On the origins of the concept of natural monopoly: Economies of scale and competition∗

 ∗ A first draft of this paper was presented at the III annual meeting of Storep (Associazione Italiana per la Storia dell'Economia Politica) in Lecce, Italy in June 2006; at the 2006 annual meeting of the History of Economics Society in Grinnell, USA in June 2006; at the Department of Economics, University of Lecce, Italy in July 2006; and at the meeting of the Association for Public Economic Theory (PET06) in Hanoi, Vietnam in August 2006. An earlier version was published as Working Paper No. 92/45 by the Department of Economics, University of Salento, Lecce, Italy.

Abstract

The present article contributes to the history of the concept of natural monopoly, focusing on the reconstruction of its origins. The paper considers various facets of natural monopoly: the expression itself; the singling out of the concrete situations to which it is applied; the inquiry into economies of scale; the consideration of their incompatibility with perfect competition; the drawing of the diagram; and the need for government intervention. In this paper each of the above features is separately examined from a historical perspective. Priorities and influences are then traced, and in particular it is found that the pivotal figure in this historical reconstruction is that of Edgeworth. The relation of the concept of natural monopoly with that of competition is also highlighted, as well as its policy implications.

Keywords:

• Natural monopoly
• economies of scale
• competition
• cost curves
• network industries
• contestable markets
• barriers to entry
• market power

Acknowledgements

Helpful comments from Giampaolo Arachi, Michael Bradley, Gilbert Faccarello, Francesco Ferrante, Vitantonio Gioia, Marco E. L. Guidi, Russel Pittman, Marcella Scrimitore, David Teira, and two anonymous referees are gratefully acknowledged. The usual caveat applies.

Notes

 ∗ A first draft of this paper was presented at the III annual meeting of Storep (Associazione Italiana per la Storia dell'Economia Politica) in Lecce, Italy in June 2006; at the 2006 annual meeting of the History of Economics Society in Grinnell, USA in June 2006; at the Department of Economics, University of Lecce, Italy in July 2006; and at the meeting of the Association for Public Economic Theory (PET06) in Hanoi, Vietnam in August 2006. An earlier version was published as Working Paper No. 92/45 by the Department of Economics, University of Salento, Lecce, Italy.

 1 For microeconomics see Kreps (1990: 302), for industrial organization see Cabral (2000: 75), and for public economics see Stiglitz (2000: 291).

 2 ‘Some of the basic factors responsible for monopoly are inherent in the economies of large-scale production’ (Samuelson 1948: 40).

 3 See the interesting contribution on the history of the treatment of natural monopoly in introductory textbooks by Ulbrich (1991).

 4 A typical example of this kind of technology is given by ‘a single, high fixed cost, indivisible facility that can realize continuous decreasing unit costs, supplying the entire foreseeable market demand more efficiently than multiple firms' (OmniTRAX 2000: 2).

 5 The question of multiproduct natural monopoly was dealt with from 1977 by Baumol, Bayley, Panzar, and Willig.

 6 The idea of contestability was dealt with in a series of articles from 1980 by Baumol, Bayley, Panzar, and Willig. See for all Baumol et al. (1982).

 7 As Bailey writes: ‘sunk costs, not economies of scale, constitute the entry barrier that confers monopoly power’ (Baumol et al. 1982: xxii). There are actually two definitions of entry barriers in the literature, one proposed by Bain, the other by Stigler. As Schmalensee points out ‘An updated Bain definition would not rule out scale economies as an antitrust barrier to entry when sunk costs are important, while the Stigler definition would’ (Schmalensee 2004: 471).

 8 Austrians do not contrast monopolistic markets with competitive markets: for them, markets are competitive by definition. See among others Kirzner (1991: 146–7).

 9 In 1969 Posner wrote: ‘In the long run, there may be few natural monopolies, perhaps none’ (Posner [1969] 1999: 115). Thirty years later he observed: ‘Natural monopolies have crumbled’ (Posner 1999: viii).

10 For example, Amir (2003: 4) proposes: ‘to define natural (unregulated) monopoly as an industry where the socially optimal number of firms is one’.

11 See for example Grossman and Cole: ‘the production of a particular good … would be a natural monopoly only if as output were expanded to meet the entire market demand, one machine or one plant or, … one dispersed firm would have to be able to achieve reduced average long term costs. That is, costs would have to be lower per unit at higher and higher levels of output’ (2003: 19); but in their view, as transaction costs are important, average cost curves for any firm are likely to be U-shaped (Grossman and Cole 2003: 28).

