Buchanan, How should Common-Access Facilities be Financed?

Introduction

This paper challenges some of the sacred cows in public finance. I demonstrate that the efficient means of financing certain common-access facilities may involve the imposition of taxes that are inversely related to the income-wealth positions of potential users. The analysis suggests, further, that the adoption of such taxes may be in the interest of those very consumers who are subjected to the relatively high rates. Although its subject matter is limited in scope, the paper adds to the mounting evidence that traditional public-finance precepts are little more than outmoded shibboleths for old-fashioned left-liberal economists who have seldom separated their ethics from their analysis.

Common Access Without User Prices

For many facilities adequate financing from direct user pricing is inefficient in an institutional sense. The costs of excluding users on a unit-of-service basis may be prohibitive. In such cases, usage of the facility may be opened to all. Access to the services of the facility may be made commonly available to all members of the relevant community without payment of a user charge. To finance such a facility requires resort to some means other than direct pricing of services as used. These means may take the form of initiation fees, annual club dues, membership subscriptions, or season tickets in the case of privately-owned facilities (golf and swimming clubs are good examples) or taxes in the case of publicly-owned facilities (examples are municipal swimming pools, and museums). The organizational arrangements, as such, are not directly relevant to the question to be examined here. The discussion is limited to the ordering of such “nondirect” prices among members of a potential user or consumer group. Somewhat paradoxically, the analysis suggests that for some common-access facilities, low-income users “should” be charged higher “nondirect prices” than high-income users.

An Example

Consider a simple example which we place in a collective-choice context. Suppose that there are acknowledged advantages to a small community of nearby residents from the maintenance and upkeep of a beach facility. Furthermore, assume that the charging of direct user prices in the form, say, of daily or hourly fees, involves unduly high collection and enforcement costs. The facility may be maintained at differing levels of quantity, which can be measured continuously in square yards of sand beach. The decision as to the quantity to be maintained is to be collectively made. Income-wealth levels differ as among members of the community of prospective consumers or users, but, for simplicity, we assume that underlying preference functions are identical for all persons.

The question is: How “should” the community of users finance the beach-maintenance charges, and how much maintenance (measured in square yards) “should” be undertaken? Conceptually at least, the second part of this question can be answered without difficulty by anyone familiar with the modern theory of public or collective-consumption goods. A necessary condition for the attainment of an optimal or efficient quantity of the “good,” in our case, the beach facility, is equality between marginal evaluations summed over all potential users and the marginal cost of providing the “good.” In terms of this example, optimality is reached when the value placed on slightly larger beach area, summed over all persons in the community, is equal to the added maintenance cost involved in the slightly larger area. As noted, this is a conceptually satisfactory answer rather than an instrumentally helpful one. The criterion tells us next to nothing about how the marginal evaluations of the members of the community may be determined.

Wicksell's Criterion for Efficiency

Knut Wicksell's approach to the problem of financing publicly-provided facilities provides more instrumental assistance in this respect.1 The costs of financing differing levels of beach maintenance may be presumed to be known in advance. If we disregard, for now, the costs of organizing for political decisions, we may suppose that some arbitrarily-chosen small initial level of beach maintenance, say for X square yards, is proposed along with a whole array of differing tax-sharing arrangements. Among the community of N persons, total tax payments, T, must be equal to the known costs of financing the initial level of maintenance, X. Individual tax shares may, however, range from zero to T, or, if we designate an individual's share as ti, the condition to be met is that 0 ≤ ti ≥ T.2 Any tax-sharing scheme that meets this condition qualifies for inclusion in the array that is matched against the proposed outlay.

In some way, say at a town meeting, the outlay proposed is presented for a vote in the form of a series of motions each one of which embodies simultaneous approval of the outlay and a specific tax-sharing arrangement for financing it. So long as unanimous consent is not secured, no decision is reached. The decision stage stops when some tax plan for financing the outlay secures the agreement among all members. For the small, initially-proposed quantity of maintenance, there may, of course, be many tax schemes that could generate unanimous support. Suppose that one such scheme is adopted. From this point, a second proposal is made which embodies the financing of some increment to X. The same voting procedure is followed, with unanimous approval being the criterion for final decision. In this way, the community proceeds by a series of finite steps to determine the appropriate quantity of beach maintenance to be provided and, simultaneously, the tax sharing of the costs of the facility will be determined.

