Stephen E. Margolis
Stephen E. Margolis: Department of Economics, North Carolina State University, Raleigh, North Carolina 27695
Network externality, the concept that a product's value to a consumer changes as the number of users of the product changes, has become increasingly influential in economic thought. In this paper we elaborate a claim that, in spite of the popularity of the concept, several important aspects of network externalities have been neglected or misunderstood. We argue that many 'network externalities' are not externalities in the modern sense of causing market failure. Some are not sources of market failures because they are pecuniary externalities, which is a class of externality that does not constitute market failure. Other supposed instances of network externality are incorrectly classified as externalities because they are internalized through market mechanisms.
We also argue that the new technologies that are thought to have spawned these externalities have been improperly modeled. The seemingly relentless decreases in costs that are associated with many new technologies are due not to economies of scale so much as rapid technological progress. And the decreased costs associated with technological progress is not a new phenomenon. We conclude that the empirical importance of network externalities, as externalities, has been greatly overstated.
Every new age is enamored of its own advances. In this "age of technology," our focus is on such highly visible technologies as computers, fax machines, and new methods of communication. So taken are we with these new technologies that we tend to treat these new inventions as sui generis, so different in essentials that we cannot even speak of them in the same terms as we have used in the past. To discuss the advances of this age of technology, the economists has invented a new concept: network externality. Network externality has been defined as the change in the benefit, or surplus, that an agent derives from a good when the number of other agents consuming the same kind of good changes. It is argued that network externality is endemic to new, high-tech industries, and that such industries experience problems that are different in character from the problems that have, for more ordinary commodities, been solved by markets (Katz and Shapiro 1985, Farrell and Saloner 1985).
The concept of network externality has been applied in the literature on standards, in which a primary concern is the choice of a correct standard (Farrell and Saloner 1985, Katz and Shapiro 1985, Liebowitz and Margolis 1994a). The concept has also played a role in the developing literature of path dependency, which maintains that the explanation for many market outcomes is mere happenstance (Arthur, David).1 While the path dependency literature has focused on technologies, the reasoning of path dependency arguments has also been extended to the choice of social institutions (Binger and Hoffman, North).
These literatures treat the concept of network externality uncritically. Thus it is natural for a reader encountering a paper discussing network externality to look for the association most commonly made with externalities: that the market fails.2 And the reader is not disappointed: papers in this literature have found market failure. As we will show below, this argument, carried to its logical conclusion, would indicate that most markets fail standard economic tests of efficiency, and thus might be thought to call for government intervention into most markets. This conclusion is too important to pass without careful scrutiny.
This paper elaborates a claim that network externalities are not well understood. We demonstrate that one class of phenomena identified as network externalities is actually pecuniary in nature, and not a cause of welfare loss. We also argue that many of the remaining network externalities are not externalities at all, but are better thought of as network effects that are resolvable by the familiar mechanisms of ownership and contract that internalize these effects. Further, we discuss the mischaracterization of technology that has been offered to justify network externalities and we elaborate upon the technical features of models that have led other authors to conclusions that differ from ours. In sum, it is our argument that, notwithstanding the enthusiasm that has greeted this literature, the concept of network externality has, in important respects, been improperly modeled, incorrectly supported and inappropriately applied.
Katz and Shapiro (1985) consider two types of positive network externalities. First, they consider direct externalities -- those generated "through a direct physical effect of the number of purchasers on the quality of the product." Their example of direct externality is the number of homes attached to a telephone network. Second, they consider "indirect effects" such as complementary goods being more plentiful and lower in price as the number of users of the good increases. Their example here is better software as the number of computers of a particular type increases.3 They go on to consider another source of indirect network externality, the availability of post-purchase service for durable goods, such as automobiles.
In a similar vein, Farrell and Saloner observe: "There may be direct 'network externality' in the sense that one consumer's value for a good increases when another consumer has a compatible good, as in the case of telephones or personal computer software. There may be a market-mediated effect, as when a complementary good (spare parts, servicing, software ...) becomes cheaper and more readily available the greater the extent of the (compatible) market" (p. 70).
Although theses writers and others observe a distinction between direct and indirect externalities, this distinction does not figure into the existing theoretical analyses. In the theoretical treatments, both types of network externalities are assumed to have the same consequences: direct and indirect interactions alike are embodied in payoff functions, regardless of their source. Farrell and Saloner, for example, postulate a benefits function Bj(S,Y) in which j denotes the firm, Y denotes the firm's technology choice and S denotes the size of the network (number of firms choosing Y). Katz and Shapiro (1986) specify that a consumer's net benefits are v(x1+x2)-p, where x1 and x2 are the sizes of the network in time period one and two and p is the price of a unit of the technology. We argue below that direct and indirect network externalities are fundamentally different and should not be modeled as equivalent. In the next section, we discuss the problems of drawing welfare conclusions regarding indirect network externalities. After that, we consider direct effects, arguing that the mere fact of a network effect does not necessarily imply a network externality.
