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Externalities in Economic Thought

Formalizing “external economies”: Viner, Chipman, and Krugman

Formaliser les externalités en économie : Viner, Chipman et Krugman
Christian Gehrke
p. 331-362


L’article retrace l’évolution de l’analyse formelle des « externalités », depuis la contribution séminale de Jacob Viner jusqu’à la modélisation par Paul Krugman des économies d’échelle en économie du développement, en économie géographique et en commerce international, en passant par l’introduction du concept d’« économie d’échelle paramétrique » par John Chipman. Le principal objectif est de clarifier les relations entre ces différentes conceptualisations. Dans un premier temps, il est démontré que la formalisation du concept marshallien par Viner est à l’origine insérée dans un « cadre ricardo-marshallien » avec des offres de facteur parfaitement élastiques : Viner dérive une courbe d’offre de long terme décroissante en invoquant en premier lieu des économies d’échelle nettes pécuniaires, rejetant le concept d’économie d’échelle technologique comme vide. Le concept d’« économie d’échelle paramétrique » de Chipman se concentre quant à lui sur les externalités technologiques. De plus, dans le but de réhabiliter l’analyse marshallienne, Chipman construit un modèle spécifique d’équilibre général — avec un seul facteur primaire dont l’offre est inélastique et sans liens entre les différentes industries — dans lequel le concept d’économie d’échelle pécuniaire de Viner ne peut exister. Enfin, il est montré que la conceptualisation de Krugman est – d’un point de vue analytique – très proche de la représentation graphique de Viner. Dans les modèles de Krugman, les économies d’échelle pécuniaires proviennent soit de l’introduction de liens entre les différentes industries, soit de la mobilité du travail (ou, plus généralement, de la mobilité internationale ou interrégionale des facteurs), hypothèse introduite dans un modèle d’équilibre général simplifié en concurrence monopolistique avec rendements d’échelle intra-firme croissants.

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Texte intégral

The fact that the “external economies” peculiar to an industry, which make possible the desired conciliation between scientific abstraction and reality, are themselves a purely hypothetical and unreal construction, is something that is often ignored. (Sraffa 1998 [1925], 347)

1. Introduction

1The concept of “external economies”, as is well-known, was introduced by Alfred Marshall

in order to explain, without resort to dynamics, the phenomenon of a negatively sloped (“forward falling”) long-run industry supply curve in terms consistent with a horizontal or rising marginal cost curve (MC) in the “representative” firm. The device permits—in logic, if not in fact—long-run competitive equilibrium of many firms within an industry, each producing at its profit-maximum price-equal-to-a-rising-MC position, without foreclosing the possibility of a falling supply price with rising industry output. (Bator, 1958, 356)

  • 1 See, in particular, Marshall (1920, Bk. IV, Ch. XIII, Bk. V, Ch. XII, and Appendix H).

2Marshall’s own treatment was conspicuously informal,1 but already during his own lifetime several attempts have been made, most notably by Cunynghame, Edgeworth, Barone, and Pigou, to provide a formal treatment of his argument. This paper reviews later contributions by three different authors to the formalization of “external economies”. It opens with a critical discussion of Jacob Viner’s famous contribution (1953 [1931]) and then turns to John Chipman’s classic paper on “parametric external economies” (1970). These authors were chosen, because each of them focuses on the formal representation of one type of external economies only: Viner’s graphical exposition put the emphasis mainly on pecuniary external economies, whereas Chipman’s formalization dealt exclusively with technological external economies. The interest in Paul Krugman’s conceptualization of external economies derives from the fact that his contributions have been instrumental in rehabilitating the concept in the 1980s and 1990s, at least in the fields of international trade and economic geography.

  • 2 The paper thus takes up a theme that was recently also studied, from a somewhat different angle, (...)

3The main purpose of this paper is to clarify the existing connections, similarities, differences, and incompatibilities between the different conceptualizations proposed by the three authors.2 The essay is in four parts. Section 2 briefly recalls Jacob Viner’s graphical exposition and discusses the novel elements introduced by him into the formal treatment of external economies. John Chipman’s critique of Viner’s conceptualization and the advantages and drawbacks of his proposed conceptualization in terms of “parametric external economies” are discussed in Section 3. Section 4 opens with a summary account of the different approaches to the modelling of external economies that were adopted by Paul Krugman in his various contributions to the theory of international trade, development, and economic geography. It is shown that Krugman’s resurgence of external economies models was unrelated to Chipman’s path-breaking “modern” formalization, which focuses attention primarily on the representation of technological external economies. Krugman in fact particularly emphasized the importance of pecuniary external economies, as did Viner in his original article, and his contributions can indeed be said to provide a modern re-formulation of Viner’s treatment, transferring it from a partial equilibrium context to a (highly aggregated) general equilibrium framework with monopolistic competition. Section 5 offers concluding remarks.

2. Viner’s treatment of external economies

2.1 Some preliminary remarks

  • 3 For summary accounts of these contributions, see Chipman (1965, 736-749) and Opocher and Steedman (...)

4A detailed account of Marshall’s own exposition of the construction of a forward-falling long-run industry supply curve, and of other contributions that have been made prior to Viner’s classic article (1953 [1931]), is beyond the scope of this paper.3 It is necessary, however, to draw attention to two features of Marshall’s approach which must be clearly recognized for a proper appreciation of Viner’s contribution. The first of these two features was recently expounded with great clarity by Opocher and Steedman (2008a), who demonstrated that Marshall’s ‘supply equation’ (1920 [1890], 852) can be conveniently written as

5p = a(Qw(Q)

6where p denotes the price of a commodity whose aggregate output Q is assumed to be produced by means of a set of factors whose amounts per unit of product at the bottom of the firm’s average cost curve are the terms of vector a, and whose long-run supply prices are the terms of vector w. Both w and a are vector functions of Q, so that the sign of the derivative, dp/dQ, depends on awQ+ aQw (where wQ and aQ are vectors of derivatives). It is the aggregate effect of the involved changes in both input prices and input quantities which Marshall’s industry supply curve was meant to depict:

The supply curve for a certain industry, then, was simply designed to illustrate the outcome of one possible set of market circumstances of supply. Many different factors were at work simultaneously: as the demand for a commodity rises permanently and aggregate production increases, some raw materials are supplied to the industry at an increasing price, some machinery is supplied at a falling price, some kinds of labour are made available at a rising wage, some technological and organisational economies dependent upon the industry’s scale are introduced. The slope of the Marshallian long-period supply curve … reflects all these factors simultaneously. (Opocher and Steedman, 2008a, 252)

  • 4 See Freni (2001, 365), who noted that this was ‘the Marshallian framework commonly employed befor (...)

