THE PROBLEM OF DEFINING COLLECTIVE GOODS

by Michel CULOT,

Supervisor of Sfudies at U8ge University

“Once a society has provided itself with food, clothing and shelter, all of which so fortuitously lend themselves to private production, pur- chase, and sale, its members begin to desire other things. And a remarkable number of these things do not lend themselves to such pro- duction, purchase, and sale. They must be provided for everyone if they are to be provided for anyone, and they must be paid for collectively or they cannot be had at all. Such is the case with streets and police and the general advantages of mass literacy and sanitation, the control of epidemics, and the common defence. There i s a bare possibility that the services which must be rendered collectively, although they must enter the general scheme of wants after the immediate physical neces- sities, increase in urgency more than proportionately with increasing wealth.”

(J. K. Galbraith: The Affluent Society.)

A. Scope of the Concept of Collective Goods

1. In his book The Affluent Sociefy Galbraith argues that, in the American context at least, there is under-production of collective goods and services. American society, he believes, would achieve progress if it were to bring about certain institutional reforms giving rise to a more balanced distribution of the country’s national product. The growing interest the general public is showing in the problems of environmental development and the preservation of natural amenities seems to bear out the view that a steady rise in standards of living leads to a more than proportionate rise in the demand for collective goods and services.

The question raised by Galbraith is fundamentally one of structure.. It implies that there are competing demands for the limited resources available; for instance, the allocation of additional capital and human resources to the construction of a motorway system can only be achieved at the expense of the allocation to some other sector (e.g. dwelling- house construction). When economic activity is at a low ieveI, such

134 MICHEL CULOT

competition does not occur; in fact, in an economy where under-em- ployment is widespread the Keynesian remedy is a policy of public expenditure designed to revive activity in the sectors supplying the market with private goods. But independently of trade-cycle fluc- tuations, argues Galbraith, the reference criteria used in American society-and possibly in all Western societies-to determine the order of priority of wants to be satisfied is such as to prevent an optimum division of resources between the production of private goods and services and the supply of collective goods and services.

2. The problem evoked by Galbraith are not new ones. Through his wide circle of readers he has simply brought to the attention of the general public a problem which has been preoccupying many economists tor a number of years. Musgrave, in his Theory of Pubfic F i n a m e l , after recalling the distant origins of the theory of voluntary exchange in the analysis of the determination and utilisation of tax revenue, men- tions that at the end of last century the Italian economist Pantaleoni explored the possibility of integrating the process of resource allocation through central and local authority budgets within the Walras model. Shortly after the First World War Lindahl studied the mechanisms whereby, in conditions of partial equilibrium (with the marginal utility of the private good used as the medium of exchange remaining con- stant), two persons, or two groups of persons with identical incomes and preference patterns, decide on the choice of a collective good and share its cost. Some 35 years later Samuelson gave the model more general application by eliminating the hypothesis of constant marginal utility of the medium of exchange and reached two related conclusions: first, it is difficult to measure accurately individual preferences for collective rather than private goods; secondly, the distinction conven- tionally made in economic science between the problems of resource allocation and those of income distribution must be eliminated. Since then, interest in public goods has steadily increased and writings on the subject are appearing in increasing numbers.

In economic theory the concept of collective goods is a kind of antithesis to the thesis which lies at the base of the Pareto-Walras construction of general equilibrium. As Samuelson points out 2, that model is based on a generalisation from the extreme case of a purely private good. Thus the challenge facing theoretical economists today seems to be one of working out the synthesis which Galbraith's affir- mation demands.

The "collective goods--private goods" dichotomy raises first of all problems of definition. It may possibly coincide with the distinction

1 R.A. MWSGRAVE: The Theory of Public Finance. A Study in Public Economy (New

2 In "Dhgrammatic Exposition of a Theory of Public Expenditure", in Review of Eco- York, McGraw-Hill, 1959).

nomics and Statistics, 1955, pp. 350-356.