Economists once argued that increasing cost industries require a tax, and decreasing cost industries require a bounty. Marshall appears to have originated these propositions, and Pigou seems to get most of the blame.4 From the modern perspective, the early twentieth-century debate on the nature of externalities may appear rather quaint, due to the nonmathematical apparatus that it used. However, this quaint apparatus did ultimately manage to distinguish between technological and pecuniary externalities.
The economic foundation for the belief that all non-constant costs lead to market failures focused on the impact of additional output on the price of the product. Pigou argued that the change in expenditure on the inframarginal units that accompanied a change in output was a social cost, and that to reach an efficient solution, this cost should be internalized. In other words, for Pigou, the marginal expenditure curve associated with the supply curve was the social marginal cost curve.
Some economists quickly understood and agreed that external pecuniary diseconomies simply involve transfers from buyers to producers: They are not instances of market failure. Though economists have not generally recognized that external pecuniary economies have the same attribute, modern interest in all pecuniary effects has waned; textbook discussions of externality barely mention them.5 The current pedagogy calls attention only to nonpecuniary externalities, and associates all externalities with market failure.
This bit of history of thought is very closely related to the literature on network externality. Almost any product with increasing or decreasing costs can be considered a network, as network is being used in the current literature: Additional consumption may raise or lower the cost of a product to other consumers and it may raise or lower the cost of substitutes and complements. Since such effects are practically universal in the economy, if network externalities are taken seriously as externalities, almost all markets must be candidates for either taxes or bounties. This, of course, is a reincarnation of the Marshall-Pigou concern that competitive market solutions would be in need of repair unless costs were constant. Any network externality that is "market mediated," meaning that the size of the network influences the price of inputs to a firm, or goods and services to a consumer, is the same as the pecuniary external economies and diseconomies that so perplexed Marshall, Pigou and at least some in the generations of economists that followed. For this reason we turn to a more detailed examination of these arguments. We consider first the familiar pecuniary external diseconomies to set the stage and establish terminology for the less familiar pecuniary external economies.
In figure 1, let C1 represent the conventional long-run industry supply function for a ordinary commodity, such as shoes. Assume for the moment that there are no external effects (price of inputs assumed constant). Assume also that the industry supply function is increasing because, say, there are limited locations for producers or an unequal distribution of shoemaking skills. The competitive equilibrium is at J. With each firm producing on its marginal cost curve, the associated price, P1 is equal to the marginal cost of shoes. We can imagine having a "network" of shoe buyers, where each buyer's purchase has an impact on other shoe buyers. If someone elects to buy one more pair of shoes, the expenditures of the network of shoe buyers will go up by more than P1, the price of a pair of shoes. The incremental expenditures are shown as C2. This is analogous to the MFC curve that is used in the context of factor demand.
The puzzle to Pigou and some others of his generation was whether this marginal expenditure curve, C2, is the socially relevant cost curve. Pigou originally wrote that it was, and suggested taxes to move market outcomes to I. The answer of the profession was, and is, that if the difference between C2 and C1 occurs as rents to the producers of inframarginal shoes, then C2 does not represent the marginal social cost of shoes. Instead, this component of the increased expenditure of shoe buyers is merely a transfer from the consumers of inframarginal shoes to the producers of inframarginal shoes. This transfer (rent) to producers has no impact on efficiency. This is the simplest example supporting the interpretation of the industry supply curve as marginal social cost, the interpretation put forward by Young, Knight, and others, as a counter to Pigou's claim.
If each shoe producer's costs are affected by industry expansion the analysis becomes more involved and it becomes crucial how and why costs are affected. One possibility is a real interaction among shoe producers that affects their costs, a technological externality within the shoe industry (congestion) that would make C2 the social marginal cost curve. Another possibility is that costs change because the price of some input increases as the shoe industry expands.
Assume, for example, that the external diseconomies are caused by increases in the price of leather as shoe output increases. In this case, the issues we raise are just kicked one market upstream. After all, as we move up the supply curve, the increased revenue per shoe, when an additional shoe is produced, does not now go to the inframarginal shoe producers, since these shoe producers all must pay an equivalently higher price for leather. Here the extra payment made by shoe consumers is not a rent going to shoe producers, but must go somewhere else.
We now must ask why the price of leather is rising. If it is due to some limited locational or other element, so that consumers' increased expenditure on inframarginal shoes is found to be a rent to inframarginal leather suppliers, then C1 is the social marginal cost curve for shoes. An alternative is that the upstream (leather) industry faces technological diseconomies external to its component firms (e.g. congestion).6 In this case, leather is not sold at social marginal cost, and C2 is the social marginal cost of shoes.
