RICHARD AUSTER and MORRIS SIL VER*. Economists stress the role of differences in relative prices (or costs) in explaining observed behavior. However, the ...
COLLECTIVE GOODS AND COLLECTIVE DECISION MECHANISMS RICHARD AUSTER and MORRIS SIL VER* Economists stress the role of differences in relative prices (or costs) in explaining observed behavior. However, the full potential of this type of analysis for clarifying a number of fundamental socio political issues involving "collective" (or "public") goods has not yet been fully realized. With scattered but notable exceptions,^ writers in the area have focused on what "shoutd be," neglecting the question of more traditional scientific interest of what "will be." We propose to provide a step towards the development of a complete comparative statics of collective goods at the same time we begin to explore some of its implications. To start with, the notion of a collective good is placed in the context of some recent advances in consumer theory. Part 1 then examines the factors causing differences in the costs of private, relative to collective, goods and, hence, in the proportion of any desire gratified by each type of good. Some demand side factors are also analyzed. Part II explores the role of differences in relative costs in determining the selection of a collective decision making mechanism: central planning or the market. The latter choice can be regarded as a special case of choice among alternative collective modes of gratifying desires, which is the second half of a complete comparative statics of collective goods.
7.
The Definition of a Collective Good
We assume (like Becker [6| and others) that consumers have certain inherent desires—i.e, the "natural arguments" of their utility functions.^ The value of any given argument is typically a function of the levels of consumption of more than one consumer good. In general, there are two classes of goods entering into any •UNIVERSITY OF ARIZONA AND CITY COLLEGE OF THE CITY UNIVERSITY OF NEW YORK, RESPECTIVELY. We wish to thank A. Alchian. J.M. Buchanan, V. Fuchs, 8. F. Herber, H. E. Klarman, R. N. Mckean and colleaQues at the City College tor their vary helpful comments and encouragement. The authors boor sole respongtbility *or any remaining errors. ^Minasian 136, p.78] , for example, states that "the theory of public goods ret ies on the technological aspects of the production of a good, with rwglect of the economic consideratkins that lead to choice of alternative technologies." More recently Buchanan f10, p. 31] has enunciated a similar position and called for a "genuine institutional economics." Damtetz has made a number of valuable contribution? 114, 151. ^Lancaster [21 ] has called these tha "characteri«ties" of goodt.
2 PUBLIC CHOICE argument: collective and private.-* Similarly, we may define "natural arguments" for production functions (this is implicit in human capital theory). Producer goods may be assumed to be produced by production functions where the input arguments are "characteristics" of factors of production, and, as in the case of utility functions, in general both private and collective producer goods may enter into any "characteristic." In this context, a good is defined as a collective good if, and only if, over the relevant range for any given quantity and "location " of the good and for a specific consumer (employer) ^roup, an increase in the atnount of the "natural argument" from the good in question by one member of the group, or an increase in the number of consuming (L-mploying) individuals in the group, does not alter the maximum (or actual) amount avaiLble to any other group member. This definition overcomes some of the objections raised to the original Samuelson definition 1351.'* First, it does not require that the actual amount consumed be the same for al! group members. Instead, like Breton [9. p. 1771, actual consumption is permitted to increase with what might be called "proximity" achieving a maximum when the individual is "located on" the collective good and consumes it all. Since real resources may be needed to increase "proximity," the proposed definition does not require that an increased "natural argument" or consumption from a given quantity of a collective good be achieved at zero marginal cost. Since it admits of the possibility that a good will enter more than one argument in some individual's utility function, cases of "impure" or "mbced" collective-private goods may be transformed to cases where che given good is collective with respect to some desires and private with respect to others; that is.
Unlike Lancaster ( 2 1 1 , b u t like Becker [ 6 ] , wa Bssume that collective arxl private goods combine in a neoclassical manner.