THE PROBLEM OF DEFINING COLLECTIVE GOODS 135

between the two aspects of resource allocation, with markets or prices indicating individual preference patterns and resolving tensions caused by shortages on the one hand and, on the other, the political process, in which economists have sought, in voting preferences and in the con- trolling activities of government, a substitute for the influence of prices in the expression of individual choices. If the validity of this hypothesis could be established the problem raised by Galbraith would be identical with that of fixing an optimum line of demarcation between the sector to be left under market control and that in which resources are allocated by policy decision.

3. The Pareto-Walras model of general equilibrium, as formulated since the emergence of the new “welfare” school, is based funda- mentally on what de Graaf calls “marginal equivalencies”. a

Subject to certain highly restrictive conditions, relating in particular to-

(a) the market structure (pure and perfect competition); (b ) return; this must remain constant or fall (i.e., price=marginal

(c) the regulation of interactions exclusively by the price mecha- nism in isolation from all external influences, i.e., external con- sumption effects (independence from individual utility functions) and external production effects (independence from processing functions of production units);

( d ) the possibility of aggregating individual utility functions into a social utility function;

cost);

economic theory tends to establish that the price mechanism, through the creation of marginal equivalencies, suffices to establish relations between producers, consumers and possessors of production factors of a nature permitting definition of the optimum relationship of each with the others (in other words, the positions meeting Pareto’s criterion of efficiency); that is to say, a relationship in which no participant in the process of exchange of goods or of services with the character of a good can improve his position save at the expense of another partici- pant. This definition of optimum positions is designed to meet the exacting requirements of the Welfare School, which is reluctant to use interpersonal utility comparisons a s a basis for defining optima and, moreover, treats individual preferences as relevant factors. The choice of the best optimum from among the relative optima available depends on value judgements by means of which the collectivity indicates its preferences in regard to income distribution, which must be manifestly

3 DB GW: Theoretical Welfare Economics (London, Cambridge University Press, 1957).

136 MICHEL CULOT

equitable. Thus the problems of allocation and of distribution are kept entirely separate. It was precisely this separation which led economists for many years to boast that they had succeeded in defining the con- ditions for optimum resource allocation in terms of criteria of efficiency and in complete isolation from all value judgements. +

4. The attempt to integrate collective goods within economic theory was undertaken with tools originally developed for the study of the market economy-consumer indifference curves, demand curves and marginal cost curves, to mention only a few. It may be wondered whether these concepts, with which every economist is familiar, are entirely suited for the study of the problems of collective goods.

Can collective choices be expressed entirely in terms of individual preferences? and is the principle that the customer rules the market applicable to such choices? Is not rather the very existence of the concept of collective goods a challenge to the validity of the separation of problems of allocation from those of distribution and of considera- tions of efficiency from those of equity?

The research programmes at present under way may well reveal, not only that the conventional tools of analysis are inadequate but that some of the most fundamental tenets of economic theory require re- examination.

Economists, under an obligation to contrast collective with private goods, have sought criteria for distinguishing them. This article briefly examines the principal criteria offered.

B. Attempts to Define Collective (As Opposed to Private) Goods

5. One might be tempted to define collective goods as goods or services corresponding to collective needs and supplied by the public authorities in pursuance of a political decision, and private goods as those corresponding to private needs and supplied by enterprises, public or private, through the market machinery.

This, however, would be over-simplifying ; such a definition might suffice for a positive analysis, but would be inadequate for the for- mulation of any theory implying the setting of standards; for it dodges the issue raised by Galbraith. The nature of institutions varies so much from country to country and over any period of time that one cannot with any certainty state that collective goods are invariably associated with collective needs and the political process of allocation and private goods with private needs and a system of allocation through market forces.

Public authorities sometimes cater for purely private needs. Many welfare activities are examples of this; the free medical examination of babies a t public creches, for instance, corresponds to a need which could

THE PROBLEM OF DEFINING COLLECTIVE GOODS 137

perfectly well be met by the market. On the other hand, there are services provided and charged for by enterprises which are consumed by groups of persons, i.e., collectively (for instance, theatrical per- formances).