7The second important feature to which attention must be drawn concerns the specific factor supply framework in which Marshall was arguing, and which for obvious reasons has been called by some commentators a “Ricardo-Marshall framework”.4 Its peculiarities have been described most succinctly by Joan Robinson, who also gave some hints regarding its probable analytical origins:

The classical analysis, which gave rise to the Ricardian theory of rent, dealt with the question of what happens when the supplies of labour and capital increase, and land remains fixed. This clearly has nothing to do with rising supply price for a commodity. It belongs to the department of output as a whole. … The problem of the long-period supply curve of a particular commodity belongs to the department of the theory of value, which treats of relative prices of commodities. Marshall’s analysis appears to be a cross between the theory of value and the theory of output as a whole. For he seems most often to be discussing the problem of the change in the supply of a particular commodity which occurs in response to a net increase in demand. The demand for one commodity increases, but the demand for the rest does not decline. The additional factors, apart from land, employed in increasing the supply of the commodity are called into existence by the increase in demand. (Robinson, 1941, 233-234; emphases added)

8As we shall see below, Viner in his original article of 1931 adhered to this peculiarity of Marshall’s approach, but subsequently abandoned it in favour of a “fixed factor supply” framework, as it is used in HOS trade theory.

2.2 Viner’s representation of “net external economies of large production”

9In addition to Marshall’s distinction between economies (or diseconomies) which are either internal or external to the firm, Jacob Viner explicitly introduced a further distinction, for both the internal and the external type, namely the distinction between technological and pecuniary economies (or diseconomies)—a distinction, which in Marshall had been only implicit:

Economies may be either technological or pecuniary, that is, they may consist either in reductions of the technological coefficients of production or in reductions in the prices paid for the factors as a result of increases in the amounts thereof purchased. (Viner, 1953 [1931], 213)

  • 5 See Opocher and Steedman (2008a, 260).
  • 6 It is noteworthy that Viner, in a different context, also dismissed Frank Graham’s argument for p (...)

10Accordingly, Viner’s four classes of “technological” and “pecuniary” external economies (diseconomies) can be associated with the negative (positive) terms of aQ and wQ, respectively, and the resulting net aggregate change, awQ + aQw, if negative (positive), was called by Viner ‘net external economies (diseconomies) of large production’.5 With regard to the two sources of external economies, Viner concentrated attention primarily on pecuniary external economies and rather de-emphasized the technological ones. This is because he believed that ‘illustrations of technological external economies are difficult to find’, although he noted that ‘a better organization of the labor and raw materials markets with respect to the availability of laborers and materials when needed by any particular plant, and improvement in productive technique resulting from “cross-fertilization,” or the exchange of ideas among the different producers, appear to be possible sources of technological external economies resulting from the increase in the size of the industry as a whole’ (1953 [1931], 217-218; emphasis added). These are, of course, precisely the illustrations of “external economies” proffered by Marshall (1920 [1890], 267-277) in his discussion of industry localization, but in the above passage Viner nevertheless almost dismissed the notion of “technological external economies” as empirically vacuous.6 He rather focused attention on pecuniary external economies, which he considered to be a much more plausible source of “net external economies”, and which he described as

  • 7 The example suggested by Viner to illustrate pecuniary external economies which are not generated (...)

reductions in the prices of services and materials resulting from the increase in the amounts of such services and materials purchased by the industry as a whole. Pecuniary external economies to industry A are likely to be internal or external economies to some other industry B. If industry A purchases materials in greater quantity, their price may fall because industry B can then produce them at lower unit cost. (Viner, 1953 [1931], 218)7

11It is important to note that Viner, just like Marshall, also considered all industries to be subject to influences making for increasing and decreasing costs simultaneously, so that their classification is not to be derived from some technical characteristics alone, but rather from the net effect of the tendencies prevailing in each. Accordingly, Viner’s well-known graphical exposition, reproduced in figure 1 below, was meant to illustrate ‘the case of net external economies of large production, irrespective of whether these economies are technological, or pecuniary, or both’ (1953 [1931], 218; emphasis added).

Figure 1: Net External Economies of Large Production

Image 10000201000001CF0000013600B476F5.png

Source: Viner (1953 [1931], 218)

  • 8 As Chipman (1965, 738-739) pointed out, the idea of firm’s average and marginal cost curves shift (...)

12Before we proceed, two further points must be noted. First, Viner apparently considered it necessary, in order to clearly separate external from internal economies, to keep the size of each firm’s output constant when the output of the industry expands,8 although his wording suggests that he was fully aware of the implausibility of this assumption:

If an industry which enjoys net external economies of large production increases its output—presumably through increase in number of plants—the average costs of the member concerns of that industry will fall even though each concern maintains a constant scale of plant and a constant output. (1953 [1931], 217; emphasis added)

  • 9 Interestingly, Sraffa did not find it necessary to introduce Viner’s restrictive assumption: In h (...)
  • 10 In the introduction of his essay, Viner pointed out that the differences between the Austrian sch (...)

13As we shall see below, one of the advantages of Chipman’s formalization is that this restrictive assumption can be dispensed with.9 Secondly, it must be noted that in Viner’s essay of 1931 the underlying assumptions regarding factor supplies are not stated clearly.10 In the section devoted to “‘Ricardian’ increasing costs” (1953 [1931], 206-210), Viner’s argument is explicitly based on the assumption that all factor prices except for the land rent rate remain unaltered, which clearly presupposes a “Ricardo-Marshall framework”. However, in the section devoted to “Net external diseconomies of large production” (1953 [1931], 220-222), Viner then began to discuss the implications of introducing assumptions on factor supplies which differ from Marshall’s. Characteristically, he opened this section with the following statement:

Although it has not ordinarily been given consideration, the case of net external diseconomies of large production is of indisputable practical importance. Pecuniary diseconomies of this kind will always tend to result from the expansion of output of an industry because the increased purchases of primary factors and materials which this entails must tend to raise their unit prices. In order that pecuniary diseconomies shall not result from the expansion of an industry’s output, it is necessary, for both primary factors and materials, that the increase in demand by this industry shall be accompanied by a corresponding and simultaneous decrease in demand by other industries or increase in the supply of the factors and materials themselves, or, failing this, that the materials, because of net external or internal economies in the industries producing them, should have negatively inclined supply curves. (Viner, 1953 [1931], 220-221; emphasis added)

2.3 Abandoning the “Ricardo-Marshall framework”: Viner’s “Supplementary note”

14In a Supplementary note (1953 [1950]) first published in 1950, Viner “corrected” his previous exposition of the construction of long-period industry supply curves, leaving a much more limited scope for the prevalence of net external economies, and thus for the possibility of a forward-falling industry supply curve, than he had done in his previous analysis:

I feel it incumbent upon me …, so as to avoid propagating serious error, to carry the analysis of costs a stage further in one respect by departing here from the traditional Marshallian pattern of assumptions to which the article adheres. The partial-equilibrium nature of the Marshallian assumptions leaves a wider range of possibilities to the long-run tendency of costs for an expanding industry than is consistent with general-equilibrium analysis. (1953 [1950], 227; emphasis added)

  • 11 Viner also discussed cases in which factors are in imperfectly elastic supply; see Viner (1953 [1 (...)