Our version o f a collective good I* only dlttantly related to the approaches presented in 141, [12l.and 132, pt. 2, ch. 91
For some purposes it may be useful to distinguish among collective goods according to their avoidance costs, i.e., the cost an individual has To incur in order to consume less than the maximum amount available to him. A television program is an example of a zero avoidance cost good, national defense is a case where the avoidance cost is "Infinite," and police protection whose quantity can be altered by changing one's residence within the city is an example of an intermediate case. Mishan (27) approaches this fWlion in his dichotomy Ltetween "optional" and "non-optional" collective goods.
COLLECTIVE GOODS 3 the good involves private and collective joint products. The hospital treatment of infectious diseases illustrates this case. Such treatment can be said to enter the arguments: "probability of not catching such a disease" and "to be cured." The former is increased collectively but, if hospital resources are fully employed, the latter is increased privately—i.e., if one stricken individual "consumes" more treatment, less of that good is available to cure other stricken individuals. Still another example is provided by overcrowded courts. Finally, like Samuclson's, our version explicitly allows a good to be collective for some defined populations but not others. The sometimes-cited case of a motion picture illustrates this possibility: it is a collective good for the audience in the theater, but not for the entire population. 2.
A General View of the Choice Between Collective and Private Goods
Suppose that society chooses between private and collective ways of gratifying any inherent desire (i.e., between private and collective goods) in a manner consistent with traditional economic theory. ' Given rational social Treating the "impure case" in this fashion allows us to expose some of the difficulties inherent in the notion of an "externality" as well as clearly indicating the relationship between the concept of a collective good and that of an externality (see also Mishan [ 2 8 ] ) . In the "externality approach," attention is focused on the course of action giving rise to the private product white the aggregate value to others of the collective component is labeled an "externality." Now for purposes of calculating the appropriate corrective tax, it is convenient if the externality can be expressed as a constant percent of the private component. Clearly, however, the collective and private components, may not be "produced" in the same proportion at all levels of output; and, even if they were, the ratio of the value of the private to the collective component would depend on their relative shadow prices. Unless the collective and private components are perfect substitutes for each other, for all consumers, their relative shadow prices will in general vary. Moreover, in the absence of Information about the relevant elasticities—nothing can be said about which way the relevant percentage moues, as the level of the activity increases, "Externalities" isa tricky notion. For additional examples see McKean [24, pp. 71-72]. We assume that the political system is devised and employed in such a way that it fulfills the desires of the society's members. Admittedly, the Arrow "Impossibility Theorem" (31 casts doubt on this possibility. The relevance of that theorem for actual political mechanisms is open to question however, as it assumes the impossibility of revealing the intensity of preferences. If the intensity of preferences can be revealed, then the problem of social choice can be solved. Ng [30] discusses this and cites several examples of solutions (see also Tullock (42] ). It is well to remember that in a country such as the United States, campaign contributions in cash or in kind do reflect the intensity of preferences-and they influence the outcomes of social decision making. g Application of conventional demand theory to questions of public choice raises the interesting question of whether the current demand for improvements in environmental quality results from a worsened environment or an increased valuation of environment perhaps due to affluence. It is not clear on a priori grounds that consumption of environmental quality has in fact deteriorated in recent years: while conditions may have deteriorated everywhere this could have been offset by population movements out of central business districts.
