The Demand and Supply of Public Goods

James M. Buchanan.
Buchanan, James M.
(1919- )
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First Pub. Date
Indianapolis, IN: Liberty Fund, Inc.
Pub. Date
Foreword by Geoffrey Brennan.
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Chapter 10Toward a Positive Theory of Public Finance



Public finance is now an exciting field of scholarship for a very simple reason. Scholars have only recently begun to look at fiscal phenomena "through a different window." Much remains obscure, but new insights are appearing. New relationships are being derived; old and established institutions and ideas are being subjected to critical analysis. Paradigms have not yet emerged to fix irrevocably the thought patterns of professionals. The theory of public goods remains in a preparadigm stage of development.


Why do we witness the blossoming of this theory only in the mid-twentieth century? In the early and mid-nineteenth century when laissez-faire served as an intellectual model for social order, few intellectual historians should have expected a theory of public goods to parallel the development of the theory of private goods. But why was such a theory absent later from the many and varied proposals for socialist alternatives? Central to socialist reform from the outset and in all its varieties has been the shifting of goods from private or market organization to public or governmental-political organization. Why did the socialist theorists neglect the allocative norms for public provision, and, when these were discussed, why did they limit analysis to private goods, publicly provided? Why do the most sophisticated socialist solutions mirror those of the perfectly working market economy, exclusively characterized by private goods?


These questions, and other similar ones that could be raised, can only be answered in part and guessed at in the large. Socialist and nonsocialist scholars alike tended to accept the dichotomy between the public and the private sectors of the economy. Socialist proposals aimed at shifting the private production of private goods to collective management. Few questions were raised about "public" supply of "public" goods, for the most part, those which had been collectivized from the outset. This sector was not, presumably, subject to economic analysis; it received little attention from socialists or nonsocialists. In this sector, decisions were presumed to be made "politically" and not to be subjected to the analysis applied to decisions on the demand and supply of private goods, whether these should be provided in markets or by governments.


In the political sphere, no attempt was made to relate outcomes to individual values, and policy analysis proceeded on the "as if" assumption of benevolent despotism. This policy presumption was maintained, surprisingly, throughout the very period of history when the extension of suffrage made democratic choice apparent to everyone. From our vantage point, the blindness of the neoclassical English utilitarians to the realities of political democracy must remain largely unexplainable. This was fostered to an extent at least by the accompanying dominance of idealist notions in political theory.


These comments are fully applicable only to the English-American tradition. Continental scholars were more enlightened. Wicksell dominates the scene and he remains the intellectual father of modern public-finance theory. In his perceptive linking of the economics of public finance to the actualities of democratic process, he was at least a half-century in advance of his professional colleagues. The Italians were less sophisticated than Wicksell, but, in Francesco Ferrara, who wrote in the 1850s and 1860s, they take the place of antecedence. Mazzola, Pantaleoni, de Viti de Marco, Einaudi, Barone, Fasiani: these are but a few of the outstanding names in a following Italian tradition that was based on a recognition of the productivity of public services to individuals, on the identity of the producers and consumers of public services in an effectively democratic model, and on the cold realities of exploitation through governmental-fiscal processes. These scholars were almost wholly spared the nonsense of utilitarian pleasure-machines, and they paid little attention to the Edgeworthian vision of measured sacrifice doled out by some omniscient fiscal brain. German-language scholarship should also be mentioned here because of the work of Sax, although his ambiguities concerning collective wants tend to overwhelm the real insights that he possessed. Finally, the Swedes span the era of continental classicism in the work of Erik Lindahl, who, although he was influenced by Wicksell, tended to concentrate attention unduly on the bargained solution to the public-goods problem and to shift attention away from the political-economic relationship properly stressed by Wicksell.