15Contrary to Viner’s assertion, however, the main difference between his earlier and his new analysis is not that the former “adheres”, and the latter does not adhere, to “the partial-equilibrium nature” of Marshall’s assumptions—it rather lies in the introduction of different assumptions with regard to factor supplies. Viner now assumed explicitly that all factors are in fixed supply, so that—given their full utilization—an expanding industry can use larger amounts of factors only if the latter are released by other industries, whose output must accordingly be contracting. But since the various factors are in general not released in the exact proportions in which they are needed by the expanding industry, there will have to be ‘a change in relative input prices whose necessary effect will be to raise the supply price of the commodity in question relative to “other” commodities (as well as to economise the relatively scarce factor)’ (Opocher and Steedman 2008a, 261). In order to demonstrate this effect, Viner constructed a simple numerical example,11 from which he concluded that

  • 12 Viner noted, however, that the “law” will operate unambiguously ‘only after the expanding industr (...)

all industries must tend to be subject to “external net pecuniary diseconomies of large production” when they expand relative to the economy of which they are a part. (1953 [1950], 228; emphasis added)12

  • 13 See Freni (2001, 364-367).
  • 14 The former distinction concerns differences in the assumptions that are made about the elasticity (...)

16Before we proceed, it needs to be stressed that Marshallian supply functions can be consistently constructed on the basis of different sets of assumptions with regard to factor supplies. While it is true that in recent decades it has become much more common in many fields of economic theory to make use of models in which all “factors” are in perfectly inelastic supply (like, e.g., in the HOS model of international trade theory), or in which all or some factors are in imperfectly elastic supply, it is nevertheless perfectly possible—and legitimate—to construct partial equilibrium models in which the amounts of all “factors”, apart from land, change with production, as in the “Ricardo-Marshall framework”.13 Moreover, it should be kept in mind that abandoning the “Ricardo-Marshall framework” in favour of an “HOS framework” is not the same thing as moving from a partial to a general equilibrium framework.14

2.4 Some post-Viner developments

  • 15 See Mishan (1960, 6).
  • 16 On the development of the notion of “externalities”, see Lagueux (1998).

17Paradoxically, it was precisely the notion of technological external economies, for which Viner claimed it was difficult to find any plausible empirical illustrations, which came to occupy a dominant position in the modelling of external economies in the post-war period, while pecuniary external economies were increasingly pushed to the background—so much so that some authors even declared Viner’s introduction of the two types of externalities to have been ‘superfluous and possibly confusing’.15 How is this shifting assessment of the relevance of the two types of externalities to be explained? With hindsight it seems to have resulted from a combination of several factors, which can be briefly summarized as follows.16

  • 17 Note that Ellis and Fellner, unlike later authors, did not abandon the notion of “pecuniary exter (...)
  • 18 As we shall see in Section 4 below, the argument that pecuniary external economies cannot arise f (...)

18First, Ellis and Fellner in their classic article (1953 [1943]) abandoned the concept of pecuniary external economies, while preserving the concept of pecuniary external diseconomies,17 which they re-labelled as “rising transfer costs”. However, unlike Robinson (1953 [1941]) and Viner in his “Supplementary Note” (1953 [1950]), Ellis and Fellner did not argue that rising supply prices emerge because net pecuniary diseconomies must always predominate. Their argument for abandoning net external pecuniary economies was rather that these could not possibly arise in fully competitive markets. They could arise only, they maintained, if either the firms in the industry under consideration have some market power vis-à-vis their suppliers or else from firm-internal economies in the supplying industries. However, ‘if an “external economy” is an internal economy to another industry, the outcome is either monopoly in the second industry, or else the complete exploitation of the internal and hence the disappearance of the external economies’ (1953 [1943], 254). According to Ellis and Fellner, this is because a monopolist will always ‘raise his price if demand increases, in which case such economies as are internal economies in the “second” industry will not lead to the realization of economies in the “first” industry’ (ibid.).18

  • 19 Both traditions are still present in reputable contemporary microeconomics textbooks.

19Secondly, in the course of the 1930s and 1940s a different approach in partial equilibrium analysis has gradually emerged. As Opocher and Steedman (2008a) have recently clarified, there are two different traditions in the construction of the long-run supply curve of an industry: A “Marshallian” tradition, to which the contributions of Marshall, Barone, Pigou, and Viner belong, and a “Walrasian” tradition, which started with the contributions by Kaldor (1934), Hicks (1938, 1946), Allen (1938), and Samuelson (1947). In contributions which belong to the first line of development other prices and quantities are allowed to change with a parametric variation of the price in the industry under consideration, and the equilibrium of the firm is determined on the assumption that the industry as a whole is in equilibrium. Partial equilibrium analyses in the “Kaldor-Hicks-Allen-Samuelson” tradition, on the other hand, derive the long-run industry supply curve by aggregating the supply curves of the individual firms, holding all other prices constant by assumption. In partial analyses in the “Kaldor-Hicks-Allen-Samuelson” tradition there is then simply no room for the concept of pecuniary external economies.19

  • 20 According to Coase (1988, 23, note 35), the term “externality” was first used by Paul A. Samuelso (...)
  • 21 On definitions of “externalities”, and on the existing confusions in the literature concerning “e (...)

20Third, the term “externalities” (which neither Marshall nor Pigou had used) was introduced in the 1950s, and then extended by Meade (1952), Scitovsky (1954), and others to cover a much wider assortment of diverse phenomena, such as pollution, noise, or congestion.20 “External economies” were accordingly seen as a particular case of the more general category of “external effects” associated with economic activities: they were identified with the case of positive production externalities. In addition, “externalities” were increasingly discussed (and defined) from the point of view of general equilibrium theory rather than from the point of view of a partial framework of the analysis.21 The associated shift from Pigouvian to Paretian welfare analysis then led to the distinction between “Pareto-relevant externalities” or “technological externalities” (also often labelled “true externalities”), on the one hand, and “non-Pareto relevant” or “pecuniary externalities” (sometimes also labelled “market-mediated externalities”), on the other hand.