4 PUBLIC CHOICE choice, if the standard convexity assumptions concerning production and tastes are taken to hold, it is expected that both types of goods would be employed to gratify any inherent desire. This may be readily shown in the context of a two-person world by means of the familiar device of a Utility Possibility Curve (UPC). If society were to gratify any particular desire using only private goods, it would have the UPC labeled "A" in Figure 1. If instead it gratified that desire using only
UII
MIXED
FIGURE 1
COLLECTIVE GOODS
5
collective goods, it would have "B". But society does not have to choose between only one or the other. Some of each type of good may be used and, in this case, the true frontier is one labeled "Mixed" which (given divisibility) is beyond "A" or "B" for some part of its range. Real societies, of course, choose the dual mode of gratification. The desire for security against foreign aggression has been gratified by family bomb shelters as well as by the "military." Fire protection is provided by sprinkler systems and fire-proofing, as well as by "fire departments." Pollen-free air provided by home electronic air purifiers, as well as by public health authorities. Similarly, protection against crime is provided by "bodyguards," bullet-proof vests, watch dogs, alarms, and locks, as well as by the "police." The point of departure for our analysis of the determinants of these relative proportions is the obvious, but overlooked, idea that given an interior solution, the ratio of private to collective goods used in the gratification of any given desire will be a positive function of the ratio of the marginal cost of the collective goods (MC^) to the marginal cost of providing the same total extra services by means of private goods (MCJ? ''•''^ We now may proceed to analyze those factors which can be expected to affect this ratio. Relative costs will respond to movements in relative aggregate factor quantities in a manner which depends on che relative factor intensities in production of the two types of goods. Thus, if collective goods tend to be relatively capital intensive, then economic growth resulting from an increase in the capital-labor ratio can be expected to increase the importance of collective goods This would seem to haue been suggested by Head and Shoup (191 , who use a diagram Bifnilar to ours, but implicitiv assume an "all private" or "all collective" social choice. Their notion of B good resembles our notion of a desire and in this sense we assume that all goods are In their third category of "ambiguous goods." It is worth noting that MC and MCp include not only the direct factor costs of producing the goods themselves b u t ' l h e indirect costs resulting from the effort to prevent "theft"—i.e.. providing individuals and/or the government with rxclusiur vnntrnl over their goods. In the case of a collective good (e.g., an anti-ballistic missile) " t h e f t " would involve a locational change within the consuming (defended) area not agreed to by its "owner(s)." Exclusive control may be provided collectively by a system of legal property rights including legislators, iails, police and so on, or privately by means of such goods as locks, vaults, and fences. Earlier discussions focusirig on the importance of the costs of producing "property rights" may be found in Minasian [26, p. 79] , Demset; [ 1 4 ] , Davis and Whinston [13, p. 367] , and Head and Shoup i 19). Failure to establish complete control results in failure to achieve Par«to-optimatity. However, society will in general choose a partial system of controls because the additional cotts necessary to achieve complete control are almost certainly greater than the additional benefits. This point is well made by Oemset^ (14) and Becker [ 7 ] , and would justify the existence ol "crime" and other "imperfections" even in a perfectly running society. 12 It is recognized that when the relevant collective (private) good is actually one dimension of an "impure" item (e.g., the hospital treatment of infectious diseases, see Section 11, a decision with respect to the fraction of a given desire gratified collectively (privately) will affect tha private (oollective} share of some other desire.
° PUBLIC CHOICE and vice versa. Similarly, differences in the "consumer time intensiyeness"^^ of the two types of goods will result in general growth having an effect, if, for example, private goods are relatively "time intensive," then they will ceteris paribus become relatively less iinportant in the gratification of all desires as a result of a uniform improvement in technology. As nothing can be said about these various intensities on a. priori grounds, a major empirical investigation is clearly called for. Increases in population density lower the ratio MC /MCp and, hence, increase the importance of collective goods. Whether accoinplisiicd by means of an increase in the number of individuals or by a reduced distance among individuals holding the number constant, an increase in density increases the total extra services flowing from any additional unit of a collective good and, hence, increases the "marginal cost of providing the same total extra services by means of private goods." Consider, by way of illustration, the desire for security against nuclear attack. This can be gratified either by fallout shelters (private) or by anti-ballistic missiles (collective). An increased population would necessitate more shelters but not more missiles to maintain a given per person level of security. If a given population was distributed more compactly, the per-person level of security from a given number of missiles would increase, but this would not be the case for shelters.'^ Changes in population density can, however, be expected to affect the relative price of land as a factor of production. To the extent that collective goods are land intensive relative to private goods this will tend to dijninish the aforementioned effect and vice 13 See Becker [6].