The failures of English-language neoclassical thought in public finance cannot be excused, nor can that of post-Lindahl continental thought. Marshallian economics had its Marshall, who, despite his own reformist urges, was yet able to cut through the normative underbrush and make genuinely scientific progress. Public-finance economists were left to flounder in the muddy mixture of incidence theory and nonsense norms, having no Marshall, and having neither read, nor if read, understood, Wicksell and the Italians. They continued blithely to ignore the whole political process. They remained unconcerned with the way fiscal decisions actually get made, and they were apparently quite willing to define the whole expenditure side of the budget as being outside the pale of their analysis.


It is but small wonder that little progress was made toward either an acceptable normative theory or a positive predictive theory of public finance until near the close of the interwar period. Musgrave's discussion of Lindahl's model, along with Howard Bowen's examination of voting and resource allocation, mark the beginnings of the modern era. These contributions were supplemented and the scope of theory expanded by Paul Samuelson's rigorous formulations of the efficiency conditions in his 1954 and 1955 papers. Wicksell was made available to English-language scholars in translation only in 1958, along with other important continental writers. Only in the decade since have we begun to witness a flowering of interest in public-goods theory, generally, and this interest has not yet reached its zenith.

The Normative Theory of Public Goods


Normative and positive strands are closely intermingled in the modern theory of public goods. As I suggested in Chapter 1, my own interpretation differs from that of other scholars largely in my somewhat greater emphasis on the positive content that can emerge from the analysis; this explains my greater interest in analyzing political choice. In any case, it seems useful to separate the normative and positive elements to the extent that is possible, despite the fact that the analysis is parallel in many of its particulars. The difference arises in the conceptual uses to which the analysis is to be put.


The normative theory of public goods, best represented in the two basic papers by Samuelson, stems directly from theoretical welfare economics. This subdiscipline is widely acknowledged to be normative in that its allocative norms prescribe the ends or "shoulds" of policy, provided that efficiency criteria are accepted. These norms are, of course, much more carefully circumscribed than were those of the old welfare economics. The formal structure of the new version was developed only in the 1930s and 1940s, although the intellectual origins lie in the work of Pareto. After 1934, when Robbins laid bare the weaknesses of the normative presuppositions of the post-Marshallian utilitarians, the search for more rigorous criteria for making policy statements culminated in a rediscovery and elaboration of the Pareto norms for optimality or efficiency. This set of norms allowed economists to classify positions, or proposals for changes in positions, into two separate categories: optimal (efficient) and nonoptimal (inefficient). This classification is accomplished with minimal ethical commitment, and the commitment that is required is such as to command near-universal consent.


In a formal sense, the Pareto constructions were highly useful, and remain so, but economists were not fully satisfied with the formal limits. They sought to find more direct application, and this search produced its own exhausting and long-continuing discussion of compensation. This digression aside, however, the multiplicity of possible outcomes that satisfy Pareto norms in other than the uniquely competitive structures disturbed those who searched for the single best state of the world. This led, in its turn, to the attempts to formulate a "social welfare function," a fictional device that draws attention away from the explicit resort to external and nonindividualistic criteria that is required for any selection from among a set of optimal positions or moves. The basic inconsistency between this and the whole Paretian edifice was either not appreciated or deliberately ignored.


This is an ambiguity that continues to plague modern welfare economics, and with it, the normative theory of public goods. The proper concern of the latter should be limited to laying down the necessary marginal conditions for the allocation of resources to public-goods supply. This task is done when these conditions are formally stated, provided that we disregard the more complex extensions to institutional efficiency discussed in Chapters 8 and 9. It should not be disturbing that distributional questions, described either in terms of some initial imputation of income-wealth or in terms of specific gains-from-trade in public goods, remain unresolved when the allocational norms are stated. Multiple outcomes are possible, each of which will satisfy the conditions for efficiency, but the role of the analysis in this normative version is not that of making a specific selection from among these outcomes. Rather its role is that of providing the formal classification scheme that allows the analyst to place all possible outcomes into one of the two sets.