  • 22 For the profession at large this shift must probably be dated much later, considering that an aut (...)
  • 23 Compare, for instance, the following statement by Mishan: ‘The term external pecuniary diseconomi (...)

21Fourth, and of course not unrelated to the previous two points, there was also a gradual shift towards general equilibrium theorizing in the 1950s and 1960s.22 This shift, which is visible even in contributions which argue on the basis of a partial analysis framework, had two related consequences. On the one hand, increasing returns that are caused by (internal or external) technological economies were generally regarded to be incompatible with the existence of a competitive general equilibrium, and hence often excluded by assumption. On the other hand, the concept of pecuniary external economies was increasingly considered to be a nonsensical notion, the use of which should better be avoided altogether.23

22To sum up, a consensus seems to have emerged in the mid- or late 1960s with regard to the formalization of “external economies” which can be summarized thus: In competitive general equilibrium pecuniary externalities are not relevant, since they are not associated with inefficiencies. The problem of monopolization, expelled through the front door by excluding “internal economies” in the industry under consideration, necessarily re-enters through the back-door, because falling input prices in an industry cannot but be caused by firm-internal economies in some other industry: all so-called pecuniary external economies must be due to technological economies somewhere in the system. Therefore, the modern formulation of external economies must be in terms of “direct interaction”, where an external variable (such as the output of the industry or the output(s) of some other firm(s) in the same or in a different industry) enters into a firm’s production function (or into its cost function). This means that external economies are formally treated in the same way as externalities. Accordingly, the author of a 1958 survey article on “Market failure” concluded that ‘in its modern version, the notion of external economies proper—that is: Viner’s technological variety—belongs to a more general doctrine of “direct interaction”’ (Bator 1958, 356-358).

3. John Chipman’s contribution: the concept of “parametric external economies”

23John Chipman’s novel conceptualization of external economies in his 1970 paper should be viewed against the historical background sketched above. Chipman had indeed first suggested a parametric treatment of external economies already in 1965, in part II of his famous survey on the theory of international trade, where he had also related his proposed conceptualization to Viner’s graphical exposition:

Viner … dealt with external economies (1931, Chart V, p. 39) by assuming each firm’s average and marginal cost curves to fall vertically, so that industry output can increase only ‘as the result of increase in the number of producers’ (p. 40). … This is an arbitrary and quite unnecessary assumption. All that needs to be assumed is that the individual entrepreneur does not take account of the fact that increases in his output lead to a fall in his cost curves, in precisely the same way that he does not take account of the fact that increases in his output lead to a fall … in his horizontal demand curve. (Chipman, 1965, 743)

24Note that in Chipman’s formulation, as opposed to Viner’s, the economies are in fact generated by the expansion of output within firms; they are “external to the firm” only ‘in the minds of the individual entrepreneurs’ (Chipman, 1970, 350). Is Chipman’s conception less arbitrary than Viner’s? Its plausibility mainly hinges on the plausibility of the idea that the economies which accrue at the industry level emerge when several firms are expanding their outputs simultaneously, and that the contribution of each individual firm to the generation of these economies is so small as to be almost negligible. In his 1965 survey article Chipman had asserted, without formally proving it, that the proposed parametric treatment of external economies would not lead to any discrepancy between private and social cost (1965: 746). As he later explained, ‘both Arrow and Hahn pointed out to me my error … in saying that there would be no distortion of Pareto optimality resulting from external economies or diseconomies of scale. … These criticisms led to my subsequent article (Chipman, 1970) on parametric economies of scale’ (Chipman, 2008a, x).

3.1 The parametric treatment of external economies

25Chipman’s formulation (1970, 347-58) can be briefly summarized as follows. The production function of a firm in the ith industry is given by:

Image 10000201000002A800000036E9736072.png

26where yiv is the amount of ith commodity produced by the vth firm in industry i. The term ziv denotes the amount of labour employed by this firm, and Ni is the number of firms in the ith industry. The aggregate amounts of inputs and outputs in the industry are then given by

Image 10000201000001320000003256C2432D.png

27and the subjective production function of industry i is:

Image 10000000000000DA00000028BC881B6A.jpg

  • 24 The scale effect can also be associated with the total output of the industry under consideration b (...)

28Chipman called this function a “subjective production function”, because Ki is treated as a parameter, although it is in fact a variable, which depends on the total input zi in industry i24:

Image 10000201000002880000003FDBBD889F.png

29The objective production function of industry i is obtained by inserting eq. (4) into eq. (1):

Image 10000000000000D900000027EF9ECC0A.jpg

30With ρi > 1, the objective production function exhibits increasing returns to scale and gives rise to a negatively inclined long-run industry supply curve. In order to explain the behaviour of the firms operating in each of the industries, and in particular to derive their factor demands, the subjective production function (with constant returns to scale) is used. The objective production function is used in welfare analysis. Both are relevant to the analysis of the determinateness of competitive equilibrium. Chipman (1970, 351) could demonstrate that a competitive equilibrium exists but that it is not, in general, Pareto optimal.

31A particular characteristic of Chipman’s 1970 contribution is the utilization of a very specific general equilibrium model, which allows for a partial analysis of individual industries independently of the rest of the economy. This is achieved by excluding all inter-industry linkages by means of appropriate assumptions. More specifically, Chipman simplified the analysis by assuming that there is only a single factor of production (“labor”) and no intermediate inputs, and that there are uniform proportions in consumption. In addition, he also assumed given factor supplies, that is, he assumed that ‘labor is in perfectly inelastic supply’ (1970, 372). Given these assumptions,

the system is completely decomposable, and solvable industry by industry. Thus the classical Marshallian and Pigovian diagrams may be used to depict the solution for each [industry] i. (Chipman, 1970, 361-362)

  • 25 See also Freni (2001, 371).

32It should be noted that Chipman’s specific general equilibrium model meets precisely those conditions which Sraffa (1998 [1925], 362-3) had identified as necessary in order to make external economies compatible with a partial framework of the analysis (that is, which are necessary to render them “internal to the industry”).25

  • 26 In his 1965 survey article Chipman had dismissed Viner’s concept of “pecuniary external economies (...)