It should be clear that the issues considered in regard to the input market are an exact echo of the issues considered for the primary (shoe) market. Every industry can be thought inefficient if its inputs are mispriced. To halt an unstoppable recursion through suppliers, then suppliers' suppliers, and so on, we will assume that input prices represent marginal social costs and confront these issues but once, in the primary market, as is normally done. Assuming that inputs are efficiently priced, and assuming no technological externality among shoe producers, C1 is the marginal social cost of shoes.
Restating these old results in terms of the current terminology, we note one immediate qualification for indirect network externalities. Those negative network externalities that are "market mediated," as when an input or complementary good becomes more expensive, and that do not reflect some upstream market imperfection, are irrelevant as externalities. Indeed, if we are consistent in our treatment of network externalities, and treat increasing costs industries as networks, we ought to conclude that most forms of consumption and production involve "negative indirect network externalities." Pecuniary external diseconomies, however, involve no inefficiency. Internalizing these externalities is harmful: such internalization merely mimics monopsony power.
Models of network externalities are concerned primarily with positive network externalities. Thus with regard to indirect effects they are concerned with decreasing prices for goods or their complements. For example, the price of DOS compatible software falls as the number of DOS users increases. For decreasing costs, the nature of pecuniary externalities is less familiar so we consider their sources and consequences here.
Decreasing-cost industries have not been treated as symmetric with increasing cost industries.7 As we have just demonstrated, for increasing cost industries, if there are no input price effects, and no real technical effects of industry expansion, the increased expenditure for inframarginal goods is just a transfer. Inframarginal units of production capacity, capable of producing at relatively low cost, remain in the industry and earn rents as price and output increase. For the case of decreasing costs the analogous explanation is not generally taken to be available. The decrease in expenditure on inframarginal units is generally not recognized as a loss in rents to producers. Downward sloping supply is not the result of low-cost units being held off the market until prices fall, and being supplied only to "take advantage" of low prices. So it is most often argued that downward sloping supply must be a consequence of some real externality or economy of scale, rather than a bidding down of producers' rents that would be the exact analog of the external diseconomies case.
But, of course, downward sloping supply could also be caused by decreasing input prices. This would seem to be the case that most closely represents actual examples of indirect network externalities. We take up that case now, using computers and integrated circuits (chips), instead of shoes and leather, to aid intuition and exposition. As in the foregoing, we maintain that the input (chips) is sold at marginal cost. Without a technological externality or simple economy of scale in the computer industry, downward sloping supply for computers will require that the price of chips falls as the computer industry expands. In order to avoid indefinite recursion up the supply chain, we consider the case in which downward sloping supply is the result of economic factors in the chip industry.
We make the common assumption that the decrease in the cost of chips is external to any computer firm. Computer producers then can have upward-sloping or horizontal cost curves in the usual manner, with each firm's cost curves being a function of industry output. The industry supply curve is rotated clockwise, relative to the summation of firm supply curves, by external cost effects. In figure 2, C1 is the supply and C2 is the marginal expenditure curve associated with C1.
The downward sloping supply curves imply that the marginal expenditure by consumers on computers lies below the supply curve. This is because the marginal cost of an additional computer is the cost of the last unit plus the (negative) effect on cost for all other units that are now made less costly by the decreased price of chips.
In the case of upward sloping supply, the increase in expenditure on the inframarginal computers was considered a rent going from consumers to producers. Here, the decrease in expenditures on the inframarginal computers is passed from producers to the consumers of computers (the shaded area in figure 3). But since the costs to the computer producers go down due to the decreased price of chips, the producers of inframarginal computers are merely passing on lower costs. Thus the benefits to computer users actually come from the producers of inframarginal chips.
If we are to treat this example consistently with the case of upward sloping supply, we must assume that all markets other than the computer market are producing at p=mc. With that assumption, downward sloping supply for chips implies that marginal costs fall as chip output increases. One possible explanation for this is that the chip industry is a natural monopoly. In that case, marginal cost pricing cannot cover total costs. This is equivalent to the familiar example of a perfectly regulated (single-priced) natural monopoly that requires a subsidy from some source to cover its unavoidable operating loss. When output increases in the computer industry, causing the price of chips to fall (increasing the absolute value of the negative producer surplus), the chip industry experiences a larger loss, requiring a larger subsidy by the regulator. Thus the transfer goes from the source of subsidy to the computer-chip industry to the computer consumer. Under these circumstances, the case of downward sloping supply is symmetric with upward sloping supply. All of this is to say that downward sloping supply may correctly represent decreasing cost, presenting no externality to be internalized.
Alternatively, the downward sloping supply of chips could be the result of technological economies that are external to individual firms in the chip industry.8 In that case, the marginal social cost of chips does lie below the supply curve. Of course, to retain our assumption that inputs are bought at a price equal to social marginal cost, we must assume that the externality in the chip industry is internalized in some way, for example, by a Pigouvian subsidy system. This subsidy must increase as the production of computers increases, and it is the increase in subsidy that is transferred, in the end, to consumers of computers. Once again, the analysis is fully symmetrical. This is to say that if a technological externality upstream (chips) is correctly internalized, the downward sloping supply in the downstream (computer) industry involves no additional externality to be internalized.