The Wicksellian collective-decision model conceptually provides us with a meaning of efficiency in financing, a meaning that might be revealed by individual behavior under a set of idealized conditions. Even Wicksell recognized, however, that these conditions could hardly be realized in any real-world decision process. Group decision-making takes time and hence involves costs. Furthermore, the existence of a unanimity rule creates strong incentives for unproductive investment in bargaining strategy on the part of individuals. On balance, the Wicksellian framework provides little more than a benchmark from which departures may be measured. In a larger institutional sense, efficiency in collective-choice making may require violations of the conditions that are required to guarantee efficiency in the narrowly allocative sense.3

Tax Institutions and Collective Decision Rules

To this end, modifications on the Wicksellian scheme have been variously proposed. Relatively little support may be found for application of a unanimity rule, but public-finance scholars have recognized that properly chosen tax-sharing schemes may partially substitute for the inclusiveness of rules. To the extent that tax-sharing institutions can be selected and imposed independently of the collective-decision process, and to the extent that the tax shares embodied in these institutions accurately reflect the strength of individuals' desires for the facility to be financed, the inclusiveness of choice-making rules may be relaxed without generating predicted departures from efficiency in outcomes. As an extreme example to illustrate this relationship between tax shares and decision rules, consider a community of equals in which a tax sharing institution requires equal payments. In this case, if the facility to be financed is of the extreme polar type that benefits all members of the community equally, any decision-making rule will yield the same result as any other, from single-person dictatorship to unanimity.4

The tax institutions that are observed to exist normally relate individual tax shares positively to income-wealth positions of individuals, and ethical norms for tax sharing embody this relationship. To the extent that these institutions are interpreted to embody efficiency at all, the relationship between income-wealth criteria and tax shares is taken to indicate a positive income-wealth elasticity of demand for the services provided by the publicly-provided facility. Since this is characteristic of so-called “normal” goods in the private economy, the extension of this assumption to apply to goods and services that are publicly-provided seems to be fully acceptable. If publicly-provided goods are characterized by a positive income elasticity, certain bounds would be set on the inefficiency of public-goods provision, almost independently of consideration for the actual rules for reaching collective or political decisions or for the practical workings of these rules. That is to say, so long as individual tax shares are positively related to income-wealth positions, and so long as the goods in question satisfy criteria for “publicness,” the inefficiencies generated by less-than-unanimity rules for decision may not be excessive. Something of this sort, at least, may describe what we might call the “conventional wisdom” among modern public-finance specialists.

I shall demonstrate, however, that there is a major error in the line of reasoning traced out briefly above. When this error is corrected, it is relatively easy to show that, for the sort of facilities examined in this note, there need not be a positive relationship between income-wealth level and tax shares for individual members of the community, even if, under some conditions, the services of the facilities should be characterized by a positive income elasticity of demand. Efficiency may require that low income-wealth recipients pay somewhat larger tax shares than their high income-wealth counterparts, and failure to allow this in fiscal institutional structures may, in fact, impose differential harm precisely on the low income-wealth users of the facilities.

Dimensions of Evaluation

Let us return to the beach maintenance example introduced earlier. If their underlying preferences are essentially identical, how could it be possible that a low-income member of the community might place a higher marginal evaluation on some given extension of the facility size than his high-income neighbor? Once the question is put in terms of this sort of example, the answer seems intuitively plausible. The marginal evaluation that an individual user places on an extension of the facility is the increment to total value that he anticipates to derive from this extension, an increment that is dependent on his anticipated total usage of the facility. If it can be plausibly argued that the low income consumer uses the services of the common-access facility more than the high-income user, it becomes logically possible that the marginal evaluation which he places on the extension of the facility is relatively larger. This will be possible even if, over wide ranges of equal service levels, the evaluation of the high-income user is relatively greater.

For a market-supplied good or service, income elasticity is defined to be the percentage change in quantity demanded divided by the percentage change in income. But this definition obscures the assumption of a fixed price. Implicitly, the adjustment that takes place in consumption consequent on the change in income is in quantity demanded. Hence, individual persons at different income levels are presumed to consume or use differing quantities. For a public good, however, the characteristic feature is precisely the absence of quantity adjustment. That quantity which is available to one user is, by definition, equally available to all users. In our example, the beach, in whatever quantity provided, is equally available to all members of the community. The common measure of income elasticity is scarcely relevant until and unless we specify a price. In this case, however, it is precisely the “price” differentials, in this case tax-share differentials, that we seek to establish. To say that the publicly-provided good exhibits a positive income elasticity of demand is meaningless without some specification of the demand price.