33Chipman (1970, 350) explicitly considered his concept of “parametric external economies” as a more rigorous formalization of Viner’s notion of technological external economies.26 He did not seem to recognize, however, that in the specific analytical framework adopted by him technological economies are indeed the only kinds of external economies that can be accommodated. Chipman wrote:

In the formulation of this paper, all parametric external economies of scale are “technological” rather than “pecuniary” in Viner’s sense … though I do not regard the distinction as at all crucial; a more general formulation could take care of both kinds, and indeed a mere redefinition of factor quantities in terms of “efficiency units” would transform technological economies into pecuniary ones. (197, 350)

34What Chipman refers to is apparently the possibility, first suggested by Robinson (1933, 332), of treating non-homogeneous factors as if they were homogeneous by providing a “corrected natural unit” for their measurement. But such a redefinition of factor quantities in terms of “efficiency units” is indeed ‘a mere aberration’, as Robinson (1953 [1941], 236n) herself later recognized—and not a method for introducing pecuniary external economies in Viner’s sense. All that could be accomplished by means of this device is to give technological economies which arise from qualitative input changes the appearance of pecuniary ones, by representing them as cost reductions. But the phenomenon designated by Viner as “pecuniary external economies” cannot be depicted by means of this device—in fact, within the framework adopted by Chipman, it cannot possibly occur: When there are no intermediate inputs and the single original factor is in fixed supply, an industry cannot possibly derive any cost reductions from falling input prices triggered by its own expansion.

3.2 Has Chipman succeeded in providing a rehabilitation of Marshall’s partial equilibrium analysis with external economies?

35Chipman’s specific modelling framework, which allowed him to conduct a partial analysis within a general equilibrium modelling set-up, was meant to be a device for pursuing two different aims simultaneously: On the one hand, Chipman wanted to ‘formulate a general equilibrium model of perfect competition, in which firms may operate under increasing, constant, or decreasing returns to scale’ (1970, 348). On the other hand, it was explicitly designed ‘to make possible a direct comparison with Marshall’s original treatment … and a rehabilitation of the doctrine evolved by Marshall, Pigou, and R. F. Kahn, to the effect that industries with greater than average returns to scale should be subsidized and those with less than average returns should be taxed’ (1970, 348, 351). However, Chipman’s specific modelling framework also prevented him from distinguishing clearly between two different problems which had beset Marshall’s analysis: First, the problem of the compatibility of increasing returns with a competitive equilibrium, and, secondly, that of the compatibility of external economies with a partial equilibrium framework of the analysis.

36In his 1965 survey article, Chipman asserted that ‘the chief casualty of Sraffa’s 1926 paper was the concept of external economies’ (1965, 742). He specified more precisely what he meant by this in his 1970 paper, which opened with the statement:

Are increasing returns compatible with perfectly competitive equilibrium? This was once a lively subject of debate. The debate appears to have petered out in the 1930’s, with nobody the apparent winner. … Most likely, the reason is that the weight of opinion was on the side of the skeptics [sic], led by Piero Sraffa, and consequently the Marshallian theory gave way to the new theories of imperfect and monopolistic competition. Since these new theories could handle internal as well as external economies of scale, the old issue no longer seemed relevant. (Chipman, 1970, 347-348)

37But as Chipman’s aim was precisely to demonstrate that increasing returns are indeed compatible with competitive equilibrium—provided they are formalized as parametric external economies—he apparently deemed it necessary to refute Sraffa’s objections to Marshall’s analysis. He wrote:

Referring to the concept as used by Marshall (1920), he [i.e. Sraffa] concluded (1926, p. 540) that “in so far as external economies of the kind in question exist, they are not likely to be called forth by small increases in production.” But it is precisely the smallness of their relative impact on any one firm which makes such economies external; external economies of the Marshallian kind may be defined as economies that are so widely diffused and so imperceptible in relation to an individual firm’s output that they are ignored, that is, treated as negligible in the mind of the entrepreneur. This discontinuity—the treatment of something small as if it were equal to zero—is essential to the whole argument. (Chipman, 1965, 742)

38Chipman’s statement clearly contains a misconception with regard to Sraffa’s objection. In the passage under consideration, Sraffa did not refer to the smallness of the relative impact on any one firm, but rather to the smallness of the output change of the entire industry. His argument was that small increases in the output of the industry under consideration are unlikely to call forth external economies of the kind envisioned by Marshall, while large increases cannot be taken into consideration in the analysis of a “particular equilibrium”. Sraffa’s objection was thus directed at the compatibility of the notion of external economies, as envisioned by Marshall, with the “particular equilibrium” method. Curiously enough, in illustrating his own concept of “parametric external economies” Chipman used precisely the same argument as Sraffa had done before:

The concept [of parametric external economies] may be illustrated in terms of Adam Smith’s pin factory. If a particular firm expands, some of the work can be divided and specialties will develop. Such specialized labor becomes available, at least part-time, to other firms in the industry. However, only a substantial expansion in the industry will provide enough openings for a pool of labor to develop with a specialized skill, and the contribution of a single firm to this process will be so imperceptible that it will be neglected by the entrepreneur. The change in the character of the labor force will be regarded as exogenous by all firms, even though each firm (by the laws of arithmetic) necessarily contributes to this process. (Chipman, 1970, 349; emphasis added)

39Sraffa’s point was precisely that “a substantial expansion of the industry” cannot, in general, be admitted in the construction of long-run industry supply curves in partial equilibrium analyses. In addition, Chipman also sought to turn an argument invoked by Sraffa (in the 1930 debate on increasing returns in the pages of the Economic Journal) against him:

In proving that competition was incompatible with decreasing costs, Sraffa thought he had triumphed when he pointed out (p. 93): “demand price is assumed to be constant with respect to variations in the output of an individual firm in a competitive market (this is merely the definition of free competition).” No one thought to add: supply price is assumed to be rising with respect to variations in the output of an individual firm in a competitive market (this is merely the definition of external economies). If a constant demand function can be given a parametric role for the individual firm, consistent with a falling industrial demand curve for the industry, then a rising supply (marginal cost) function can play a similar role, consistent with a falling supply curve for the industry. (Chipman, 1965, 743)

40But this argument also misses its target. Whereas the parametric role of demand prices is a logical implication of free competition, there is no such logical relation with regard to the parametric role of external economies. However, the real point is that Sraffa, in his 1925 and 1926 contributions, had not denied the compatibility of decreasing costs at the industry level with competitive conditions. (N.B. In the passage under consideration Sraffa (1930, 93) was in fact concerned with the incompatibility of firm-internal decreasing costs with competitive conditions.) His argument was rather that these could be taken into consideration in a partial equilibrium analysis, where those economies must be external to the firm but internal to the industry, only in exceedingly special cases—such as Chipman’s specific model in which all inter-industry linkages have been excluded by assumption.

  • 27 Chipman’s concept was adopted, among others, by Panagariya (1980), Inoue (1981), Suzuki (1996), a (...)

