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Journal of Law and Economics, Vol. 13, No. 2. (Oct., 1970), pp

The Private Production of Public Goods Harold Demsetz Journal of Law and Economics, Vol. 13, No. 2. (Oct., 1970), pp Stable URL:
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The Private Production of Public Goods Harold Demsetz Journal of Law and Economics, Vol. 13, No. 2. (Oct., 1970), pp Stable URL: Journal of Law and Economics is currently published by The University of Chicago Press. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact Sun Jun 17 05:48: THE PRIVATE PRODUCTION OF PUBLIC GOODS* IIAROLD DEMSETZ University of Chicago T m s paper analyzes the production of public goods through private means under conditions that allow nonpurchasers to be excluded from the use of the good. Two conclusions are reached. First, given the ability to exclude nonpurchasers, private producers can produce public goods efficiently. Secondly, the payment of different prices for the same good is consistent with competitive equilibrium if the good is a public good. The allocation of resources to the production of public goods can be understood with the aid of the model formulated long ago by Alfred Marshall for the analysis of joint supp1y.l Just as the slaughtering of a steer provides goods to both leather users and meat consumers, so the production of a public good, by definition, yields benefits that can be enjoyed by more than one individual, for one person's use of public good services does not prevent simultaneous use by others. Under competitive conditions the rate at which steers are slaughtered is determined where the sum of the market prices for the hide and the meat is equal to the cost of slaughtering a steer. The geometry of equilibrium for jointly supplied products is shown in Figure I. Curve d is the market demand for hides and D is the vertical summation of d and the market demand for meat, hence D-d measures the demand for meat. The vertical summation of the demand prices equals the marginal cost of slaughtering cattle, shown by curve S, at the slaughter rate Q. No special problem arises in the allocation of resources to joint products in this, the standard case, nor does any *The author would like to thank the Lilly Endowment for financial aid received through a grant to the University of California at Los Angeles for the study of property rights. 1James M. Buchanan, The Demand and Supply of Public Goods (1968) explicitly views the demand for a public good as the demand for a jointly supplied good. I suspect that isamuelson, whose views will be considered later, when criticizing the use of the joint supply model for this purpose had Buchanan's view in mind. Paul A. Samuelson, Contrast Between Welfare Conditions for Joint Supply and for Public Goods, 51 Rev. Econ. & Stat. 26 (1969). The reader who is familiar with Buchanan's book will realize that the present paper extends the use of the joint supply model to problems of supplying public goods. Armen A. Alchian and William R. Allen, University Economics (2d ed., 1967) discuss the relevance of exclusion costs to joint consumption of both private and public good. THE JOURNAL OF LAW AND ECONOMICS problem arise in allocating the equilibrium production rates among consumers of meat and hides. The analytical similarity between the joint product problem and the public good problem is seen most easily in a two-person world in which a unit of the public good can be used to satisfy the demands of both individuals for the good. Thus, a unit of the public good, say, the televising of a taped program, can satisfy the demand of Mr. H and Mr. M, just as the slaughtering of a steer can satisfy the demand for hides and meat. Let curve d be the demand of Mr. H for the public good and let D be the vertical summation of d and the demand of Mr. M for the public good. The appropriate equilibrium rate of output again is given by Q. (The problem of allocating output from a given inventory of the public good is discussed later.) Now, PRIVATE PRODUCTION OF PUBLIC GOODS 295 just as the number of goods which are supplied jointly (meat, hides, bones, etc.) is not limited to two except for expositional convenience, so the number of persons demanding a public good is not limited to two. With joint supply if the number of goods is increased or with a public good if the number of persons is increased, we will merely have complicated the geometry without changing the analytical similarity of the two cases at all. What then is the difference between the two cases insofar as rate of output is concerned? There is no difference (an assertion that I plan to defend in more detail), provided that Mr. H and Mr. M can be excluded from consuming the public good if they fail to pay for it, which, of course, is implicitly assumed to be true in the joint supply problem. There is nothing in the public good concept that disallows the ability to exclude. Frequently, there is confusion between the public good concept, as I understand it, which states that it is possible at no cost for additional persons to enjoy the same unit of a public good, and a different concept, that might be identified as a collective good, which imposes the stronger condition that it is impossible to exclude nonpurchasers from consuming the good. The technology of modern weaponry may in fact make it difficult to exclude nonpurchasers from benefiting from national defense purchases, and national defense might be termed an approximate collective good, but it is easy to exclude nonpurchasers from viewing pay TV, an approximate public good. Ability to exclude nonpurchasers is compatible with both private and public goods. Although the joint supply model suggests that the rate of production of public goods responds to demand and supply conditions in exactly the same way as jointly produced private goods, there remains the problem of the utilization of an already produced unit of goods. How can market price be used to direct resources into public good production and also to ration the use of existing units of the public good, when the cost of allowing additional persons to use the existing inventory of the public good is zero? In the case of private goods the existing inventory is rationed by the price mechanism to those who are willing to bid the highest prices. Hides and meat are jointly produced but an individual's use of each of these goods usually precludes its use by others. The price mechanism