Moreover, the criterion of distinction between the market and the political process of resource allocation is itself ambiguous. In many local collectivities a charge is levied for refuse disposal; the assignment of the proceeds for a specific purpose constitutes an exception to the general principle that all government revenues must go into a con- solidated fund, while the charge itself is analogous to a price in that it is normally fixed at a level which will cover costs. On the other hand, the charge is payable whether the service is utilised or not; thus no individual is in a position to work out the equivalency between a price ratio and a substitution rate derived from an indifference curve.‘ The appearance of encumbrance phenomena in the use of certain collectively- owned infrastructural assets permits the implantation of dissuasion factors consisting of tolls in a manner very similar to the system of “rationing by the purse” (parking meters on city roads). Under such a system the road user is free to use or not to use the meter spaces; the charge is not a compulsory tax and is not destined to cover a cost factor (the resource cost of parking a car is nil). However, we also find in the market prices corresponding to a marginal cost of nil (e.g., the cost of seating an additional spectator in a theatre not filled to capacity). The mechanism of rationing by the purse and that of exclu- sion by tolls are so similar that it is difficult to establish a clear distinction between the provision of a service respectively through the market and through political decisions.

6. The initial position taken by Samuelson throws some light on the problem. In one of his first articles on collective goods he observed that the only way economic theory had ever progressed was by gener- alising from polar cases and by devising models which can easily be shown not to correspond to reality. The hypothesis of two extreme cases-the purely private good and the purely collective one S - c a n according to him be advanced; and the not very original conclusion

4 For purposes d brevity the term ‘substitution rate” will be used thmughart this article to &aignate a substitution rate daivsd fmm an idffmznea curve.

5 ‘Dhgnmmatic lhpoaitfon of a Theory of Public Expenditure’, op. cit., p. 350. Later on Samuelson shifted his position somewhat in a rather confusing fashion. In the important contribution he made to the htunatiod symposium on public m o m y held in Biarritz on 2-9 September 1%6 he made the following statement: ‘Thus, amsider what I have given in this paper as the definition of a public good, and what I might have better insisted on as a definitlon in my first and subsequent pnpers: ‘A public good is one that enters two or more persons’ utility.' what am wc left with? Two pol- and a continuum in betweu~? No. With a knife-edge pole of the private-good case. and with df the rest of the world in the publicgood d o h by virtue of invoking some ‘consumption externality’.’

138 MlCHEL CULOT

that the reality usually lies somewhere between the two extremes does not detract in any way from the value of the method itself, involving as it does argument starting from clear distinctions.

National defence is the classical example of the collective good quoted by nearly all authors. Public parks are a typical case at the level of the local collectivity. Bread and clothing are to all appearances common examples of private goods.

There seems to be little possibility of argument about the examples of bread and national defence. But even such items as public parks and clothing come within the realms of controversy. Public parks may be crowded at certain times of day, and the very fact of being crowded is enough to create an exclusion factor affecting persons seeking peace and quiet there (one can already conceive the possibility of charging an entrance fee). Samuelson-at least on the basis of his most recent contributions to the study of collective goods-would deny that clothing is a purely private good, arguing instead that the desire to be well dressed is evidence of a consumption externality (ostentatiousness and demonstrative effect), and that clothing bought for the owner’s sole use frequently enters, when worn by him, into the utility functions of other persons and may even affect their consumer functions.

When one feels the need to analyse specific cases rationally one is either unsure of one’s basic concepts or attempting to check their validity. It would seem that a theory of collective goods which cannot be elabo- rated save on the basis of a clear distinction between purely private and purely collective goods does not, for the time being at least, offer suffi- ciently precise definitions.

There are any number of possible criteria to distinguish between purely private and purely collective goods-whether they are purchased privately or collectively; whether they are to be consumed by an indivi- dual or a group; whether they appear solely in the utility function of their owners or simultaneously in those of several persons; whether or not certain categories of persons can be debarred from making use of them (by the market mechanism of prices or by a political decision to levy a charge for access or even as a consequence of the appearance of encumbrance phenomena); but none of them are acceptable to all economists.