Indirect network externalities thus appear to be either pecuniary externalities, which require no remediation, or the reflection of conventional market failures in upstream markets. Introduction of the concept of indirect network externalities takes something that has long been recognized and (to some degree) understood and presents it as something new and unfamiliar.
There exists a casual empiricism that suggests that computer users are better off when there are more of their like. But if computer users are better off because of an external economy or natural monopoly in the chip industry, misdiagnosing this phenomenon as an externality pertaining to the number or type of computer users will prompt incorrect policy responses. Internalizing such an indirect network externality will not, for example, move us toward the correct number of chips per computer, or computers per user. It will not prompt efficient expansion into other uses of chips outside of the computer "network." Thus the labeling of an upstream market problem as a downstream "indirect network externality" is not a harmless semantic shift. It interferes with understanding and would prompt, if taken seriously, improper policy responses.
The reader may note that this analysis has been couched in terms of changes in input prices. Although the network externality literature is often couched in terms of price changes for complementary products, such as computers and software, this is not really an important distinction. The complement is really an input in the creation of a product or service jointly provided by the two goods. A computer producer, who buys the software and bundles it at sale, fits the description above, with software replacing computer chips. Even if a customer buys both the computer and the software from separate vendors, the costs of the joint services are the same as if the customer had bought both from a single firm (if both markets are competitive). As in the above, misdiagnosing the externality as one pertaining to the number of computer users misdirects our attention and prompts policy measures directed at the wrong margin of adjustment.
There are many activities in which the phrase "the more the merrier" applies. It is this simple interaction that we have termed a network effect. But network externality -- unexploited gain from trade regarding network effects -- is not an inevitable consequence of network effects. Nor is it a consequence that is escaped only by coincidence. Network effects may be shown to be more like other social interactions than has previously been supposed. Accordingly, theoretical cases of network externalities may be shown to be consequences of particular assumptions of about technologies, tastes and markets. With that, market failure in this context may be understood as arising not from networks effects per se, but rather from conditions that economics associates (rightly or wrongly) with inefficiencies for goods in general. It is also of note that the restrictions invoked in some cases to construct a network externality preclude consideration of network size, an important margin on which network effects might operate.
Many of the most conventional externalities studied by economists can be eliminated by some configuration of ownership. For example, if exterior maintenance of apartment buildings creates external benefits for proximate units, common ownership of nearby units should have survival value. The tragedy of the commons has a solution in property rights to the commons. We might well expect that ownership of a network would resolve these externalities as well. Such a conclusion would be important, because many network activities are "owned" or, in the terminology offered by Katz and Shapiro, "sponsored." Some networks are owned by their very nature: They are literal physical networks, such as telephone or power grids that must be constructed as networks through coordinated action. Figurative networks, such as the "network" of Apple computer users, or of Airstream trailer owners can also be owned through patent, copyright, or trademark protection. Of course, some networks, such as the network of English speakers, seemingly cannot be owned.
A prior expectation that ownership solves network externality problems encounters dissonance in the network externality literature. Katz and Shapiro conclude that market failures due to network externalities are not resolved by sponsorship. "Sponsorship can internalize some of the externalities through below cost pricing at the beginning of a technology's life. But sponsorship can create problems of its own." (p. 825)
We begin an alternative examination of these issues by offering a simple model, a variant of the well-known fishing-on-the-lake model. Although this model captures many fundamental features of the costs and benefits of networks, it clearly cannot cover every case. But the cases its does not cover are, we will argue, special cases. In particular, they are special cases that we encounter elsewhere in economics and treat (elsewhere) as special cases.
In figure 4, the horizontal axis denotes the number of participants in some network. It can be the number of telephones, computer users, or fishermen on a lake. Assume that participation in the network consists of buying one unit of some basic element of the network; telephone service, a computer, a day on the lake. As is fundamental to positive network externalities (and in contrast to our usual fish stories), we assume that the private benefit of each network participant increases as the number of participants increases. We assume that network participants are identical. This assumption is the familiar one in the fisheries example: We seldom take note of differences in fishing ability. Analogously, homogeneity is a fairly common assumption in the contemporary network literature. (See, for examples, Church and Gandal, 1993 p. 243, Katz and Shapiro 1986, p. 826.) Figure 4 shows a relationship between average benefit, AB, and the number of network participants. The height of AB represents each participant's willingness to pay for one unit of network participation; willingness to pay that rises as the number of network participants increases. (Note that absent a network effect, AB would be horizontal, at the common benefit received by all participants.) MB, the marginal network benefit, represents the change in total benefits to network members when an additional member joins. MB lies above AB since an additional member raises the benefits for all network participants.