But the commonly available facility may be used variously by different members of the community. Usage of the services of the facility, the beach in our example, depends on the action of the individual in availing himself of the privilege. And it is in this respect that the low-income or low-wealth consumer may be motivated to use the services of the facility to a relatively more intensive level than his high-income counterpart.

It will be helpful to think of a common-access facility, in whatever quantity provided, as being made available to users at a zero direct price, although the analysis would be unchanged if some nominal user fees should be charged. At a zero price, why should we predict that the consumer with relatively low income would utilize the services of the facility more than the user in a more favorable economic position? If usage were genuinely “free,” we should predict that, with comparable utility functions, the intensity of usage would be approximately the same for all persons. But, despite a zero money price, the actual usage of a facility cannot be “free” in a utility sense. Consumption takes time, and facilities of the sort discussed here are likely to be relatively time-intensive when compared with other consumption goods and services. As Gary Becker has emphasized, it is necessary to consider “time prices” as well as money prices in any complete theory of individual consumer adjustment.5 The time-price, unlike money price in market transactions, will not be uniform as among separate consumers because of the differing opportunities for using time in other ways, either in the production or in the consumption of income. Almost by definition, these opportunities are relatively greater for the potential user who receives the relatively higher income. The services of the publicly-provided facility, available at zero user prices, are, therefore, “cheaper” for the low-income person than for his high-income cohort because of the differential in time price. From this it follows that there will be a difference in the intensity of usage of the facility as between income levels, and that the relatively low-income user will consume more services of the facility. In our example, the number of trips that the relatively low-income user will make to the beach each year may be predicted to be greater than the number made by his high-income counterpart, assuming similarity in underlying utility functions. The potential user who has a relatively high income can spend his time in alternative ways, either by consuming substitute services (he may go to the mountains), or by earning more income.

The relationship between usage and alternative opportunities can be empirically observed and is, of course, widely recognized. The “beach boys” are those who do not have either income or alternative employment opportunities readily available. The only point that is at all novel in this analysis involves the implications of this for tax-share adjustments and for determining the efficient quantity of facility to be provided. To examine these implications more carefully, let us return to the Wicksellian collective-choice process introduced above. Suppose that the community is currently financing a quantity of beach maintenance, say Y square yards of beach area, and that this is being financed from the levy of equal per head taxes, regardless of the fact that persons with differing incomes are among the group of users. An increment in quantity is now proposed, say a shift from Y to Z in quantity, with the unanimity rule in force. The cost of financing the increment is known, and the proposal to add this quantity is placed before the group, along with a whole array of tax-shares arranged so as to cover the outlay that is required.

Consider the positions of two separate members of the decision-making group, A and B. The first person, A, uses the common-access facility, say, six times per year, and he places an evaluation on the incremental change in quantity based in this anticipated usage. The second person, B, who has fewer opportunities for alternative consumption and for productive employment, uses the beach, say, twelve times per year, and his evaluation on the incremental change in quantity proposed is based in this anticipated usage. It is surely possible, indeed it is plausible to think, that individual B may place a somewhat higher valuation on the incremental change in beach maintenance quantity than individual A. To the extent that he does so, the Wicksellian decision process might attain unanimous agreement on the extension only through B's expressed willingness to pay more than one-half of the tax costs involved in the extension under consideration. If institutional rigidities or incorrectly derived norms for the allocation of tax shares prevent any negative relationship between tax shares and income levels, inefficiency would characterize the final outcome. And the incidence of this inefficiency may well cause more harm to B than to A.

Real World Applications

It seems possible that the factors emphasized here may be a relatively significant source of public-sector inefficiency in the real world, although detailed empirical investigation would be needed to support this as a generalized hypothesis. Municipal governments are alleged to be in financial crises everywhere, but crises are defined with respect to traditional and orthodox sources of tax revenues. Widespread discussion of reform includes the replacement of traditional tax sources by direct user pricing when and where this may be at all applicable. Objections to user pricing can be, and are, made on distributional grounds. Those who are likely to be harmed are low-income beneficiaries of what are now largely “free” services, that is, free of direct user prices. In light of these quite legitimate distributional arguments against direct user pricing, consideration should perhaps be given to the replacement of traditional taxing sources by unorthodox ones. It seems quite possible that the relatively poor members of many communities would secure net benefits from the levy of taxes that are actually related to incomes negatively rather than positively. If such a negative relationship seems bizarre, the limiting case of equal-per-head taxes might be considered. The distinction between equal-per-head taxes and direct user prices should be noted. Direct user prices are uniform for all persons, per unit of service demanded. Equal-per-head taxes are uniform for all persons, but services of the facility consumed may vary as among these persons. Hence, to the extent that low-income persons utilize the services of a common-access facility more intensively, the final money “price” per unit of service remains lower for them than for their high-income cohorts.