rations the existing stock according to the dictates of opportunity cost. For in this case the cost associated with the consumption of a unit from the inventory is the foregone opportunity of allowing someone else to consume this same unit. The rationing of the inventory by market price minimizes the loss in value due to others being excluded from consumption (that is, minimizes opportunity cost) by allocating the inventory to those who find it most valuable; those who do not acquire a unit from this inventory fail to do so because the value of a unit of the good to them is less than it is to others. Since the measure 296 THE JOURNAL OF LAW AND ECONOM~CS of opportunity cost is the value of the good to those who forego it, the market price minimizes the opportunity cost associated with the allocation of an inventory of a purely private good. If, because demand or supply were forecasted poorly, the existing stock of a private good is so plentiful that the market clearing price falls below the cost of producing more units, then production to replenish inventory will dwindle. The loss in not consuming a unit for those who do not obtain a unit of the good from the existing inventory is less than the production gained elsewhere by not diverting resources from other uses for the purpose of increasing the inventory of this good. Since efficient allocation requires that resources be channeled into their highest value use, this message correctly guides resource allocation. While, if the market price of a unit of good from the existing inventory is above the cost of replenishing the inventory, then resources properly will be moved into the activity of producing more units of this good. The market price of private goods serves efficiently both the function of rationing the existing inventory and rationing resources into replenishment of the inventory. It would seem that any scheme for pricing the use of a unit of the public good, once an inventory of the good is available, will unnecessarily restrain the use of the existing inventory. The burden of the next few paragraphs is to demonstrate that if the cost of excluding nonpurchasers is negligible, then competitive markets can in principle resolve efficiently both the inventory allocation and the rate of output problems. But perhaps the most interesting aspect of the efficient equilibrium to be described below is that it yields for competitive conditions different prices for the same good. 2 I assume that the production of the public good is subject to diminishing returns at the level of firm output so that it is possible for the structure of the industry producing the good to conform to the traditional (although, I believe, superficial) view of competition. The production of television tapes for viewing over pay TV might approximate this condition since the production of additional tapes requires more resources while the cost of enlarging the viewing audience for a given telecast can be assumed to impose negligible cost on other viewers. In addition to the assumption that many producers of these tapes compete, I assume also that the cost of excluding nonpurchasers from viewing a telecast is negligible. I shall consider in the context of pay TV a special case of private produc- zthe compatibility of competition and different prices for the same good is discussed from a different viewpoint by Earl A. Thompson, The Perfectly Competitive Production of Collective Goods, 50 Rev. Econ. & Stat. 1 (1968). Thompson, however, reaches the contrasting conclusion that these prices characterize an inefficient solution to the production problem. But the model that he employs to reach this conclusion, in my opinion, so strains the concept of competition that a full discussion of the Thompson paper would carry us far beyond our subject. PRIVATE PRODUCTION OF PUBLIC GOODS 297 tion first and then a more general case. Figure IIb shows the market demand for and supply of TV tapes on the assumption either that all individuals have the same demand or that it is too costly to distinguish differences in demands. I assume that buyers are indifferent to the order in which they view first-run TV tapes. D, is the vertical summation of these individual demands so that under the present assumption the height of any single buyer's demand curve is D,/n where n is the number of buyers. One buyer's demand curve is shown in Figure IIb as Db. With the stipulated assumptions, private production of TV tapes will yield an equilibrium output equal to q, (number of TV tapes televised per period). For each viewing of a TV tape, the price paid by each buyer for a ticket allowing one person to view the tape is pb and the total revenue collected for each showing of a TV tape is npb since each of n viewers pays pb. The typical firm, pictured in equilibrium in Figure IIa, produces tapes at a rate equal to qf and incurs a marginal cost according to curve mc. The industry, I assume, is subject to constant returns so that curve S shows industry supply. The revenue or aggregate price per program is npb and this equals mc at qi. This completes the description of the equilibrium. I now turn to an explanation of just why it is an equilibrium. There are four tests for competitive equilibrium: (1) each firm should be maximizing profits while taking market price as given, (2) the price 298 THE JOURNAL OF LAW AND ECONOMICS should clear the market, (3) there should be no incentive for resources to enter or leave the industry, and (4) buyers should maximize utility while they take the price they face as given. All four conditions are satisfied by the equilibrium just described. Consider condition (1). Given large numbers of firms producing TV programs, p~, will be taken as given by each firm and, also, since each unit of the public good sold by a firm will be sold to all buyers simultaneously, the firm will earn an aggregate price per unit, npb, that is equal to marginal cost. Therefore, qf maximizes profits and no firm seeks to change its output rate. Since profits are zero, resources will neither leave nor enter the industry so that condition (3) also is satisfied. If price pb persists the market will clear so that condition (2) will be satisfied. There is no reason for the behavior of sellers to lead to a change in price. Each seller offers TV tapes at rate qi which means that the tapes of each seller will be available for viewing qf/q, fraction of the time. If, in order to conform to the usual notion of competition, I