For the moment, we assume that the marginal cost of the network commodity increases with output. This is a conventional assumption about cost, and it has intuitive appeal for many networks. For example, literal networks, like cable television, connect the closest customers first, and expand by connecting ever-more-distant customers at ever-increasing costs. Kahn (v. 1 p. 124, v. 2 p. 123) provides empirical support for this pattern in public utilities networks. For figurative networks, such as a network of computer users, additional marketing effort may be required to reach customers less familiar with the product. Finally, network participation frequently requires the use of some "entry" commodity (for example, a telephone or computer), and that commodity may be subject to ordinary production costs.
Since AB represents the willingness of participants to pay for network participation, it is the highest price that the network owner can charge. Thus, it is the average revenue function for the network owner as well as the average benefit function for network participants. The marginal revenue captured by the network owner when an additional participant joins the network is equal to the price paid by the marginal participant, plus the increase in price that can be charged to all network participants. In this example, MB is also the marginal revenue function associated with AB. The network owner maximizes profit, equating marginal revenue with marginal cost. Q* is the network size, and P* is the price. P* obviously is less than marginal cost.
Because the return to the network owner of serving a participant is greater than price, there is no credibility problem with sub marginal cost pricing. A problem that can be constructed in network settings, in which a sponsor could not credibly commit to sub-marginal-cost pricing (Katz and Shapiro 1986 pp. 834, 838) does not necessarily arise for networks. It does arise, as it does for many allocation problems, where enforceable contract is unavailable, and where a potential transaction would span more than one time period.
It is fairly trivial to relate this outcome to the social wealth-maximizing optimum. The optimum conditions are the familiar equivalence of marginal social cost and marginal social benefits. Since the change in benefits to society when a consumer joins the network is represented by the MB curve, the marginal social benefit thus coincides with the network owner's marginal revenue function, and Q* is the optimal network size for both society and the network owner.
An upward sloping benefits function does introduce some unfamiliar features to this analysis. In figure 2, while P*, Q* does clear the market, stability will not originate on the demand side. In the more familiar fishing problem, with optimal pricing of participation (the right to fish), the implicit dynamic story is that if too many fishermen show up to fish, they will find the optimal price of fishing to be unattractive, given the expected catch, and fishermen will leave until fishing on the lake is as good as anything else. It too few fisherman show up, again at the optimal price, fishing is too good a deal, and more fishermen will arrive. In contrast, for the positive-effects network, stability must originate with the supplier. The network owner would announce P* and provide Q* positions in the network. Here, if more than Q* seek to participate, the network owner could ration demand, or alternatively, the network owner could offer to accommodate all participants, but would optimally charge a price equal to average benefit, plus the difference between marginal benefit and marginal cost. ( That price equals the net marginal cost of an additional network participant) Such a price is above average benefit, so network participants would depart, moving the equilibrium to Q*. Similarly, at participation levels below Q*, the profit maximizing price is marginal cost less the difference between marginal and average benefit; again the net cost imposed on the network. Such a price is below average benefit, and so would attract additional participants. Stability thus originates on the supply side, so in still another respect, the model is a mirror image of the usual fisheries problem.
It is possible to construct a "chattering disequilibrium" model. No one joins the network, then everyone joins etc. But the same can be done for the ordinary fisheries problem: If too many fishermen show up, they all go home, If no fishermen show up, they all want to fish. Ordinarily these knife edge problems are ignored.
A network market failure can be found, however, when the network is not owned. If we reinterpret MC as the supply function of a group of atomistic suppliers of the basic network commodity, rather than the marginal cost of a single producer, then equilibrium occurs at Q. Notice here, however, that the manifestation of the market failure is the size of the network. It is not in the choice of networks.
This analysis of the operation of an owned network is an exact analog of the standard example of overfishing a lake. That particular network externality is a negative one, but the analysis is the same. Replacing common ownership of a lake with a single owner results in efficiency precisely because the owner takes into account of the interactions of the fishermen in order to maximize the surplus, which, of course, he appropriates. In the fishing example, without network ownership, the network is too big; but for the case of positive network externalities, the network is too small. Of course, if the lake is the only source of fish, we might have to worry about monopoly in the output market, or if the lake is the only use of labor, we might worry about monopsony in the labor market. Similarly the owner of a network may or may not be a monopolist in the supply of network services. But monopoly is monopoly, and monopsony is monopsony, and either are only coincidentally associated with network problems.
A number of other writers emphasize the likelihood of market failure where there are network effects. Two seminal articles, Katz and Shapiro (1986) and Farrell and Saloner (1985) find these problems, as does some of the most recent work on the subject (for example, see Church and Gandal 1993) The many models of network externality differ in particulars, and our problem is not to reconstruct each of them here. There are, however, structural features that are common to many of the models of network externality, and these structural features can be shown to support particular outcomes that are consistent with market failure.