The four criteria most frequently referred to are consumption exter- nalities (Samuelson), the impossibility of excluding specific categories of consumers (Musgrave, and also Galbraith in the passage quoted at the beginning of this article), the non-competitive character of different items of consumption (Musgrave) and the indivisible nature of demand (Boweri). The rest of this article will be devoted to an examination of these criteria.

THE PROBLEM OF DEFlNlNG COLLECTlVE GOODS 1 39

C. The Points Which the Four Criteria for the Definition of Collective Goods Have in Common

7. The market distributes private goods among those seeking them by a system of allocation in which access to the ownership of a unit of goods or to the usufruct of a unit of services is dependent on payment of the price (exclusion through the price mechanism, or rationing by the purse). The limitations on the quantities of goods and services available in relation to the demand for them (consumption rivalries) forces would- be acquirers to divulge their degrees of preference for each through a system of bidding which brings total demand into line with total supply at the equilibrium price. In optimum conditions of competition and in a situation of constant or decreasing returns, this price will be equivalent to the marginal cost. By paying the price the purchaser covers exactly the cost to the collectivity of the resources the collectivity could have used for some other purpose but has sacrificed for his benefit. For each purchaser the price is a factor in his economic calculations; he adjusts his behaviour by adjusting the quantities he wishes to acquire at the level of his own marginal substitution rate. This process of quantitative adjustment keeps the marginal substitution rate of each individual in line with cost (MRS = MRS2 = MC). 6 The total required by all purchasers is the aggregate of the requirements of each and all of them (divisibility

of demand: X1 = Xll + X*l.. . Xn, = X X*l). The global demand curve, according to Bowen7, is arrived at by aggregating the individual curves horizontally. In the process of allocation through the market, the price plays a threefold part: it forces purchasers to reveal the levels of their individual preferences, excludes would-be purchasers for whom the marginal utility of the good is less than that of the medium of exchange, and eliminates consumption rivalries arising from shortages of supply relative to demand in that it makes for the distribution of the total supply in such a fashion that for each person satisfied the marginal rate of substitution is equal to the alternative resource use cost.

n

8. ,Public goods are the subject of indivisible demand and cannot be split up among the different seekers after them. In a system of allocation comprising only two persons, both wishing-but with different degrees of intensity-to acquire an indivisible good (the building of a bridge needed by two landowners on the same side of a river, when the

6 "A remarkable duality property of private and public goods should be noted. Private goods whose totals add-such as XI = XI1 + X*r-lead ultimately to marginal conditions of simultaneous equality-such as MC = M R S = M R S . Public goods whose totals satisfy a relation of simultaneous equality-such as XI = Xi2 = X*z-lead ultimately to marginal con- ditions that add-such as MC = MRS1 + MRS2." (SAMIJ~LSON, loc. cit., p. 353, footnote 5.)

7 *The Interpretation of Voting in the Allocation of Economic Resources", in The Quar- terly Journal of Economics, 1943, reprinted in Readings in Welfare Economics, American Economic Association Series (London, George Allen and Unwin, lW), pp. 115-132.

140 MICHEL CULOT

public road runs along the other side) each will indicate the amount he is prepared to contribute towards the total cost. The latter is not necessarily established once and for all (for instance, a choice may be possible between a wooden or a concrete bridge). The two persons are certainly not competing for the use of a collective good; on the contrary, they are willing to co-operate with one another, as their needs are complementary (absence of consumption rivalry). As their pre- ference levels are not identical-even if their income and wealth levels are-they will bear unequal shares of the cost, the actual allocation of expenditure being determined by a process of negotiation analogous to that which takes place between two monopolies fixing a selling price between them. The important thing is that the total good (the bridge) is not the sum of the amounts required by each of the persons con- cerned; each one wants the use of an entire bridge and has no use for half a bridge or that fraction of a bridge corresponding to the level of his marginal rate of substitution. A collective good is included, simul- taneously and in its entirety, in the utility functions of each of the persons interested by it (X, = Xll = X21). The over-all demand curve, according to Bowen, is obtained by vertical aggregation of the individual curves; in such a case one is adding up, not units of a homogeneous product, but marginal substitution rates varying from person to person but which, added together, must cover the total cost (MC = MRSl + MRS2). Bowen’s method of obtaining unit cost is to divide the total by the

number of persons concerned -); this gives the cost, not per unit, but

per user. The choice of this method can probably be explained by the difficulty-of which more la ter-of defining the unit of output of a collective good. The difference in the method of calculating unit costs-per unit of output for private goods and per user for public goods-possibly offers a field for useful research.