14 Casual observatron tends to confirm our conjectures with respect to the role of population density—private goods are relatively rnore important in suburbs than in citws. Continuation of the trend tovuard suburban residence might be expected to reduce the overall Importance of collective goods In our society. 15 Aaume that the effect of density on the ratio MCp/MCj. through its effect on tha price of land can be neglected. In this case, some information concernino the degree to which collective and private goods are substitutes in the aggregate may be obtained by examining the tigna of the coefficients of density in the following regressions: (1) Regressions of government expenditure as a percent of gros* national product (E) on population density (D) and per capita gross national product (O> across 28 developed and less developed countries; (2) Regressions ol U.S. state and local government expenditures on fire (F), police (P), and sanitation (S) services as percentages of state income on population density (D) and per capita state income (Y). Of cOurse.government expenditures are not only for collective goods nor do they exhaust expenditures on collective goods- While this finding is in no way conclusive, the coefficients of density in the regressions {available from the authors upon request) are consistently positive Which suggests that the aggregate elasticity of lubstitution in consumption is greater than one. J.M. LItvack and W. E. Oatet |22] independently reach the same conclusion we do about the role of density and then go to an interesting analysis of fiscal centralization. To do so they require the introduction of impurities and congestion costs. In our judgment they could have replaced their assumptions about the relative impurity of state and local government outputs with assumptions about their land intensiveness.
COLLECTIVE GOODS 7 In addition to these "supply side" effects several factors may influence the relative importance of collective goods through the "demand side." A distinguishing feature of a collective as opposed to a private good is that for the former no member of the defined group can to any degree exclude any other member from the use of the good by consuming (employing) more of it himself. We might then say that a crucial property distinguishing one type of good from the other is that private goods are endowed with "exclusivity," while collective goods are endowed with "non-exclusivity." It is possible that individuals derive satisfaction from these characteristics themselves- i.e., that "exclusivity" is itself an argument of individuals' utility functions. Changes in tastes for "exclusivity" (eg., resulting from changes in social cohcsiveness) would then, given relative marginal costs, influence the share of collective goods in the gratification uf any given desire. In this way, the share may also be influenced by changes In income, but it is not clear whether in a world of complicated interrelationships between utility functions, "exclusivity" is a superior or inferior good. Income also plays its more traditional role. If desires with larger income elasticities have higher collective-private "intensities," income would be observed to have a positive effect on the aggregate percentage of collective goods and vice versa. Monsen and Downs [29|, for example, appear to suggest that the desire to express individuality through differentiated consumption patterns is both relatively income elastic and relatively private goods intensive.
7.
The Choice of Collective Decision Mechanism
If any good is to be produced, decisions must be made concerning methods of production and the amount of output. The pure or polar forms of the necessary decision making mechanism (DM) are the market (M) and imperative central planning (CP). While imperative central planning is popularly linked with government, it is important to remember that it is done by the "managers" of all "institutions." Both types of DM are certainly producer goods. Should individuals derive psychic income directly from the decision mechanism, they are also concumer goods. Further, both types of DM are collective goods: an increased participation in the market or the centrally planned sphere by one member of the group, or an increase in the number of participating individuals, does not alter the amount of the DM available to any other group member. The question of central planning or the
3 PUBLIC CHOICE market is, thus, a special but crucial case of choice among alternative collective modes of gratifying a desire. Real world D. M. s are combinations of M and CP. Holding the amount of the particular good constant, substitution of one pure form for the other will alter the total cost of production. Figure 2 depicts the curve relating the increment to total cost to the ratio CP/M (labeled ITC). if society is indifferent between the two forms of DM, then the equilibrium DM will occur at the intersection of ITC with the CP/M axis (pointA), provided that the curve does in fact have a positive slope.