One important feature of many network externalities models is the assumption of constant marginal cost. See, for example, Chou and Shy (p. 260), Church and Gandal (1993 p. 246), Katz and Shapiro (1986 p. 829) and Farrell and Saloner (1992 p. 16). This assumption is common in economics, and commonly results only in reduced complexity, as in classical duopoly models. (For an example related to compatibility, see Matutes and Regibeau). But the assumption is decisive in network externality models for this reason: The assumption of some fixed costs, together with constant marginal cost, installs an inexhaustible economy of large scale operation. This, in turn, installs an externality if goods are priced at average cost.
Another structural feature is an assumed limitation, or predetermination, of the total number of network participants. Typically it is assumed that there are N consumers (or users, or participants, or adopters, etc.) who all adopt some product, network, or technology. For example, Katz and Shapiro specify, "each consumer is infinitely lived and has inelastic demand for a single unit of infinitely durable hardware." (1992 p. 58). Their 1986 paper specifies Nt identical consumers in each period. Either all of these consumers adopt a particular technology, or none of them do. In Farrell and Saloner (1985), N firms adopt or don't adopt a new standard.
As we will see, what is dispositive is that the models are constructed so that posited economies to scale are not exhausted when all potential participants are served by a network. So long as the stipulated technology is characterized by inexhaustible economies to scale, it does not particularly matter what the number of potential consumers is, so long as it is finite.
Figure 5 reproduces our model with a fixed number of participants and constant marginal cost. Again the average benefit is upward sloping, and marginal benefit lies above the average private benefit. Since marginal cost is constant, however, marginal cost must intersect the benefits curves from above. With this, the optimum must lie at infinity, or at some other maximal boundary. That boundary is, of course, the predetermined full set of demanders, each of whom demand the good with zero elasticity. Thus both the limitation on demanders and the restriction on marginal cost play a role. In this setting, the nature of the problem cannot be the number of network participants: that is established by assumption.
The contrast between the results shown in figures four and five illustrates the importance of the assumptions on cost and participation. Our point here is not that there cannot be economies to scale, but rather that many of the results associated with network externalities are anchored in the assumption of inexhaustible scale economies. This is important in two regards. The first is that for many of network commodities, economies to scale are exhaustible The second is that the cause of some of the putative problems with networks would also result in problems for ordinary goods, and thus the apparent network problems have less to do with networks per se and more to do with economies to scale.
Because these models suggest that only a single network (or standard, or technology, etc.) will survive, the network externality literature implies a possible coordination problem: Which network gets the franchise? Natural monopoly does raise legitimate questions, but these questions are not well addressed as externalities. As we demonstrate in our (1994a) paper, the coordination problem is not removed by internalization, strictly defined as allowing consumers to take account of the effects of their behavior on others. To remove all coordination problems, consumers would also need to take account of the behavior of all coalitions on everyone else in the economy, which is a far greater task than can be accomplished by mere internalization of network externalities. Other models (Economides, Chou and Shy) have demonstrated this coordination problem without network externalities.
The literature on network externalities challenges economists' traditional use of decreasing returns and grants a fundamental role to economies to scale. Though economists have long accepted the possibility of increasing returns, they have generally judged that except in fairly rare instances, the economy operates in a range of decreasing returns. The literature on network externalities has attained some of its influence by choosing as its examples some new-technology products that appear to exhibit increasing returns. Following the lead of futurists, writers in this field predict that as modern technologies take over a larger share of the economy, the share of the economy described by increasing returns will increase. Brian Arthur has emphasized these points to a general audience: "[T]he prevalent view is still that things happen in equilibrium and that there are constant or diminishing returns... A high-tech, high value-added world calls for a new kind of economics." (Arthur, quoted in Wysocki, 1990).
Arthur approvingly cites Marshall for an early emphasis on the importance of increasing returns. But Arthur appears to be unaware of the intervening criticism of Marshall's view. Marshall's views on increasing returns were largely erroneous, a confusion of movements along cost curves and movements of cost curves (see Stigler, pp. 68-76, Ellis and Fellner, p. 243). Our criticism of the current view of increasing returns expands on these early criticisms of Marshall.
The support for a belief in increasing returns is based largely on anecdotes and casual characterizations of technology. The past decades have evidenced a number of technologies that have experienced two correlated phenomena: first, enormous declines in price; second, tremendous growth in sales. In recent years the prices of VCRs have declined remarkably, and at the same time, there has been an incredible increase in their use. The same story applies to computers, lasers, and cellular phones. The simple explanation is that these technologies are subject to increasing returns. Since bigger has been cheaper, it has been assumed that bigger causes cheaper. But an available alternative is that as the technology has advanced with time, the average cost curves are shifting down. Consider for example, the history of old technologies, such as refrigerators and automobiles. These industries, currently thought to exhibit conventional decreasing returns, experienced tremendous cost decreases early in their history.9 Thus the currently popular association of new technology with increasing returns may well be treacherous.