If the number of persons desiring a good forming the subject of an indivisible demand increases, each one will indicate the amount of his contribution through a system of voting. Thus we are here thinking in terms of a system of resource allocation of a political character operating along the ideal lines of direct democracy.

MC

N

9. Let us return to the criteria suggested. For private goods offered on the market, demand is divisible according to the divisibility

of the product (X, = XI1 + XS1. . . = Z XI,); there is rivalry among the consumers, who, by a system of bidding, divide among themselves a total amount falling short of total needs, with the price acting as the exclusion factor. In the case of a collective good, demand is indivisible (XI = XI1 = XZ1. . . Xn,); there is no rivalry among users, who con- tribute to its total cost, and therefore no exclusion. .An increase in the number of persons desiring to use a collective good will mean that each one will have a smaller share of its cost to pay and will consequently

n

THE PROBLeM OF DEFINING COLLECTIVE GOODS 141

have more income available for the purchase of private goods, and thus constitutes an external consumer saving. This last criterion does not have the same significance as the other three, which are designed to distinguish between the processes of ailocation through the market and through political decision.

D. Significance of the Criterion of External Consumer Effects

An analysis of collective goods on the basis of the criterion of external consumer effects calls for the following qualifications:

10. (a) Samuelson's model relies principally on consumer indiffer- ence curves as the tool of analysis. The individual is faced with a private and a collective good the relative utilities of which he alone can assess, the indifference curve being the expression of a system of purely individual preferences. "I assume no mystical collective mind that enjoys collective consumption goods; instead I assume each individual has a consistent set of ordinal preferences with respect to his con- sumption of all goods (collective a s well as private). * Most writers who have studied the allocation of resources to the supply of collective goods on the basis of concepts designed for the study of the market economy have come out in favour-either implicitly or, in the cases of Samuelson and Musgrave, explicitly-of the principle of the suzerainty of individual choice.

This postulate, which implies a certain concept of social utility, raises three questions:

(i) Is the comparison of the respective utilities of a private and a public good possible within the individual psyche?

(ii) Is not the individualistic concept of the social utility function invali- dated if one takes welfare needs into account?

(iii) Unless the rider is added that the political decision of resource allocation must be unanimous, no collective choice can comply with Pareto's criterion of efficiency, and recourse to interpersonal utility comparisons becomes inevitable.

11. (b) In a model of general equilibrium-even one comprising two persons only-constructed on the basis of indifference curves the marginal utility of a private good is not constant, whether that good is used as the medium of exchange or whether its utility is valued in money terms; it varies for each individual in accordance with the amount of his contribution to the cost of collective goods. However, this amount

8 SAMUELSON: "The Pure Theory of Public Expenditure", in The Review of Economics and Statistics, 1954; reprinted in Readings in Welfare Economics, op. dt., p. 179.

1 42 MICHEL CULOT

depends on the amount contributed by the other person. A change in B's decision regarding the allocation of his total income between private and collective goods will increase or decrease the amount of income available to A for the purchase of private goods and will move his indifference curve higher or lower. In this very specific sense one can speak of external consumption economies (or diseconomies); for A, the relation between the price of the private good and the pseudo-price he will have to pay for the collective good will depend on B's system of preferences. The external consumption economy, understood in the very narrow sense of a change in a price ratio, acts as a factor making for redistribution of income quite independently of any transfers decided upon on grounds of equity. As Samuelson points out Q, this redistribu- tion factor brings into question the validity of the method involving separate treatment of the problems of allocation directed towards an nbjective of efficiency and those of redistribution directed towards one of equity.