12 For Shy, ‘the introduction of competition into these industries is welfare improving … on the consumer side, [without worsening] anything on the production side’ because ‘the introduction of access pricing … preserved the efficient large-scale use of existing infrastructure by letting all firms use the existing infrastructure while paying access charges to the firm that owns and maintains the infrastructure’ (Shy 2001: 8). It is also claimed that ‘competition, by forcing firms to operate at the cost frontier, may be less costly despite sacrificing some scale economies' (Kwoka 2006: 127).

13 See for example Schmalensee (1995).

14 ‘Market forces alone are unlikely to reduce market power in a number of cases (if sunk costs are important, if consumers have switching costs, if there are network externalities, and if a monopolist can engage in anti-competitive practices)’ (Motta 2004: 71).

15 Sharkey (1982: 15) also cites Lowry (1973).

16 All these works will be recalled later in the paper.

17 Note that Malthus uses the same phrase as Smith: ‘soil and situation’.

18 J. S. Mill writes: ‘All the natural monopolies (meaning thereby those which are created by circumstances, and not by law) which produce or aggravate the disparities in the remuneration of different kinds of labour, operate similarly between different employments of capital. If a business can only be advantageously carried on by a large capital, this in most countries limits so narrowly the class of persons who can enter into the employment, that they are enabled to keep their rate of profit above the general level. A trade may also, from the nature of the case, be confined to so few hands, that profits may admit of being kept up by a combination among the dealers. It is well known that even among so numerous a body as the London booksellers, this sort of combination exists; though individual interest is often too strong for its rules, nor, indeed, does the combination itself include the whole trade. I have already mentioned the case of the gas and water companies' (Mill 1848: II.15.9).

19 Sharkey writes: ‘John Stuart Mill … was the first economist of note to speak of natural monopoly’ (Sharkey 1982: 14). We think that he was absolutely the first, if we limit our concern to the meaning of monopoly due to technology. Also, Hazlett states that it was J. S. Mill ‘who introduced … the term natural monopoly’ (Hazlett 1985: 2; emphasis added); again, he should have added: in the meaning of monopoly due to technology.

20 According to Ekelund and Hébert: ‘Walras may have been the earliest writer to employ the actual term in its modern sense’ (Ekelund and Hébert 2003: 665; emphasis in original). But, as we have seen, we think it was Mill.

21 As in the case of Hadley (1886), who used ‘natural monopoly’ both for highways and for land ownership.

22 The title of the article is ‘Natural monopolies and the workingman’.

23 See for instance Hadley: ‘This monopoly, due to the advantages of large organizations of capital, is characteristic of the present day. … Natural monopolies, like that of land ownership, are still important; but they are not the matter of supreme importance in productive industry any more than in transportation’ (Hadley 1886: 40).

24 In these industries, high start-up costs and low marginal costs give rise to economies of scale; as much of the cost for the infrastructure is sunk, it is considered a barrier to entry also by the contestable market theory.

25 ‘Positive network effects […] have impacts that are very similar to conventional firm-level economies of scale. […] If larger networks have a forever widening advantage over smaller networks, we have entered the realm of natural monopoly […]. It is critical to note, however, that network effects are not in general sufficient for natural-monopoly-type results' (Liebowitz and Margolis 1998: 672; emphasis in original).

26 These three circumstances are also identified by Tynan (2007: 51–2).

27 Elsewhere, talking about wages, Smith claims that where there are few agents, competition cannot work: ‘The masters, being fewer in number, can combine much more easily’ (Smith 1776: I.8.12); the same reasoning could be applied also to the case of ‘large size firms', and we could push his argument to the statement that when firms are large, they are few, and when they are few, competition cannot work; but this would be forcing Smith's meaning. This is actually what Stigler claims: ‘Smith's … view was that nothing could be done about the instances of monopoly and collusion of small numbers of rivals' (Stigler 1982: 1).

28 De Viti de Marco's article on the telephone industry is examined in Mosca (2007).

29 While for the aspects examined in the previous sections there is only the secondary literature focused on the specific issue of natural monopoly, the topics dealt with from now on have been widely studied from many historical points of view; the literature cited here only shows a small part of this abundance of references.

30 This is true if the price of inputs does not change.

31 For the meaning of ‘increasing returns' in Marshall, see Loasby (1989: 62), while on the terminology concerning the laws of returns used in the cost controversy see Aslanbeigui (1996: 278–80).

32 We limit our inquiry here to scholars, and we do not mention all those who applied the decreasing average cost concept to their businesses – like, for example, Gottfried Härtel, a German music publisher who, around 1800, plotted the data on average costs for printing sheet music (see Scherer 2001).

33 Again, this is true if the price of inputs does not change.

34 We think Schumpeter exaggerates Serra's insight when he writes: ‘a general law of increasing returns in manufacturing industry, also in the form of a law of decreasing unit cost, had been stated explicitly and in full awareness of its importance by Antonio Serra’ (Schumpeter [1954] 1986: 258).