Both Samuelson and Musgrave fail to sense what to me seems to be the basic contradiction between the social welfare function approach and the use of Pareto criteria. Samuelson defines the necessary conditions for allocative efficiency with respect to public goods, but after having done so, he then resorts to a social welfare function to select the single best state of the world. It is impossible, of course, to isolate the allocative problem from the distributional one, since the sharing of the inframarginal gains-from-trade as well as the initial position will determine allocative outcomes through the operation of income-effect feedbacks. Conceptually, however, this presents no issue since, in my view, the normative theory should end with its formal statement of the necessary conditions that must be met. Musgrave follows a pattern similar to Samuelson's when he conceptually separates the allocation and distribution functions of the budget. It is difficult to understand the logic of this segmentation if a consistent analytical model is desired. If external criteria are introduced to resolve distributional issues, to produce some unique outcome, why should norms based exclusively on individual preference orderings be honored in allocating resources to public-goods production and supply? Since the distribution will, in itself, have feedback effects on allocative outcomes, is not such a separation empty?


My interpretation is that one can present a consistent normative theory of public goods which derives allocative-efficiency conditions from individual preference orderings and which makes no attempt to select from among the set of Pareto-optimal outcomes. The search for a unique solution is misleading since the multiplicity of optima is a characteristic of all interaction processes where gains-from-trade are possible. The apparent uniqueness present under perfectly competitive conditions in the private-goods market should be treated as a bizarre exception, not as a characteristic to be mirrored in other settings.


By classifying this theory as normative, I do not suggest that explicit value judgments are involved or even that the analysis lacks positive content. My usage of the designation "normative" implies that the objective of analysis is to lay down the "should" criteria for resource allocation, given the presumed acceptance of efficiency norms. Much of orthodox economic theory is normative in this sense, oriented to providing "government" with "advice" as to the "shoulds" of economic policy, presuming that efficient resource allocation is desired. In the context of my discussion, the contrast between "normative" and "positive" theory is not one between explicit value espousal and objective or detached analysis. Instead the contrast is one between two sets of objective analysis, the first aimed primarily at specifying precisely the characteristics of results that "should" be aimed for in governmental action on the presumption that efficiency is desired, and the second aimed primarily at explaining and predicting the outcomes of collective decision processes involving the participation of many persons.


The possibility of separating these two strands of analysis is greater in the theory of public goods than in the theory of private goods, the analysis of markets. In the latter, thorough analysis of the necessary conditions that must be satisfied for overall allocative efficiency carries with it a parallel analysis of the interaction processes through which the voluntary exchange behavior of individuals produces efficient outcomes, given that the familiar set of side conditions is also met. Micro-economic theory becomes at one and the same time a normative theory of public policy to the extent that efficiency objectives are paramount, and a positive theory of market interaction. In the former, the theory conceptually tells the government what conditions should be satisfied; in the latter, the theory predicts the results that will tend to emerge.


In the ordinary normative version of the theory of public goods the positive content is largely contained in its implied prediction concerning what will not happen. The normative theory states the necessary conditions that should be met if the relevant decision makers accept overall efficiency criteria. It does not contain in the process an explanation or prediction about the voluntary interaction of individuals operating to meet these conditions. Quite the opposite; the theory more or less directly implies the positive statement that these voluntary interactions will not meet efficiency requirements, even in some acceptably proximate sense. In other words, the normative theory of public finance contains a positive statement about "market failure" in the presence of public goods. It stops short of analyzing the institutional processes that might be required to generate efficient outcomes.

The Positive Theory of Public-Goods Supply


A positive theory of public finance must begin with the basic efficiency analysis that is contained in the standard normative theory. In addition, it must incorporate the negative result that wholly voluntary behavior of individuals in exchange may not produce outcomes satisfying allocative efficiency requirements. Beyond these essentials, a positive theory must analyze the behavior of persons as they examine organizational alternatives to markets, along with their behavior as they participate in collective decision processes that may be designed to secure mutual gains-from-trade in public goods.