12. (c ) When Samuelson, in his statement to the Biarritz sym- posium, made the point that consumption externalities reduced the private-good sector to a "knife-edge pole" he attached a very broad interpretation to the notion of consumption externality. The case of clothing is significant. The consumption externality for an individual no longer expresses a change in a price ratio but instead the effects on his utility function of the consumption acts of another person. Although the absence of consumer externalities may be considered to be char- acteristic of a purely private good, one would hesitate to advance the converse, namely that the presence of consumption externalities is a characteristic of a purely collective good. In fact, the adoption of this criterion would bring Samuelson's concept of the public-good domain, as he defined it in Biarritz ( d l the rest of the world in the public-good domain by virtue of involving some consumption externality) into contradiction with his initial two-person model of general equilibrium in which the share of the cost of a collective good which A is prepared to pay determines the amount of income available to B for the purchase of a private good. The only way to escape from the contradiction is to conclude that Samuelson offers us no criterion for a collective good save that derived from positive economics, namely that a collective good is any good which the public authorities decide should be paid for by contributions from the citizenry. From the point of view of estab- lishing economic norms-which is the substance of the problem raised by Galbraith-the consumption externality criterion is of no help.

Samuelson's analysis confirms that the market cannot achieve opti- mum allocation of resources; as has been seen, the absence of all externalities in price relations is a necessary hypothesis for the effec-

9 S~~UPISON: "Aspects of Public Expenditure Theories", in Review of Economics and Statistics, 1958, p. 337.

THE PROBLEM OF DEFINING COLLECTIVE GOODS 143

tiveness of conditions of marginal equivalency in the process of alloca- tion through the market.

E. The Criteria of Non-exclusion and Non-rivalry Among Users

13. Musgrave defines a good as collective when it fulfils one of the

(a) physical impossibility of exclusion of users;

(b ) absence of any rivalry in the use of the good.

A collective good may meet both conditions (e.g., national defence) but need not necessarily do so. If either condition is met, the good or service in question should be made available without specific charge, but-as Musgrave explained in his paper on the supply of collective goods submitted to the Riarritz symposium-the reasons for free supply are different in each case.

Thus for Musgrave supply without charge is an essential char- acteristic of a public good; however, one cannot conclude therefrom that all services supplied free of charge are collective (example: services designed to meet welfare needs).

The recognition that the decision to make the good available without charge is motivated by different considerations according to which of the two conditions mentioned above applies permits a division of collective goods into two categories; those exclusion from which is physically impossible and those exclusion from which, even if conceivable, is undesirable since there is no consumer rivalry. In the former case the good is provided free because its nature is such that the public authority has no alternative. In the latter (use of a road, a bridge, a public park or a museum) the underlying factor is a decision of economic policy, and we find a link with the principle of charging at marginal cost in branches yielding increasing marginal returns. Supply without charge is in line with Pareto’s criterion of efficiency in resource allocation; for the condition of marginal equivalency of price (nil) and marginal cost per user (also nil) is satisfied.

Consumer rivalry emerges when demand outstrips supply capacity. Its symptoms are a lowering in standards of service. Except where exclusion is physically impossible (as in the case of the use of the public highway by pedestrians)-in other words, where the levying of a deter- rent charge is conceivable (e.g. by means of parking meters for cars)- the decision to levy a charge may be based on a desire to achieve optimum allocation without any clear idea of the pattern of marginal equivalency which that optimum involves.

One might argue that the optimum amount of a toll is that which equals the marginal encumbrance cost. On the other hand, it has yet

following two conditions :

144 MICHEL CULOT

to be established that encumbrance cost is a genuine cost factor in that it corresponds to a diversion of resources from other possible uses. Closer study is needed of the nature of the resources sacrificed in encumbrance phenomena.

Should a given tariff be considered optimum because i t ensures the maintenance of a particular standard of service? In the absence of dissuasive charges, that particular standard could only be maintained by an expansion of capacity the encumbrance cost of which can be measured from the saving achieved by the imposition of charges. How- ever, a cost saving is not a cost item; and in any case it is practically impossible to measure an optimum standard of service without recourse to value judgements.