Unless some such fiscal devices are introduced, common-access facilities in existence may be allowed to deteriorate rapidly as their usage by high and median income residents of municipalities continues to fall. Low income central city residents can secure genuine advantages from municipal provision of additional common-access facilities. But higher income residents who have privately available substitutes may be unwilling to finance added municipal facilities through orthodox taxing formulae. If they are forced to do so, they may continue to migrate to independent suburbs in increasing numbers.6 The introduction of imaginative tax devices that are designed to reflect the realities of common-facility usage and evaluation rather than outmoded norms of traditional public finance may allow additional common-access facilities to be financed which would otherwise be impossible.7 Rather than opting out through migration, relatively high-income members might be willing to contribute to the fiscal surplus potentially available to all members of the community, even if this surplus should be differentially enjoyed by low-income members. Even the resident who has his own private swimming pool may be willing to pay some tax share in the financing of a municipal common-access pool. He may, however, be unwilling to pay a tax-share that is dictated by the orthodox tax institutions which relate payments not to relative evaluations, but to an income-asset base.

Generalizations

The argument of this paper should not be interpreted as a general attack on particular tax institutions. The analysis has been limited to common-access facilities that are publicly-provided. The argument does lend support for multi-sector budgets which would allow differing components of a public-goods mix to be subjected to differing fiscal choices. Tax institutions that may provide some approximation to efficiency in the array of tax shares for certain categories of publicly-provided goods and services may be quite inappropriate for other categories. Methodologically, the argument re-emphasizes the importance of separating efficiency and distributional norms in the analyses of fiscal institutions. In the attempts to make all fiscal institutions incorporate distributional objectives, important potential efficiency gains may be neglected, which, themselves, might have desirable distributional by-products.

Privately-Owned Facilities

As suggested at the outset, much of the analysis applies to privately-owned and organized facilities as well as to publicly-organized, governmental facilities. Only the latter have been discussed in detail here. Consider a privately-organized, cooperative swimming club, which is confronted with a decision concerning whether or not to construct an addition to the facility. There seems to be no apparent reason why the incremental subscriptions required from members need be uniform, and, indeed, it seems likely that for many situations nonuniform subscriptions would secure approval more quickly. Members or potential members who are anticipated to use the services of the common facility more intensively may place differentially higher evaluations on the proposed extension in size. And these members may, on balance, be classified below other members on income-wealth criteria. To restrict subscriptions to uniform levels per member may inhibit construction of the proposed extension, with the resultant concentration of opportunity loss on those who stand to benefit most from the incremental addition.

[∗]I am indebted to my colleagues, Charles Goetz and Gordon Tullock for helpful discussions on this paper.

[1]See Knut Wicksell, Finanztheoretische Unter-suchungen (Jena: Gustav Fischer, 1896), major portions of which are translated as “A New Principle of Just Taxation,” and included in Classics in the Theory of Public Finance, edited by R. A. Musgrave and A. T. Peacock (London: Macmillan, 1958), pp. 72-118.

[2]This assumes that no member of the community considers beach maintenance a “bad”; that is, no members place a negative evaluation on the proposed change. In this case, ti might, of course, be less than zero; that is, negative taxes might be required.

[3]For a generalized discussion, see James M. Buchanan and Gordon Tullock, The Calculus of Consent (Ann Arbor: University of Michigan Press, 1962).

[4]For a complete discussion of the relationship between tax institutions and decision rules, see, my, Demand and Supply of Public Goods (Chicago: Rand McNally, 1968).

[5]See Gary Becker, “A Theory of the Allocation of Time,” Economic Journal, LXXV (September 1965), 493-517.

[6]The possibilities of “voting with their feet” through outmigration effectively shifts collective-decision processes in the direction of a unanimity rule.

[7]This conclusion is in the Wicksellian tradition. Although his proposals for introducing a unanimity rule or a relative unanimity rule in fiscal choice making has often been interpreted as restricting the scope of approved projects, Wicksell himself interpreted his proposals as means of securing political approval of public projects that could not otherwise secure support. Wicksell's emphasis was on introducing greater variability in tax-sharing arrangements.