The possible failure of voluntary exchange or market mechanisms to generate efficient outcomes arises because of the large-number setting in which individuals find themselves. The free-rider dilemma expresses this critical feature. Despite the presence of this dilemma, however, there exist mutual gains-from-trade in public goods and services, and these motivate individuals to seek agreements or changes in the rules governing behavior, even if there is no incentive for them to engage in person-to-person bilateral exchanges of the ordinary sort. Before such generalized agreements can be properly analyzed on their own account, small-number models may be introduced provided that these are interpreted as useful analogues to large-number models. It is in this context that the small-number models are presented early in this book. These allow us to develop the basic elements of the normative theory in a positive context. The models show that, in the absence of the large-number problem, efficient outcomes will tend to emerge from voluntary-exchange processes. Through these models the theory of public-goods supply is placed in a position roughly comparable to the theory of private goods which, in this respect, remains always in small-number settings.


The models of bilateral (and later of trilateral) trade or agreement on the supply and financing of public goods are not intended to explain real-world fiscal structures. They should be considered as demonstrations of the pressures that mutual gains-from-trade will exert on persons, who will on the basis of their own preferences organize "public-goods trades," save as they are prevented from so doing by the large-number dilemma. In this particular aspect, the bilateral models developed by Lindahl, although they are formally similar to those developed in this book, seem to have been misinterpreted, even by some of their expositors. These models should never have been aimed at explaining how voluntary exchange might lead to efficient outcomes in the presence of public-goods phenomena. Properly interpreted, they show how and why efficient outcomes will emerge, given public-goods phenomena, in the absence of the large-number dilemma. In this context, the small-number models represent helpful abstractions in a whole chain of related theoretical reasoning. Much of the criticism of the Lindahl-type models has concentrated on the bargaining or strategic-behavior difficulties encountered in small-number interactions. The attempt of individuals to conceal their own preferences in such situations has been discussed at some length. This line of criticism is, in my opinion, misdirected because it treats the small-number setting as a conceptually real situation, and not as an analytical device that is helpful in extension to large-number situations. If public-goods phenomena should arise only in small groups, and if the analysis of the response of individuals in such groups should be the object of ultimate interest, both the Lindahl-type models and the criticisms of these would serve quite a different function from that under discussion in this book. The primary task of theory is to explain behavior in the presence of public-goods phenomena over large-number groups. Here, the small-number models should, and must, abstract from the specific characteristics of behavior that arise only in small-number interactions. If they do not do this, these models can be of no use in explaining the large-number models that must finally be developed.


The simple trading models demonstrate only that efficient outcomes will tend to emerge in the extremely rarefied conditions imposed. If the number of persons is small, and if they behave vis-à-vis other persons as if they are in large-number circumstances, ordinary exchange will generate outcomes that may be classified as optimal. The free-rider analysis, following hard on these trading models, demonstrates that the extension of numbers is sufficient to eliminate the optimality properties of predicted trading outcomes. The next stage of a positive theory is apparent. Individuals, recognizing the failure of voluntary-exchange organization, but also continuing to recognize the presence of mutual gains-from-trade in public goods, may propose "rules changes" that will so modify the conditions for individual choice as to secure at least some if not all of the gains-from-trade that are promised. This stage involves the logical derivation of "fiscal systems" as a part of the whole political order from the basic preference orderings of individuals.


The "constitutional rules" that describe the fiscal system must include rules concerning the making of budgetary choices in all aspects. These must include rules for deciding among alternative proposals that might be presented, rules for selecting which goods and services are to be supplied publicly rather than privately, rules for determining the characteristics and the extent of provision for those goods and services that are to be privately supplied, and, finally, rules for allocating the costs of these publicly supplied goods and services among individuals and groups in the whole community.