Closer study of this problem would take us far beyond the scope of this note. To realise this it suffices to consider the fact that, save in the relatively rare cases where exclusion is physically impossible, a given good may be collective when used at less than the capacity avail- able to provide it and yet take on some of the characteristics of private goods when, as a result of the likelihood of demand exceeding capacity, rivalries begin to develop among its users which make the implantation of a system of dissuasion desirable. Thus the criterion of non-rivalry has the disadvantage of being relative.

14. Musgrave seems to have selected the criterion of non-exclusion of users-on account of the nature of the collective good concerned or i n pursuance of a decision of economic policy-with the aim in mind of pinpointing the main difficulty economists come up against in their endeavours to integrate the political process of allocation in a demo- cratic system within the model of general equilibrium in allocation of resources through the market. In a model of general equilibrium com- prising two persons, each with his own pattern of preferences for collective and private goods respectively, the amount of any collective good acquired and the sharing of the cost are determined by negotiation. Every increase in the number of participants improves the market process and brings the system nearer to a competitive model which economic theory considers as perfect. Where political considerations are involved, however, an increase in the number of participants, while eliminating the imperfection in the two-person model arising from the possibility of a game of competing strategies, gives rise to a new imperfection in the form of a new strategy which, if pushed to its logical extreme, will prevent the achievement of the essential condition of marginal equivalency (MC = XMRS). In the market the exclusion ele- ment inherent in the price compels would-be purchasers to reveal their preferences for private goods through a system of bidding; in contrast, the lack of any exclusion from access to a public good gives every participant in the political process an incentive to conceal his marginal rate of substitution, If the public authorities seek contributions on the basis of avowed preferences through the voting system, every partici-

THE PROBLEM OF DEFINING COLLECTIVE GOODS 145

pant has manifestly an interest in minimising the marginal utility of the collective good in question for him; in an extreme case his con- tribution will be nil. Contributions levied by taxation, not containing the exclusion factor inherent in prices, have to be imposed, and thus cannot give any clue to patterns of relative preference for collective and private goods.

The same difficulty exists for all individual services which, although their marginal cost is not nil, are provided without charge in virtue of a decision of a public authority (welfare services), irrespective of whether those services are optimal (public creches) or compulsory (vac- cinations). The decision to remove these services from the domain of the market by supplying them without charge is a departure from conditions of marginal equivalency. It is based on value judgements whose only interest here resides in the fact that they must necessarily appear in some form or other a s an argument in the social utility function through which the preferences of the collectivity regarding resource allocation (not distribution of income) are expressed.

F. The Criterion of Indivisibility of Demund

15. (a) Indivisibility of demand is not exclusive to collective goods and services. It is a feature of all goods and services consumed simultaneously by groups of persons. Some of these goods and services are available through the market. A theatrical or cinema performance, a concert and a football match all form the subject of an indivisible demand. Of n spectators present, not one would be satisfied with only I/n of the performance; each wants to see it in its entirety, and it is an element in the utility function of each (X, = XI1 = XZ,.. . X",). Within the limits of capacity available the marginal cost of an addi- tional spectator is nil. As in the case of a collective good, the over-all demand curve is obtained from the sum of the individual curves by vertical aggregation. However, there is one most important difference. In the case of a service for group consumption supplied by the market, payment of the price is a voluntary act; for no member of the group does the marginal utility of the money paid exceed that of the service. In the case of a collective good provided by the public authorities the payment of the pseudo-price (the amount of each person's share of the cost) is not voluntary. From this situation springs the delicate problem of the unanimity requirement, which Wicksell 10, a precursor of the Welfare school, considers essential to ensure that a political decision concerning resource allocation in a regime of direct democracy is in line with the conditions for a definition of a movement towards an

10 In 'A New Rinciple d Just Taxation" (English tmnslation), reprinted in Muscluve and Pmcax: Clptsics in rhc Theory of Public Pinuncc (London, Mamillan, 1958): see in particular pp. 89-91.