ITC
A
B
CP/M
-ITU
Figure 2
Society, however, may prefer to decide things via CP or via M. Accordingly, Figure 2 also depicts a curve relating the increment to total utility to the ratio
COLLECTIVE GOODS
9
CP/M (labeled ITU). The law of demand assures that the curve will slope downward. The equilibrium ratio CP/M occurs at the intersection of the two curves (point B) whether or not this occurs above the CP/M axis. Factors which shift either ITC or ITU will have a predictable effect on the CP/M ratio. We shall focus on the ITC curve. Initially we are interested in showing that its slope is positive. For both CP and M the total cost of decision making (c) may be decomposed into three components: (1) the cost of the information on which decisions will be based (cj); (2) the cost of decision making proper (cj-j); (3) the cost of enforcing decisions on the subdecision units (Cg). The incremental cost resulting from the substitution of CP for M at any level of CP/M (dcj, dcp, dc^ respectively) is the sum of the incremental costs for each component. Let us proceed to discuss each of these components in turn. Central planning necessarily requires the relevant decentralized information to be centralized. Hayek makes this point eloquently. The most significant fact about the market system is the economy of knowledge with which it operates, or how little the individual participants need to know to be able to take the right action. . . . Our theoretical habits of approaching the problem with the assumption of more or less perfect knowledge on the part of almost everyone has made us somewhat blind to the true function of the price mechanism and led us to apply rather misleading standards in judging its efficiency. [18, pp. 526-7] More recently Davis and Whinston [13, p. 367| have pointed out that "the relative intensity of desires can be at least partially revealed in even an imperfect market system while this kind of information is much more difficult to obtain under any other arrangement."''^ Of course, dc, may be negative initially since the market requires decentralization of some information, but it is reasonable to assume that, as the ratio CP/M increases so does dcj. More information must be centralized more at higher CP/M. The market proceeds to its equilibrium by an iterative ("trial-and-error") process which presumably converges. In this case the decision costs of the market result from being out of equilibrium. The central planner must use the information gathered to compute this equilibrium and then issue the appropriate orders. His
The incremental information cost would be affected by the si^a of the central planning unit to which the information has to be brought and the existence of economies Of scale in the production of information.
10
PUBLIC CHOICE
decision costs are the costs of the computation. ^ There is no reason to expect dcj-j to always have one sign or the other. It must, however, increase as the ratio CP/M increases. Computational expenses increase at least at a constant rate as the number of equations and unknowns are increased. On the other hand, ceteris paribus, the fewer the number of interrelated markets, the quicker they all can clear. For each market there will be fewer "other readjustments" to readjust to. Just as wishing wiH not necessarily make it so, the mere promulgation of a central plan docs not insure that it will be carried out, and merely charging planners to behave in the public interest does not guarantee that they will.^° On the other hand, setting a price on a good does not guarantee its collection; firms left alone to compete may collude. Again there is no reason to expect a uniformity of sign for dcg. It does, however, increase as CP/M increases. As one moves towards the market, marginal collection and metering costs will increase if the factor intensities of "collection" differ from the factor intensities of other "products," unless economies of scale in the production of "collection" are sufficiently large to offset this. It is at least as likely, however, that there are decreasing as well as increasing returns to scale in the production of "collection." On the other hand, as one moves towards greater central planning "abuse of power" problems with planners in general, should become more severe, if only because power is being made more concentrated and therefore easier to abuse. Moreover, we have shown in an earlier paper [36] that the advantages of substituting "authority" for the market (see [11 [) are ultimately cancelled by the need to enforce "contracts" with hired labor resulting in a limit on firm size even in a static world. 1) Information: Where demand curves vary greatly from household to household (or firm to firm) more information will be required for correct planning and its level will be lower and vice versa. Radio, television, and the telephone have to a certain extent tended to obliterate regional and ethnic differences in tastes. At the same time, the telephone has reduced the costs of gathering information. While there has probably also been some increase in the speed of adjustment of markets as a result of the telephone, the net effect of these inventions has almost certainly 1 Q
See Arrow i4, pp. 17 18]. If the. planning were done by a central planntng board whose membership represented diverse interests and/or experience, the costs of achieving agreement might be high. However, the decision to have a board rather than a single planner (like the decision to have "market socialism") can be viewed as a movement toward the market based on a desire to lower either the information or the enforcement cost of planning. 19 dcp has undoubtedly been shitted downward by the development of sophisticated computers. 20 With a few exceptions such as Becker I S ] , Meckling and Alchian [25] , McKean |23). Silver and Auster | 3 6 ] , and Stigler [ 3 9 ] , enforcement problems are usuallv ignored in the literature.