The casual argument for the association of new technology with increasing returns imposes a very restricted structure on production. Products are argued to be knowledge based, and the knowledge costs of a product are generally argued to be associated entirely with fixed costs. For example, the programming costs of a new piece of software are large, and the costs of copying disks are very small and constant. This leads to the conclusion that average costs will fall indefinitely as output increases. But this argument fails on several grounds. First, the knowledge-based part of costs are not all fixed. Support services and sales services, for example, are knowledge based, but are variable costs. Goods that are sold to a broader market generally must accommodate more diverse requirements than products that are sold to a smaller and more specialized group. Second, this characterization of production leaves other conventional components of cost out of the picture. Conventional variable costs easily coexist with fixed cost components in common textbook examples of U-shaped cost curves. As output increases, the decrease in average fixed costs must itself eventually decrease, and is more than offset by increases in average variable costs. Without investigation, it is unreasonable to accept that the law of diminishing marginal product somehow takes a vacation in new-technology industries. While the scale properties of a technology pertain to the simultaneous expansion of all inputs, it seems evident that resource limitations do ultimately restrain firm size. Economists have long supposed that limitations of management play a role in this, a relationship formalized in Radner (1992).
It is arresting, at first glance, to observe that the disks and paper that constitute a software product are worth only a few dollars. Observations like that appear to support the view that such products are unlike older, more familiar products. But we might as well observe that the ingredients in a nouvelle cuisine meal are worth only a few dollars or that the constituent items in sneakers, automobiles or Corn Flakes are only a small percent of their final price. That observation does not lead us to conclude that efficiency requires us to dine at the same restaurant, or wear the same kind of shoes, etc. The additional costs involved with catering to slightly different tastes, or transporting consumers to products, or vice-versa, are the types of costs that are easily overlooked in simple models. These other costs are exactly the type of costs that can cause average cost to rise even though average fixed costs fall as output increases. Thus the observation that disks and paper are of trivial cost is insufficient to allow the conclusion that we will and should all compute with the same spreadsheet. This caution is reinforced by the observation that software markets are not monopolized, and in fact seem to accommodate numbers of firms comparable to numbers in such "old technology" industries as steel or automobiles.
It is also far from clear that current high-tech items have a greater knowledge-based component than previous incarnations of high-tech items. For example, it is not clear that creating a spreadsheet is a more challenging conceptual enterprise than inventing the Bessemer process. For most new products, the costs of "figuring it out" are fairly significant. And once the technology is figured out, additional units of the good, embodying the solutions developed, will come cheap. Once a caveman had discovered the technology to get one fire started, he could easily make many fires. The producer who has figured well will have an advantage for a time, and will, for that time, dominate the market. RCA, Ampex, and Ford serve as examples of pioneering firms that engineered downward shifts of their cost functions. If these firms merely moved down fixed average cost functions, they would today still be the leaders in televisions, video recorders, and automobiles.
We don't deny the importance of progress. Certainly the state of knowledge is changing. We don't even make a claim about changes in the rate of progress (whatever that might be). Our claim is only that knowledge is always a component of goods, that the knowledge share of total cost is not necessarily greater now than it was in the past, and that the fixed-cost attribute of knowledge need not overwhelm other cost components.
It is generally considered infeasible for consumers to transact with one another to internalize an externality such as air pollution, since consumers are many, transactions are costly, free riding is possible, etc. Along similar lines, it seems unlikely that network participants would be able to internalize indirect network externalities, since such interactions involve large numbers of participants. In contrast, direct network externalities involve direct interaction of individuals, so the number of people who affect each other may well be a reasonable few. Thus transactions to resolve an inefficiency cannot be ruled out.
Take the example of a telephone network. It is often observed that each additional phone attached to the network enhances the value of the network to other users of the network. But most users make most of their calls to only a small number of phones. The Smith family, for example, may frequently call friends or parents on the phone. Each call is a transaction of sorts. The Smith family will derive the greatest value from those network participants they intend to call most frequently. But it is not difficult for the Smith family to transact with their parents or friends to get them to install a phone on a common network. A similar story applies to video recording. If Smith's parents are thinking of getting a Beta format machine, and the Smiths already have VHS, Smith might remind his parents that he can provide videotapes of the grandchildren only on VHS, and thus help to internalize the joint value in tape exchange between parents and children. And it is not only family relationships that allow this internalization. Companies that do significant business with one another will try to standardize on similar products, in order to allow greater interaction. It is not terribly difficult to negotiate over the terms of enhancing this interaction. Since the very nature of these networks is interaction among individuals, it is unreasonable to invoke the usual condemnation of transacted solutions, which is that individuals are unable to interact. Transactions to resolve these direct network effects tend toward desirable outcomes. It is fortunate that indirect network effects are unlikely to be addressed in this way, since any such transactions would tend to emulate monopsony outcomes.