146 MICHEL CULOT

optimum based on considerations other than interpersonal utility com- parisons. 11

16. (6 ) The individual demand curve, which is derived from a utility function, expresses a relationship between a price and an output. The price (or rather the pseudo-price) of a collective good is the amount of the share of cost each person is prepared to pay. The second term of the relationship-the output-is more difficult to define. How is one to measure the output of national defence or police protection corre- sponding to the demand function? Bowen brings up this problem in connection with the particular case of education schemes 12; he points out that output can be defined in terms of a wide range of criteria- school buildings, numbers of teachers or pupils, number of hours of teaching per pupil, etc. By weighting the different criteria a complex but measurable unit can be established, with the money cost of each of the weighted elements offering a common denominator.

The selection of the elements to be included in this complex unit and their weighting-which necessarily implies recourse to value judgements-raise difficult problems from the point of view of empirical research. In addition, the procedure proposed by Bowen is inapplicable to the services which Shoup calls “preventive”. *s How is one to quan- tify the amount of crime which does not take place because of the existence of a police force? or the number of cases of sickness prevented by a public health scheme? or the number of civil or commercial con- tracts the execution of which gives rise to no dispute simply because each of the parties knows that the other will not hesitate to take him to court if he does not honour his obligations? Shoup observes that input and output are frequently confused: for instance, the output of national defence or of fire protection tends to be measured by the number or quantity of factors put in. He concludes that instruments of economic analysis based on a quantitative relation between units of input and of output (production functions, input-output tables, etc.) cannot be applied to collective services, at least those of a preventive character. Even demand curves, considered as tools of economic analysis, are subject to the same ambiguity; in the absence of any easily definable unit of output, an increase in demand finds expression in a request for an increase in the relevant budget item. Thus the over- all curve obtained by vertical aggregation expresses only the relation between the sum of contributory shares and the amount of output. In fact, we have here two formulations of the same factor, for the sum

11 The new W e h e school argues that there is no evidence that an allocation decision reached with one vote short of unanimity (i.e., an opposition of one) will ensure a level of welfare for the collectivity preferable to the previous one.

12 “he validity of this example is questionable. It may be wondered whetber education- compulsory or not-is not a service designed to satisfy a weltan need rather than a genulnely collective good.

13 In Public Finance (Chicago, Aldine Publishing Co., 1969). pp. 7879.

THE PROBLEM OF DEFINING COLLECTIVE GOODS 147

of the contributory shares will of necessity-assuming the rather unusual feature of allocation of revenue items to specific purposes-be equal to the amount of the budget alIocation.

The cost curve for a collective good or service is equally ambiguous. What is the cost of a unit of service? and how is the level at which the pseudo-price is to equal marginal cost in conditions of optimum allocation of resources to be calculated? As was mentioned earlier, the unit cost figure normally used is that of cost per user (per inhabitant of a town or locality for a local police force, per inhabitant of the country for national defence).

However, it is clear that the “user” unit, while certainly appropriate for the study of some economic problems, is not the unit required for analysis seeking to define, on the basis of individual utility functions, the conditions for an optimum allocation of resources. The satisfaction an individual derives from the maintenance of public order may be enhanced by an improvement in the efficiency of the machinery of justice; it will not be enhanced by an increase in the number of persons covered by the service. Save in the event of an encumbrance, which finds expression in an inverse relation arising from a deterioration of standards, there is no relation, within the individual utility function, between the level of satisfaction he enjoys and the number of persons using the service in question.

The definition of conditions of marginal equivalency, within the framework of the working out of a scheme of optimum allocation of resources between private and collective goods, based on individual utility functions, itself rests on an ambiguity-the absence of any pre- cise definition of the output of a collective good.

G . Conclusion

17. The implications of Galbraith’s thesis raise a number of problems in the field of economic theory. There are many and widely differing reasons why the public authorities take over the function of supply of certain goods and services from the market. Can all these reasons be encompassed within a single theory of collective goods?

The welfare character which is being attributed on an increasing scale to certain private needs, the degree of conformity of collective decisions on resource allocation with the requirements of Pareto’s criterion of efficiency, and the redistributive role played by certain services provided without charge by the public authorities all create major problems for economic theorists which overflow into other scientific fields.

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