35 The translation from French is by Edwin Cannan (1892: 55).

36 The literature shows that if the economies of specialization generated by the division of labor are at firm level, they create a trade-off with the costs of coordination, communication, transaction, and so on, which are specifically associated with the division of labor; therefore they do not lead to monopoly.

37 Schumpeter writes: ‘Senior – or West and Senior – must be held responsible for the tradition, which took such time in dying, that agriculture was the domain of the latter [decreasing returns] and ‘industry’ the domain of the former [increasing returns]. This quite misleading arrangement was not set right until the next period’ (Schumpeter [1954] 1986: 585).

38 As for the shape of this function, he adds that: ‘it may happen however … that when the exploitation is carried beyond certain limits … [the function] … again begins to increase’ (Cournot [1838] 1960: 60), thus indicating the possibility that the marginal cost curve might be U-shaped.

39 On the mentioned railway engineers see also Locklin (1933).

40 See Staehle (1942).

41 In his words: ‘the average cost, y/x, of each ton actually transported is represented by the trigonometric tangent of the angle XOA=OAA₀ [the slope of the radius vector], and the marginal cost, dy/dx, is represented by the trigonometric tangent of the angle CAD=BAA₀ [the slope of the tangent] … since the angle OAA₀ > BAA₀, marginal cost is always lower than average costs' (Nördling [1886] 1960: 69).

42 The data used by Cheysson are an elaboration on Nördling's data, and concern an Austrian railway; therefore they are internal to the firm.

43 We know that, in considering the class of increasing returns industries, H. C. Adams is referring to firm-level economies of scale, because he writes: ‘The railroad business may be cited as a good illustration of this third class of industries'; and he adds: ‘The cost of plant is necessarily great in proportion to the business that may be immediately expected’ (Adams [1887] 1969: 114).

44 Pantaleoni seems to believe that the minimum efficient scale can only be a small proportion of the market demand.

45 The sources of economies that he mentions are: ‘the stage of civilisation attained, … every advance in the technical arts and in the organisation of labour, the facilities of communication’ (Pantaleoni [1889] 1957: 187).

46 Sylos Labini points out that: ‘Pantaleoni is perhaps the first of the few economists who have dedicated a systematic, albeit brief, reflection on the question of overhead costs' (Sylos Labini [1995] 1997: 197).

47 Internal economies are very much considered by Marshall, not only in his Economics of Industry but also in his Principles, despite the growing importance of the concept of external economies: he devotes chapters IX and XI of book IV of his Principles to them. See Stigler (1941: 76–83) and Marchionatti (1992: 559–61) among others.

48 In an interesting article by Keppler and Lallement (2006) the authors, while giving Barone a well-deserved place in the history of the origins of the U-shaped average cost curve, write that this history ‘would have been quickly over, if Barone had not decided to display total cost and total revenue on the vertical axis rather than per-unit cost and price’ (Keppler and Lallement 2006: 748). It is true, Barone did not draw a diagram with the average cost on the vertical axis, but he did actually say: ‘la curva della fig. 12a, se si riducesse ad un diagramma di cui le ordinate fossero i costi di produzione unitari, sarebbe decrescente fino ad un certo punto e poi crescente’. This quotation is not only a verbal illustration of the U-shaped average cost function, it is the very description of a graph. In our opinion, this quotation should have a crucial role in Keppler and Lallement's historical reconstruction.

49 Moreover, his 1913 article has probably the first diagram of U-shaped average and marginal cost curves, and the demonstration that the marginal costs curve intersects a U-shaped average costs curve at its minimum (Edgeworth 1913: 214, fig. 3). This is confirmed by Keppler and Lallement (2006), whose article is entirely devoted to the history of this concept. See also Harrod (1931), Robbins (1934), and the literature cited in Aslanbeigui and Naples (1997).

50 ‘Adam Smith did not appear himself to be in the least troubled by the thought that competition and increasing returns might not be able to coexist’ (Richardson 1975: 354); see also Stigler (1951) and Groenewegen (1999). In the light of the successive studies on economies of specialization, we can say that he was right.

51 According to Tynan ‘Senior recognized the existence of partial barriers to entry due to fixed costs, but argued that […] as costs increased with network expansion, partial barriers were overcome and new firms entered to compete with incumbents' (Tynan 2007: 49).

52 This is perhaps one of the reasons why Stigler writes that Senior ‘was wholly promiscuous in his use of the concept of monopoly’ (Stigler 1957: 3).

53 Referring to the case of the London water supply, Tynan confirms that for J.S. Mill ‘competition was largely illusory and that ultimately it was destructive due to excessive entry and over-investment’ (Tynan 2007: 50).