The reception given to the idea of network externalities is based in large part on the general impression that there are a large and increasing number of activities in which costs or benefits rise or fall as the number of participants increases. And this impression seems to apply particularly to new, high-tech industries.
Network externality has been promoted as a new concept that deals with new technologies. Such a new concept would seem to require models that are new as well. But as we have seen, some of what is new here is mistaken. In some instances, the focus on the network itself merely prevents proper diagnoses of more familiar problems in related markets, conventional problems such as natural monopoly and ordinary production externality. In other instances, special cases are too readily taken for the general network problem. Finally, these new models have detached the analysis from an important body of understanding. In this regard we note that the problems with pecuniary externalities were noticed almost immediately upon publication of Pigou's book in 1912, while the modern version of the error has remained in the literature for quite some time.
We may often find that we are better off when more people make the same choice that we make. Who has not considered a party invitation without wondering who else will be there? But that behavior does not imply that all guest lists are wrong. It is a grand conceptual leap from observing a network effect to concluding the existence of a socially relevant externality. So long as we have only the vague impression that "bigger is better" (or "smaller is better"), we should be slow to conclude that there are externalities of the sort that suggest the need for social remedy.
* The authors thank Lee Craig, Neil Gandal, Craig Newmark, Pierre Regibeau, George Stigler, Richard Zerbe and workshop participants at North Carolina State University. Errors are our own. 1 But see Liebowitz and Margolis (1990, 1994b) for a critical examination of the empirical and theoretical support for the view that happenstance is a controlling factor in market outcomes.
2 The market failure, however, is somewhat unusual in that the choice of a network, or type of product, is the dimension in which the market fails. Discrete failure contrasts with conventional externalities, in which the problem is a matter of degree - too much pollution, too little gardening.
3 Having a larger market will increase the supply of auxiliary goods, but it will also increase the demand. Whether the prices will go down is another question entirely. These papers may have in mind that the auxiliary market is more competitive when it is bigger, which would tend to lower price. But it also seems to imply that production of the complementary products embody economies of scale, which need not lower price, even though costs would be lowered.
4 Pigou first made these statements in his text Wealth and Welfare, published in 1912. Allyn Young criticized these conclusions in a 1913 review of the book. With the publication of the revised text in 1920, renamed The Economics of Welfare, Pigou took back these statements in cases where the increase in cost was due to rising factor prices, but clung to the general arguments. He was then subject to further criticism, and in 1924 revised his doctrine once more, still clinging to a narrow version related to international trade, which was then shown to be deficient by Knight in 1924. According to Ellis and Fellner, Graham and Hicks were among the more notable economists to embrace Pigou's vision.
5 Not only do they receive merely cursory treatment in most textbooks, but the entry in Palgrave's Dictionary under "external economies" states: At an earlier stage, external economies in the meaning now given were called technological external economies,...... During the early part of the 20th century, external economies were defined so as to include beneficial price effects of producer activity.. termed pecuniary external economies..... When the debate had arrived at this point, pecuniary external economies could be dropped as a cause of market failure and hence, the concept lost its specific economic interest (Peter Bohm, p 262). In the discussion of 'externality' from the same source, J. J. Laffont states: A quite general consensus was that pecuniary externalities are irrelevant for welfare economics (p. 264). See also Farrell 1988, who presents pecuniary externalities, and a version of Pigou's reasoning, as a puzzle to modern economists.
6 There are important instances in which the prices in upstream industries do not reflect social marginal cost. First, it may be that the upstream industry consists of firms facing economies of scale. This situation is likely to lead to monopoly, or oligopoly at least, and the price charged will not reflect the marginal production costs. Even when there are constant returns to scale and competition, it is possible that the price will not reflect social marginal cost. Such an outcome would occur, for example, where industries used some common, but unpriced, input, or where firms simply got in each other's way. One example is the well known congestion externality.
7 Worchester deals with this case. Interestingly, this 1969 paper anticipates some of the recent interest. To exemplify pecuniary economy he offers "increased specialization via purchased inputs or subcontracting with expansion of industry output: clothing , aircraft." (p. 884)
8 This opens up a whole new problem that was of interest to Pigou and his compatriots: Is it possible to have a technological external effect? Knight and Sraffa are notable in their view that a firm could grow and emulate any economy that was available to the industry as a whole, thus negating the possibility of a technological external effect.
9 For example, Sloan tells us that the real price of refrigeration services dropped by 77% from 1931-1955 (p. 422) and that the Frigidaire .50-caliber aircraft machine gun dropped from $689.95 in 1941, to $169 by 1944 (p. 449). Rae tells us that the price of the Model T dropped from $950 in 1909 to $360 in 1916 (p. 61)
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