burden inefficiencies.
Additional inefficiencies are also likely to arise when the allocational decision is faced. If the supply is organized collectively, the allocation question must be settled, finally, by resort to some rule for making collective or group choices. Since separate individuals are likely to prefer different quantities of the good provided, under almost any taxing scheme, and since all persons must adjust to the same quantity, some persons are likely to be disappointed in each direction. For some individuals, the group choice will determine a level of public-goods provision that is below preferred levels. For other individuals, the level will be above preferred levels. These allocational inefficiencies must be considered along with the financing and distributional inefficiencies in any final organizational comparison.
If the provision or supply of a good is collectivized, the distributional efficiencies are reduced to zero in the case of the polar public good. But both financing and allocational inefficiencies emerge. If, on the other hand, arrangements are introduced which, in effect, convert the category (5) good into one that is privately divisible, distributional inefficiencies are necessarily introduced. Against this, however, the conversion of the good into one that allows for direct user pricing tends to reduce both the financing and allocational inefficiencies. To the extent that user financing replaces tax financing, the excess burden is reduced. And to the extent that revenues collected from users provide a criterion for determining the quantity of good provided, no explicit resort to a uniformly imposed and collectively chosen quantity is indicated.
The summary results of this analysis suggest that comparisons must be made on a case-by-case basis, even for goods and services that independently qualify as purely public in the category (5) sense. For such goods and services any attempt to introduce user prices will exclude some persons from access although the real costs of such access to the community do not exist. On the other hand, financing such goods through a tax structure and determining the quantity through a political-choice process introduce inefficiencies of other sorts. By necessity, comparisons are made in a world of second bests.
Public Supply and Public Production
In one sense, the title of this book may seem misleading despite the warning in the Preface. "The Demand and Supply of Public Goods" remains a discussion of demand with little reference to the organization of supply. This comment is relevant to this chapter where the basic elements of a theory of organizational choice are discussed. Here we have referred to public or collective organization of public-goods supply, but precisely what does this mean? Collectivization, or public organization, refers to the provision of the good, its financing and its distribution among separate demanders. Nothing in the discussion implies anything at all about the actual organization of production. Whether or not the good is purchased from privately organized firms and individuals in the domestic economy, purchased from privately or publicly organized supplying agencies abroad, or produced directly by government itself should depend on an efficiency calculus which compares these various alternatives. Collectivization of the supply, to meet individuals' private demands, says nothing about the relative efficiency of producing the good in any one of the several ways. This is a self-evident point, and it would not be necessary to mention here were it not for the widespread confusion that seems to exist.
The advantages of collectivization of supply, to be compared with the advantages of the institutional alternatives, stem from the possible indivisibility of a good or service over separate persons as demanders. This indivisibility, which arises in the consumption or utilization of a good or service, should not be confused with the more orthodox type of indivisibility that arises only in production, that which extends over discrete units of production. It is the second type of indivisibility that may exert some influence on the efficiency of organizational alternatives in producing the good. Once a decision is made to collectivize the supply of a good or service, the choice among alternative means of producing this supply is important, and careful analysis is required. This analysis, however, does not properly belong to the theory of public goods as we have interpreted it here.
This chapter has done little more than introduce some of the complexities of the question posed in its title: "Which Goods Should Be Public?" Any positive approach to this question must proceed on a case-by-case basis and provisional conclusions reached only after careful comparison of institutional alternatives in the broadest sense. The descriptive characteristics of a good or service, the technology of common-sharing and the range of such sharing, are important determinants of organizational efficiency. Care should be taken, however, not to presume that these characteristics, taken alone, allow a priori judgments to be made. The pound of ceteris paribus must be used with caution here, since other things are not at all likely to remain equal over the institutional variants that may be examined. The predicted working properties of the institutional structures, imposed as constraints on individual behavior, must be evaluated.
The modern theory of public goods, as it is widely interpreted, tends perhaps to overemphasize the descriptive characteristics of a good or service as a determinant of the efficient organizational arrangements to the neglect of other relevant factors. Analysis must start somewhere, however, and the modern theory can be extremely useful in providing the foundations upon which a more complete analysis can be built. Hopefully, some elements in such extended analysis have been suggested here, but this short book cannot include more than this.
The recent exchange between Jora R. Minasian and Paul A. Samuelson is directly relevant to the question posed in Chapter 9 [Minasian, "Television Pricing and the Theory of Public Goods," Journal of Law and Economics, VII (October 1964), 71-80; Samuelson, "Public Goods and Subscription TV: Correction of the Record," Journal of Law and Economics, VII (October 1964), 81-84]. Otto A. Davis and Andrew Whinston have also provided a recent contribution ["On the Distinction Between Public and Private Goods," American Economic Review Proceedings, LVII (May 1967), 360-73]. The paper by R. N. McKean and Minasian also bears on some of the points ["On Achieving Pareto Optimality—Regardless of Cost," Western Economic Journal, V (December 1966), 14-23].