41While it is true that Chipman’s conceptualization of external economies offered a solution to the problem of ‘reconciling increasing returns, static conditions and pure and perfect competition’ (Bobulescu, 2007, 368), it would be wrong to infer that it also offered a solution to the problem of reconciling external economies with Marshall’s partial equilibrium analysis. What Chipman has achieved by means of his formalization was to provide a rigorous formulation of technological external economies in a competitive general equilibrium framework.27

4. External economies in Krugman’s contributions to development, geography and trade

42Scale economies are, of course, a key ingredient in almost all of the models for which Paul Krugman is known. However, Krugman’s contributions are best discussed in two parts, because there is a clear divide with regard to the role he attributed to external economies in his early contributions to trade and development theory and in his later contributions to economic geography and trade.

4.1 Krugman’s early contributions to trade and development theory

  • 28 See Dixit and Stiglitz (1977).

43The early contributions to the new trade theory (Krugman, 1979, 1980, 1981; Helpman und Krugman, 1985) concentrate on decreasing costs at the level of the individual firm, applying the monopolistic competition model with product differentiation in a general equilibrium setting, simplified by symmetry assumptions following the Dixit-Stiglitz approach.28 In these models it is typically assumed that there is only one factor of production (“labour”) and that all goods are produced with the same cost function,

Image 10000000000001A800000027269A1E7B.jpg

44where li is the amount of labour used in producing the ith good and xi is the output of that good. Obviously, there is a fixed cost element (“set-up costs”) and constant marginal costs, so that average costs decline at all levels of output, though at a diminishing rate. As Krugman (1980) has shown, the introduction of transportation costs into these types of models can give rise to the so-called “home market effect”: With two industries, each producing many differentiated products, a country will tend to export those goods for which it has a relatively large domestic market. This effect is due to a “demand linkage”, which Krugman associated with an “externality” that is generated by the existence of firm-internal increasing returns.

45Krugman showed only little interest in pure external economies models with perfect competition, claiming that it is difficult if not impossible to find plausible empirical illustrations of technological externalities which are compatible with competitive markets:

It is possible to imagine bees-and-flowers examples in which externalities arise from some physical spillover between firms, but empirically the most plausible source of positive externalities is the inability of innovative firms to appropriate fully the knowledge they create. … In traditional international trade models with their reliance on perfect competition, however, externalities resulting from incomplete appropriability could not be explicitly recognized, because the knowledge investment by firms that is the source of the spillover could not be fitted. Investment in knowledge inevitably has a fixed-cost aspect; once a firm has improved its product or technique, the unit cost of that improvement falls as more is produced. The result of these dynamic economies of scale must be a breakdown of perfect competition. As a result, perfectly competitive models could not explicitly recognize the most plausible reason for the existence of external economies. (1987b, 137)

46According to Krugman, it was only with the development of the monopolistic competition trade models that it became possible to incorporate also the empirically most relevant type of technological external economies into international trade theory:

The dynamic scale economies associated with investment in knowledge are just another reason for the imperfection of competition that has already been accepted as the norm. External economies can now be identified with incomplete appropriability of the results of R&D, which immediately suggests that they are most likely to be found in industries where R&D is an especially large part of costs. So by making tractable the modelling of a specific mechanism generating externalities, the new trade theory also seems to offer guidance on where these externalities are likely to be important. (Krugman, 1987b, 137-138)

47In his early contributions Krugman adopted a model specification with pure technological external economies only in “Trade, Accumulation, and Uneven Development” (1981), where he presented a two-sector model (agriculture, manufacturing), which was meant to capture some ideas of the “uneven development” literature (Hirschman, Rosenstein-Rodan). While agriculture is supposed to exhibit constant returns to scale, manufacturing is supposed to be subject to firm-external economies, which are introduced in the following way:

Manufacturing will require both capital and labor. It will be assumed that, from the point of view of an individual firm, the unit capital and labor requirements are fixed. In the aggregate, however, unit capital and labor requirements will not be constant; instead, in each region they will be decreasing functions of the region’s aggregate capital stock. Letting cN, cS, vN, vS be the unit capital and labor requirements in North and South, respectively, we have:

cN = c(KN), cS = c(KS), vN = v(KN), vS = v(KS),

Where c’, v’ < 0. I will, however, assume that the absolute value of the elasticity of unit input requirements with respect to output is less than one, so that total input requirements rise as manufacturing output rises. (Krugman, 1981, 150-151; emphasis added)

48This specification clearly has some elements in common with Chipman’s formulation, although the latter’s contribution is not mentioned. But unlike Chipman, Krugman saw little benefit in formally preserving competitive conditions. He claimed that the source of external economies is likely to be found in the existence of firm-internal economies, and that this is obscured by adopting a modelling approach such as the above. He asked rhetorically:

Can external economies be justified in microeconomic terms? … The justifications for technological externalities have, of course, been familiar since Marshall. Even if economies of scale are internal to firms, internal economies in the production of intermediate inputs can behave like external economies for the firms which buy them. So it is certainly legitimate to make use of the concept. What may be questioned is whether external economies are empirically important or, if they are, whether they are more important in manufacturing than in agriculture. (Krugman, 1981, 151)

49A systematic exposition of the analytical treatment of increasing returns in the new trade theory was provided in Helpman and Krugman (1985). In this book the main focus is, of course, on internal economies and monopolistic competition models, but the authors also provide a brief survey of external economies models in the new trade theory literature (Ethier, 1979, 1982a, 1982b; Panagariya, 1980, 1981). According to Helpman and Krugman, ‘it is possible both to streamline and to generalize this approach’ (1985, 45). The formulation they suggest is in fact very general:

The production function of a representative firm in sector i of country j, is assumed to depend on the worldwide vector of external effects ξ and on the vector of inputs vi employed by the firm. Letting xi be the firm’s output level, we have

xi = fi j (vi, ξ), i ∈ I , j ∈ J ,

Where fi j(·) is strictly quasiconcave and positively linear homogenous in vi, with non-negative marginal products of vi. … The vector of external effects ξ describes all the elements in the world economy that can potentially affect productivity of a firm in any sector and any country. … We allow for output-generated external effects, input-generated external effects, and any other external effects that can be represented in this form. This formulation allows for sector-specific effects, country-specific effects, worldwide effects, and spillover effects, both across sectors and across countries. The external effects can be positive or negative. (Helpman and Krugman, 1985, 45-46)

50In spite of this general formulation, however, the two authors saw a very limited role for external economies models in international trade theory. They argued that although the analytical representation is pretty straightforward, the underlying explanations for increasing returns are not convincing. According to Helpman and Krugman, there are three different justifications—but none of them is fully convincing:

How does one justify the way industry output enters into the firm’s production function? One justification, invoked by authors from Marshall (1920) to Ethier (1979), is the argument that a larger industry is able to support production of a wider variety of intermediate inputs at lower costs. If this is the reason for industry economies of scale, however, the problem of handling the effects of scale economies on market structure has not really been solved. Rather, it has been concealed through an incomplete specification of the model. As we will show …, certain special assumptions about the market structure of the intermediate goods industry can cause the economy to behave as if there are true technological external economies, but this is by no means a general result. (Helpman and Krugman, 1985, 37)