The mere enumeration of these different sets of rules or institutions suggests the magnitude of the task required before the construction of any complete positive theory. The simple efficiency norms provided by the orthodox Pareto criteria are no longer directly applicable. At another level, efficiency criteria can be evoked, as suggested in some of the earlier discussion, but these are more complex. An extension of Pareto criteria to the predicted operation of rules or institutions becomes possible, and, in one sense, the standard normative theory of public goods can be extended in this manner. This extension goes beyond the problems of determining how much and which public goods should be supplied and moves toward the problems of determining which set of fiscal institutions should be selected. The extended normative theory involves the discussion of the optimal or efficient fiscal constitution.


This extension of theory to the analysis of alternative rules or institutions is more natural in a positive than in a normative approach. In the former, the extension of analysis to the problems of choice among rules becomes an essential follow-on stage. With the normative theorist, having completed his derivation of the required efficiency conditions, there is the underlying presumption that the collectivity, the government, will somehow implement his implied recommendations, or, at the least, will take these into account in the policy mix that it does finally select. With the positive theorist, there is no such underlying presumption since the collectivity simply does not exist apart from the individuals that make up the community. Collective action must be "explained" and "understood" through individual behavior. The questions that must be asked are: How do publicly supplied goods and services get organized in large-number groups? Who decides, and on what basis, which goods and services are to be publicly supplied? Who decides, and on what basis, how much of each good and service to provide? Who decides, and on what basis, how costs are to be shared among members of the community? Who decides, finally, on who is to decide?


There are two separate parts of this institutional stage of a positive theory of public finance. The first consists in the development of a logical theory of individual choice among alternative institutions. This is closely akin to the economist's standard theory of individual choice, and it creates no conceptual difficulties. The procedure here is one of examining the choice among alternative institutional structures in terms of an individual decision calculus. Given a utility function that satisfies the usual conditions, how would an individual order alternative rules and institutions through which certain goods and services will be supplied publicly? To answer this question, even at this logical stage, requires that predicted working properties of alternative institutions be analyzed. The models of Chapters 8 and 9 do little more than to suggest the sort of theorizing that is needed.


The second part of a theory of institutional choice, as an integral part of a positive theory of public finance, is essentially empirical. Perceptive observations of real-world fiscal structures are needed, and the analyst must try to isolate the central elements in such structures that serve best to explain and predict. Conceptually, models of real-world institutions can be tested; hypotheses can be refuted, and, in turn, different hypotheses can be suggested. Painstaking accumulation of the record of historical experience, careful presentation of descriptive detail, and comparative analysis: these are all necessary.



This small book does not contain a complete theory of public finance in the positive sense idealized. This should be emphasized, and no claims in this direction are advanced. Hopefully, I have been able to clarify some of the ambiguities in the elementary stages of analysis. At the same time, I hope that more interesting avenues for further and more complex theory-building have been exposed. If broad agreement among specialized scholars can be attained concerning the theory of public goods in the limited one-good, one-period model, progress will have been considerable. This is true whether these scholars work within either the normative or positive version of analysis. From this limited base, further elaboration and development of the theory of fiscal institutions can take place.


There seems to be no need for a normative-positive clash on methodological principle here. The normatively oriented economist who remains within the Pareto-efficiency framework and who is willing to stretch his constructions beyond their normal limits can be of great assistance to his positivist counterpart who explicitly rejects global efficiency criteria and seeks to predict the results of individual behavior in institutional constraints. The distinction between these two need not lie in the particulars of analysis; the distinction lies instead in the somewhat greater willingness of the normativist to stop short of full explanation, to consider his strict role as "economist" finished once he has completed what, to the positivist "political economist," seems only a part of the job.


In conclusion, I return to the first paragraph of this chapter. The theory of "The Demand and Supply of Public Goods" remains in a preparadigm stage of development. Herein lies its current interest. Also for this reason, no single treatment or presentation is likely to command universal assent among informed scholars nor is it likely to be free of its own ambiguities, confusions and contradictions. This book is surely no exception. It is based on my current (February 1967) interpretation of the central subject matter. On the basis of my own experience in discussing these materials in graduate seminars for more than a decade, I can make only one prediction with certainty. My own views and interpretation in 1977 will not be in full accord with those presented in this book.

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