Other works that may be cited refer less directly to the central question and for the most part these analyze goods and services falling within particular sub-categories of the classification scheme presented. The recent work on small-number externalities by R. H. Coase deserves special mention ["The Problem of Social Cost," Journal of Law and Economics, III (October 1960), 1-44]. Other works in this same area of analysis include papers by James M. Buchanan and Wm. Craig Stubblebine ["Externality," Economica, XXIX (November 1962), 371-84]; by Ralph Turvey ["On Divergencies Between Social Cost and Private Cost," Economica, XXX (August 1963), 309-13]; by Davis and Whinston ["Externalities, Welfare, and the Theory of Games," Journal of Political Economy, LXX (June 1962), 241-62].
Large-number externalities, goods and services classified under (3) in Chapter 9, have been the subject of much practical interest in terms of air pollution and water pollution. Only a limited amount of this discussion is of theoretical interest, but especial note should be made of the works by Allen V. Kneese [The Economics of Regional Water Quality Management (Resources for the Future, 1964); "Quality Management of Water Supply," in The Public Economy of Urban Communities, edited by J. Margolis (Resources for the Future, 1965), pp. 170-91].
Three papers explore the predicted differences in results under different forms of organizing the provision of impure public goods [James M. Buchanan and Milton Z. Kafoglis, "A Note on Public Goods Supply," American Economic Review, LIII (June 1963), 403-14; James M. Buchanan and Gordon Tullock, "Public and Private Interaction Under Reciprocal Externality," in The Public Economy of Urban Communities, edited by J. Margolis (Resources for the Future, 1965), pp. 52-73; Wm. Craig Stubblebine, "Institutional Elements in the Financing of Education," Education and the Southern Economy, edited by J. W. Mackie, Southern Economic Journal Supplement, XXXII (July 1965), 15-34].
The problems raised by limited publicness in the spatial sense, where the range of common consumption does not extend over the entire area of the inclusive political jurisdiction, has been explicitly discussed by Albert Breton ["A Theory of Government Grants," Canadian Journal of Economics and Political Science, XXXI (May 1965), 175-87]. Some implications of this problem in a slightly different context are discussed in my paper ["An Economic Theory of Clubs," Economica, XXXII (February 1965), 1-14]. Some of the models developed by Mancur Olson are also relevant here [Mancur Olson, The Logic of Collective Action (Cambridge: Harvard University Press, 1965)]. In a somewhat more general setting, Mark Pauly has examined some of the organizational problems for goods in the (4) category with tools of modern game theory ["Clubs, Commonality, and the Core," Economica, XXXIV (August 1967), 314-24].
Some aspects of public-goods theory in application to local government finance are found in papers by Charles Tiebout and by Alan Williams [Tiebout, "The Pure Theory of Local Expenditure," Journal of Political Economy, LXIV (October 1956), 416-24; "An Economic Theory of Fiscal Decentralization," in Public Finances: Needs, Sources, and Utilization (National Bureau of Economic Research, 1961), pp. 79-96; Williams, "The Optimal Provision of Public Goods in a System of Local Government," Journal of Political Economy, LXXIV (February 1966), 18-33].
The degree of divisibility over units of production is relevant to the organization of production. Given full divisibility of this sort, production of a good may be competitively organized even if the supply is fully collectivized. By combining full divisibility in this respect with complete indivisibility among separate consumers, Earl Thompson has developed an extremely interesting variant of the standard public-goods theory. Under this combination of circumstances, he argues that collectivization is not suggested, even for the usual "market failure" reasons, because competitive sellers of the good will offer their services, unit by unit, to the common demanders and they bid prices down to such an extent that an oversupply rather than an undersupply will be generated. Here collectivization as an alternative institutional form might arise for reasons just opposite to those presumed relevant in the orthodox treatment. This model seems to be of limited relevance in the general case, but it may be applicable to particular kinds of public goods, notably those relating to research and education. This summary is offered as my own interpretation of Earl Thompson's complex analytical model [The Perfectly Competitive Allocation of Collective Goods, MR-49, Institute of Government and Public Affairs, University of California, Los Angeles, September 1965].
Neither in this book nor in most of the recent discussion is a distinction made between public goods as consumption goods, and public goods as intermediate goods that enter into the production of final private goods. The theory, in its essentials, is not modified, but this distinction has been precisely formulated by Keimei Kaizuka ["Public Goods and Decentralization of Production," Review of Economics and Statistics, XLVII (February 1965), 118-20].
Notes for this chapter
This chapter is not well integrated with the other parts of this book, and earlier attempts to locate the material elsewhere in the manuscript were not successful. Although the analysis builds on the models previously discussed, a new question is introduced which cannot be adequately explored in all of its complexities. Despite this acknowledged incompleteness, I have decided to include the chapter because of its relevance for the interpretations that many scholars, correctly or incorrectly, have placed on the modern theory of public goods, and finally, because of the fundamental and general interest of the question itself.
This is an important and necessary qualification. For goods and services exhibiting publicness over large groups (and inoculations may be excellent examples here) the way in which any available quantity is distributed may affect the degree and extent of spillover benefits generated. This is only one type of difficulty that is likely to be encountered in any attempt to classify goods and services by criteria that are inherent in the descriptive characteristics of the goods themselves.
End of Notes
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