assume that each firm's TV tape is a substitute for that of each other firm (at a particular first viewing, but that once seen it becomes an inferior rerun), then when a specific tape is shown it will be shown to all n buyers because the price to each buyer is reduced to the lowest common level, mc/n =pb, if everyone views the program. Each seller, then, will find the entire viewing audience purchasing telecasts of his tapes q Jq, of the viewing time. But since there are many competing bidders for the viewing audience, no single seller can raise his price above p, without losing his entire audience to some other seller. Moreover, no seller has an incentive to cut price below pb because he will find that rates of output higher than qf can be produced only at costs that are too high to be covered by incoming revenues; if one buyer receives a price reduction from pb equal to Ap then other buyers must in total pay an increment greater than Ap if the new higher marginal cost of the firm is to be covered. But none of the other buyers will accept a price increase since other sellers stand ready to serve them at pb. Hence, from the viewpoint of sellers the price pb will persist, especially since any general expansion in output beyond q, must force price below average and marginal cost and any reduction in output below q, must attract entrants. Since q, is the only industry output consistent with zero profit it will be produced and will be made available to all buyers at whatever price it can fetch. The optimum firm size, qf, determines what fraction of this output will be produced by each firm. The only difference between the public good case and the private good case is that the sales of each firm receive the exclusive attention of the entire audience. With private goods, it is possible for the outputs of competitive sellers to be consumed simultaneously. With public goods, once a unit is sold to someone there is no cost to selling it to others also. There exist economies PRIVATE PRODUCTION OF PUBLIC GOODS 299 of scale in consumption, that is, the price to each buyer is lowered as more buyers purchase the same unit. The various portions of the output produced by different sellers cannot, therefore, be consumed simultaneously. Each producer will sell each of his units of output to the entire market to the exclusion of other sellers. But since all potential sellers compete for this market none can exact a price higher than pb from each buyer.3 Each buyer will take price pi, as given, so that condition (4) also will be satisfied. Each buyer (in the case we are now considering) of course, would like to have the output rate q, increased, for then, obviously, a price lower than pb will clear the market. But no buyer will have an incentive to exaggerate his demand for the product in order to bring this about. Nor will a buyer have an incentive to under-reveal his demand. The reason that the buyer takes the price as given in the public good case is the same as the reason that he takes it as given in the private good case. There is no individual action that he can take to lower the price that he pays that is worthwhile for him to take. The buyer of wheat naturally delights in bumper crops that are large relative to demand because the larger supply can clear the market only at lower prices. But the buyer of wheat does not, therefore, increase the quantity he purchases, for if he did so in significant quantities he would increase the price he pays and he would consume units that have a lower value to him than does the payment he makes to purchase them. Similarly, the buyer of wheat would benefit from a collusion among buyers to reduce the demand for wheat relative to the supply of wheat-if the collusion could be policed successfully at little cost to the buyer. An individual buyer, if he withholds his demand foregoes the viewing of TV tapes that would cost him less to view than the benefit he would derive. Since nonpurchasers are excluded, if an individual did not reveal his demand he would not view TV programs for which the marginal value exceeds the price he would pay. Industry output would, of course, fall as a result and so would the number of producing firms. The price to each remaining buyer would increase since n is reduced. But the same would be true for any overhead cost in the private good case, just as it would be for the case in which private goods are jointly supplied. It might be thought that an individual buyer could extort other buyers into subsidizing his purchases under the threat that otherwise he would purchase nothing, for if he purchases nothing, the price to other buyers, because there are fewer of them, must be increased to cover production cost. But similarly, we may ask why a prospective buyer of hides does not threaten 3 This is an excellent example of competition for the market as distinct from competition within the market, a concept that I have discussed in greater detail in a refutation of the logic of natural monopoly. Harold Demsetz, Why Regulate Utilities? 11 J. Law & Econ. 55 (1968). 300 THE JOURNAL OF LAW AND ECONOMICS to withdraw from the market unless purchasers of meat reward him. Since the reduction in hide demand would result in an increase in the price of meat the incentive for such threats exist in the production of private goods also. A similar incentive exists in the production of private goods subject to scale economies since here, also, the reduction in demand would raise the price paid by other buyers. Conceptually nothing bars such bargaining in the markets for both private and public goods. It just is not worthwhile in most cases. If one purchaser of hides or of TV programs withdraws his demand he raises the cost to others by a magnitude of the order of l/n of the price that he would have paid. Where n is large it just does not pay to incur the costs of withdrawing one's demand plus the cost of contacting other buyers to exact a reward to reenter the market, especially since these other buyers could utilize their would-be contributions to such a reward to purchase more units for themselves instead. Since the game is seldom worth playing, the problem does not often arise as an empirical matter. This is not to say that the problem never arises. It does, even in the world of private goods, as when certain landholders hold out for higher prices after other landowners have sold to some land developer. The normal adjustment t
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