51In the relevant chapter Helpman and Krugman then introduce differentiated “intermediate goods” which are produced with firm-internal increasing returns in conditions of monopolistic competition, whereas the final goods using these intermediates as inputs are produced under constant returns to scale. As the authors show, the implications for the resulting trade equilibria depend crucially on the tradability or non-tradability of the intermediate inputs. If all goods are tradable, one obtains international economies of scale (Ethier, 1979, 1982): There are ‘effectively increasing returns to the production of the final good’, because the larger its output, the larger can be both the varieties and scale of production of the intermediate goods. On the contrary, if the intermediates are non-tradables, all industries with ‘backward’ and ‘forward linkages’ must be concentrated in one country. In this case there are implicit economies of scale in the production of the final good at the national level. In both cases, the external economies are generated by “pecuniary externalities”. Helpman and Krugman note that in their “external economies” model they could also allow for the possibility of cross-industry external effects:

However, in an external effects approach, the nature of inter-industry linkages is obscure because it is hidden inside a black box. It is not clear what one ought to look for as a source of linkage effects. (Helpman and Krugman, 1985, 87)

52According to Helpman and Krugman, the same objection can also be levelled at the second “standard justification” of external economies models:

  • 29 This justification was also invoked by Ethier (1979, 4, 1982b, 1245) and Panagariya (1980, 502).

A second potential justification for the external economy type of model is to argue that it is really an internal economy story in which something [i.e. thread of entry] is constraining firms to price at average cost.29 … As we will show …, however, average cost pricing imposed by the thread of entry is not always the same in its implications for international trade as average cost pricing resulting from perfect competition and constant private returns to scale. (Helpman and Krugman, 1985, 37)

53The implication is, of course, that internal economies should be modelled explicitly, by applying imperfect competition models, rather than invoking them as implicit justifications for using external economies models. Similar problems arise with regard to the third justification:

  • 30 Krugman (1987c) presents a model with dynamic economies of scale in which cumulative past output (...)

Finally, it is possible to argue that there are external economies resulting from the inability of firms to appropriate knowledge completely. … This is a true externality ; however, it is hard to envisage it leading to a relationship such as [xi = fj (vi, ξ)]. In the first place, innovative industries will ordinarily not be perfectly competitive. Further, an emphasis on the generation of knowledge points one in the direction of a dynamic rather than a purely static model.30 (Helpman and Krugman, 1985, 37)

54According to Helpman and Krugman, then, external economies models, although pretty straightforward as regards their formal representation, are beset with conceptual and analytical difficulties: ‘Given these objections, it seems that one should regard the static external economies model as at best a rough proxy for more complex models’ (1985, 37).

55Krugman’s assessment of the merits and demerits of external economies models appears to have changed in the early 1990s. In the “Introduction” to a collection of his essays titled Rethinking International Trade (1990) Krugman observed:

The principal obstacle to formal modeling [sic] of increasing returns in trade before the 1970s was the problem of market structure. In general, increasing returns are inconsistent with perfect competition …. The only exception is where the increasing returns are wholly external to firms … . External economies are, however, theoretically awkward and empirically elusive. Although a small literature on trade in the presence of external scale economies existed before the great change in the field, it was a literature with little influence. (Krugman, 1990, 4)

  • 31 In another paper Krugman observed that earlier authors (the reference is to Ohlin) tended to ‘fuz (...)

56According to Krugman, the newly developed monopolistic competition models and the oligopoly models with Cournot competition paved the way for the resurgence of interest in models with external economies:31

Somewhat surprisingly, a side product of the emergence of models that combine industrial organization and trade theory has been a mild resurgence of interest in external economies. This is partly because some models with increasing returns give rise to effects that closely resemble external economies, for example, when there are increasing returns in the production of intermediate goods. More important, perhaps, is that once the role of increasing returns was legitimized as a concern of trade theory, all forms of increasing returns were given greater respect. It is also true that some of the modeling tricks used to make industrial organization models tractable turn out to work on external economies too. (Krugman, 1990, 4-5)

  • 32 Chipman’s concept was explicitly adopted, however, by Panagariya (1980, 1981) and, in a slightly (...)

57The rehabilitation of external economies models in international trade theory seems to have been unrelated to Chipman’s concept of parametric external economies.32 According to Krugman, the decisive factor in terms of new modelling techniques had rather been the development of the concept of the “integrated economy”, first introduced by Ethier (1979, 1982),

who showed that the analysis of trade in the presence of Marshallian external economies is greatly clarified if we work from the allocation of resources to production and trade rather than the other way around. (Krugman, 1990, 65)

4.2 External economies in Krugman’s contributions to the “new economic geography”

58In his early contributions Krugman saw a very limited role for external economies models and focused his attention primarily on monopolistic competition models with firm-internal economies. It was only in the early 1990s when he turned his attention to industry localization and agglomeration phenomena that Krugman began to emphasize the importance of external economies:

During the early years of the new trade theory, I was strongly committed to the view that internal economies of scale, leading to intra-industry trade in differentiated products, were where the important action was; … I now tend to believe that external economies are at least equally important. (Krugman, 1994, 23)

59In Krugman’s account, this change in his assessment of the role of external economies was primarily motivated by his realisation of the importance of pecuniary external economies. In the core model of his new economic geography contributions, the so-called “core-periphery” model, pecuniary externalities are one of the main forces pushing towards agglomeration. At the same time, Krugman retained his objections to models which rely exclusively on technological external economies:

I shall adopt the working assumption that the externalities that sometimes lead to emergence of a core-periphery pattern are pecuniary externalities associated with either demand or supply linkages rather than purely technological spillovers. In competitive general equilibrium, of course, pecuniary externalities have no welfare significance and could not lead to the kind of interesting dynamics we shall derive later. Over the past decade, however, it has become a familiar point that in the presence of imperfect competition and increasing returns, pecuniary externalities matter; for example, if one firm’s actions affect the demand for the product of another firm whose price exceeds marginal cost, this is as much a “real” externality as if one firm’s research and development spills over into the general knowledge pool. At the same time, by focusing on pecuniary externalities, we are able to make the analysis much more concrete than if we allowed external economies to arise in some invisible form. (This is particularly true when location is at issue: how far does a technological spillover spill?). (Krugman, 1991b, 485)

  • 33 For a similar model, see also Krugman (1991c).
  • 34 See Marshall (1920 [1890], Bk. V, Ch. XII).