54 We do not understand how DiLorenzo (1996) can include Ely among those economists who saw economies of scale ‘as a competitive virtue’ (1996: 44).

55 We just mention Newman (1960), Whitaker (1990, 2003), Hart (1991, 1992, 1996, 2003) Marchionatti (1992), Prendergast (1992), Loasby (1996), Groenewegen (1999), Quéré (2003), and Niman (2004).

56 While it was Marshall himself who defined the choice between increasing returns and competition a ‘dilemma’, it was named ‘Cournot's dilemma’ after Newman (1960). In the secondary literature the expression ‘reconciliation problem’ is also widely used to indicate the problem of reconciling increasing returns and competition; it probably comes from Stigler (1951: 186).

57 We also know that Marshall changed his views over the years on this question (Whitaker 2003).

58 The same concept is found in his Principi di economia finanziaria (Barone 1911–12: 120–1). Barone's view of market power is examined in Mosca (2005).

59 Before his articles on railway rates (1911 to 1913), Edgeworth had already briefly stated the incompatibility: ‘The law of diminishing costs, as Cournot argues, is only intelligible on the supposition of monopoly’ (Edgeworth 1897: 69).

60 The literature devoted to Sraffa's criticisms of Marshall's theory is also massive; see the up-to-date references in Rosselli (2005).

61 In his words: ‘it is clear that, if a firm can decrease its costs without limit by increasing production, it would continue to reduce the selling price until it had acquired the whole market. We would then have abandoned the hypothesis of competition’ (Sraffa [1925] 1998: 344–5).

62 He writes: ‘reductions in cost connected with an increase in a firm's scale of production arising from internal economies or from the possibility of distributing the overhead charges over a larger number of product units, [are] incompatible with competitive conditions' (Sraffa 1926: 540).

63 Roncaglia points out that in Sraffa's later work ‘no general static functional relationship can be established connecting unit cost … to output levels' (Roncaglia 1991: 393).

64 In particular we recall Knight (1921).

65 See Marchionatti (2003: 60).

66 Correctly, Keppler and Lallement interpret this curve as ‘the cost (supply) curve of an individual monopolist, rather than as the cost curve of a firm under competition’ (2006: 753); in fact, Edgeworth's article is primarily devoted to the railway industry, and his main focus is on monopoly rather then on competition. Consider this passage from another section of the same article: ‘I need not enter further into particulars which are not characteristic of monopolized industries like railways' (Edgeworth 1911a: 359).

67 There are many other occasions, like the monthly meetings of the Société d'économie politique between 1853 and 1864, in which Dupuit expressed his opinion in favor of public management of natural monopolies. See Mosca (1998: 265). Ekelund and Hébert (1999) give an opposite interpretation of Dupuit's opinion on the role of the government in this kind of market failure.

68 For the proto-history of franchise bidding see Ekelund and Hébert (1981).

69 Crain and Ekelund (1976) illustrate which kind of government regulation Chadwick thought to be necessary; they also show that his principle was not intended only for natural monopolies, but that it holds for every kind of monopoly.

70 For a different analysis of Dupuit and Walras on railroads see Ekelund and Hébert (2003).

71 See the criticisms of Ely's belief in government superiority for the regulation of natural monopolies by O'Driscoll, who thinks that: ‘he was in error in almost all his contentions' (O'Driscoll 1982: 197–9).

72 On Adams' opinion of regulation, see Sharkey (1982: 15–16).

73 This is also the opinion of O' Driscoll (1982); he thinks that, for Smith, ‘No form of monopoly, save perhaps that of specialized land, is a natural market phenomenon’ (O'Driscoll 1982: 195).

74 Sharkey writes that Adams ‘is one of the first to suggest direct regulation of natural monopoly’ (1982: 15), but actually we have seen that Dupuit and Walras did this before him.

75 In addition to the references cited in Blaug (1997), see DiLorenzo and High (1988), Groenewegen (1999), Machovec (1995), and Morgan (1993).

76 For a history of the concept of competition up until recent times see Backhouse (1990).

77 Pantaleoni's view of market power is examined in Mosca (2007).

78 The ‘fundamental importance of natural monopoly is a legalistic entity that facilitates the efforts of political coalitions to restrict output in the manner predicted in the capture view of regulation’ (Hazlett 1985: 2).

79 An interesting point by DiLorenzo and High is that: ‘Perhaps the clearest link between economists' changing views of competition and their support of antitrust in the post 1920s era is found in the structure-conduct-performance paradigm of industrial organization theory’ (1988: 431).

80 For example, Marchionatti states that both Sraffa and Knight ‘take the rigorous notion of equilibrium from Pareto and Enrico Barone’ (2003: 66). For a recent acknowledgment of the importance of the Italian contribution to microeconomics, see Keppler and Lallement (2006).