COLLECTIVE GOODS
11
Along the same lines, we expect concentration in local markets to be ceteris paribus, in geographical areas where the variation in household incomes is larger, or where the underlying population is more heterogeneous. If the technology available to firms in general varies less than the tastes of consumers, as seems likely, we would expect, ceteris paribus, the production of intermediate goods to be more concentrated than final goods which it is. For the same reasons, where the quality of and hence demand for the good being exchanged is difficult (i.e. expensive) to determine, CP/M will be lower, ceteris paribus. Thus, services are expected to be less concentrated than goods, which they are. 2) Computing Equilibrium: Where the lengths of the time lags are larger (the speed of market adjustment is slower), iteration costs will, ceteris paribus, be gj-eater, while the costs of computing the equilibrium will be unaffected. Thus, the ratio CP/M can be expected to increase. Durable manufactures generally have greater lags and are generally more concentrated than non durables, which is consistent with our argument. The "permanence of equilibrium" will also affect the ratio CP/M by effecting relative computation costs. The more often equilibrium changes, the more often the central planner must recompute his orders. The fact that equilibrium changes, however, has no predictable effect on the distance, at any point in time, of the market from equilibrium. Therefore, the more static (traditional) the society, the higher the ratio CP/M in general. Contrary to Marx, the more traditional societies have been the most receptive to his rather complete form of CP. Moreover, the attempt to induce rapid growth has often been accompanied by a retreat to the market (e.g., Lenin's "'New Economic Policy"). All of which is consistent with our theory. 3) Hnforcement: For some goods collection costs are inherently relatively important. For these goods we expect CP/M to be larger. Because of their very nature, collective goods will generally require expensive exclusionary collection devices if they arc to be provided through the market. Thus, one expects central planning to be more important for these goods than for private goods. In cases where the collective good has an important private joint product (e.g., collective goods such as vaccinations and schooling), or where some form of sociological
12 PUBLIC CHOICE control mechanism is operative, this would have to be modified.^^-^^ Modification is also required for private goods whose collection costs (e.g., the costs of devices such as turnstiles and gates) are relatively large. Entrepreneurs typically find it profitable to allocate resources to enforcing contracts with their hired labor, suppliers of non-human factors of production, and customers. In certain cases enforcement via measurement of the quality and quantity of non-human factors supplied by other firms is quite costly relative to the cost of indirectly controlling the quality of these items by controlling the inputs used to produce them (e.g., when testing a costly item requires its destruction). In the real world we rarely observe the buyer stationing "observers" in the supplier's factory. No doubt the reason is that this approach to contract enforcement would to some extent lead to a duplication of "entrepreneurial activities"—i.e., it would raise market enforcement costs by increasing the resources required to achieve a given level of contract enforcement. Our conclusion is that, ceteris paribus, the higher the cost of directly controlling the quantity and quality of nonhuman inputs relative to achieving control via their own inputs, the greater the degree of vertical integration. This, of course, represents a greater reliance on central planning relative to the market. Government officials have to choose between providing a particular good (collective or private) directly by means of a "nationalized" industry or purchasing it from private firms. In general "services" present greater contract enforcement problems than goods, which would be consistent with a tendency for government to purchase goods (e.g., tanks and typewriters) but to produce services itself (e.g., various "welfare" services). Similarly, the high relative cost of contract enforcement via output measurement might also help to explain why government officials choose to control schools and libraries directly rather than through subsidies. 21 Such mechanisms include "social pressure," "love," "emulation," " d u t v , " ate. Sociological controls are present in all groups of people, especiallv "small" ones 131, Chap. I j , and appear to be quite adequate for goods soch as style of personal dress and lawns In a communitv of home owners. 22 Some recent discussions of the market production of collective goods [17, 32, 34, 40, re rnot relevant to Our analysis because of their assumptions concerning the perfection of 41) are inforrnation, etc. 23 On such collection costs, see Friedman [16, pp. 30-311 and Alchian and Aden [ 1 , pp. 131-32, 420-211. "Public pari