60In Geography and Trade (1991d) Krugman set out a prototype version of the so-called “core-periphery model”, which is yet another variant of the symmetric monopolistic competition framework originally proposed by Dixit and Stiglitz (1977).33 Economies of scale in manufacturing are introduced in terms of a linear cost function, in which a fixed cost in terms of manufacturing labour must be incurred in order to produce any individual variety of manufactures (Krugman 1991d: 103). In addition, there is an agricultural sector with a constant-returns-to-scale technology. The introduction of transportation costs then leads to the possibility of the emergence of a core-periphery pattern, with a concentration of industry (and manufacturing labour) in one location (or country), and an agricultural periphery. He also discussed an industry localization model, in which he focused on the three arguments advanced by Marshall for economies from industrial agglomeration: “labour market pooling”, “specialized suppliers”, and “knowledge spillovers”.34 According to Krugman, the “labour market pooling” argument for economies which arise from a regional clustering of firms can indeed be shown to be valid, even with fully competitive labour markets, provided there is uncertainty (1991d, 38-40 and 123-127). However, Krugman stressed that the “labour market pooling” argument also depends crucially on the presence of firm-internal increasing returns:

Uncertainty alone won’t generate localization. You need increasing returns as well. The key point is that in order to make a pooled labor market advantageous, I needed to assume that each firm had to choose one location or the other, not both. If each firm could produce in both locations, or for that matter if each firm could be split into two identical firms, one in each place, then the full “portfolio” of firms and workers could be replicated in each location, and the motivation for localization would be gone. But the most natural justification for the assumption that firms do not locate in both places is that there are sufficient economies of scale to militate for a single production site. So it is the interaction of increasing returns and uncertainty that makes sense of Marshall’s labor pooling argument for localization. (Krugman, 1991d, 40-41)

61In Krugman’s version of the “specialized suppliers” story increasing returns at the industry level are also modelled as arising from firm-internal economies. And Krugman stressed that this is done not just as a matter of analytical convenience, that is, because it allows him to apply the technical tricks of the monopolistic competition models developed in the new trade theory:

The intermediate inputs story, like the labor pooling story, depends crucially on at least some degree of economies of scale. If there were no economies of scale in the production of intermediate inputs, then even a small-scale center of production could replicate a large one in miniature and still achieve the same level of efficiency. It is only the presence of increasing returns that makes a large center of production able to have more efficient and more diverse suppliers than a small one (Krugman, 1991d, 49).

62In the sequel Krugman then showed that it is possible ‘to construct a model of intermediate goods and industry localization that is formally exactly analogous to the core-periphery model’ (1991d, 51). Thus, firm-internal economies again turn out to be an indispensable ingredient.

  • 35 However, this did not prevent him from adopting a pure “external economies” representation of Mar (...)

63“Knowledge spillovers” between nearby firms, on the other hand, are assumed by Krugman to be tractable as a ‘more or less pure externality’ (1991d, 52-53), without any firm-internal increasing returns. However, Krugman pointed out that there is no specific need for conceptualizing knowledge spillovers in this way. From his point of view, the main reason for adopting this formalization had been that ‘economists with a conventional background still have a hankering to preserve perfect competition in their models; purely technological externalities do this’ (1991d, 53). Krugman nevertheless felt uneasy with this formulation. First, because knowledge spillovers typically occur in R&D intensive industries characterized by imperfect competition and, secondly, because they belong to a type of external economies that cannot be modelled ‘other than by assumption. … Knowledge flows … are invisible; they leave no paper trail by which they may be measured and tracked, and there is nothing to prevent the theorist from assuming anything about them that she likes’ (1991d, 53-54). According to Krugman, then, increasing returns from the regional clustering of firms generally result from a combination of internal and external economies in conditions of imperfectly competitive markets—and they should be modelled as such.35

64And Krugman claimed, again, that the recent developments in trade and location theory had paved the way for a rehabilitation of the concept of external economies:

In the early years of the new trade theory, external economies were something we were trying to get away from, for at least three reasons. First, the existing tradition of external economy models suggested that they were analytically very awkward. Second, the whole thrust of the theory was towards trying to model the role of imperfect competition, as a way of saying something new. Finally, external economies, which by definition don’t leave a paper trail, were thought to be very elusive. At this point, however, all three objections to looking for external economy explanations of trade have lost much of their force. … the same tricks that make monopolistic competition models tractable seem to work pretty well on external economy models too. The respectability of the new trade theory is now sufficiently established that one need not differentiate it by emphasizing the imperfect competition aspect—and in any case we now know that imperfectly competitive markets in labour, intermediate goods and so on give rise to aggregate results that are in effect external economies. Finally, some useful approaches have emerged for at least identifying cases in which external economies may be significant. (Krugman, 1994, 21)

  • 36 See, on this, also Neary (2000, 26).

65According to Krugman, the new external economy models are mainly driven by applying to the case of external economies the same technical tricks which have been successfully used in the new trade theory for internal economies. Basically, these tricks consist of two major simplifications by means of which those models became analytically tractable: “symmetry” and “large numbers”.36 By supposing, first, that ‘all n goods produced in each of the two countries are symmetric’, and, secondly, that ‘n can be treated as if it were a continuous variable’, the Krugman-type models of inter-regional trade and agglomeration are considerably reduced in complexity. It was the application of these “technical tricks”—and not some novel idea in the formal treatment of external economies—that allowed Krugman to come up with simple but interesting external economies models. In the paper under consideration, Krugman’s formulation of external economies consisted, in fact, of no more than simply assuming that

both countries [i = 1,2] share the same technology, with increasing returns that are country-specific and completely external to firms: Qi = Liα α>0. (Krugman 1994: 28)

  • 37 For a critical summary assessment of the new economic geography model presented in Fujita, Krugma (...)

66The model used in Development, Geography, and Economic Theory (Krugman, 1995) and in The Spatial Economy (Fujita, Krugman, and Venables, 1999) is again one of monopolistic competition with a symmetric CES utility function of the Dixit-Stiglitz type, where each variety of manufactures is produced at decreasing average costs, and an agricultural sector with constant returns to scale. The introduction of transportation costs into the model then gives rise to the so-called “home-market effect”: the country (or region) with higher demand (that is, with the larger home market or the higher income) has a larger share of manufacturing, and tends to export manufactures. Firm-internal increasing returns and transportation costs thus lead to models which exhibit a propensity to agglomeration. In addition, the authors consider two different forces pushing towards agglomeration: international (or inter-regional) labour mobility and “intermediate inputs”. Both of these forces give rise to pecuniary external economies. If workers migrate in response to real wage differences, entry of a new firm in one country (or region) might encourage migration (via wage rises from increased labour demand), which in turn raises demand for local varieties (this is called a “demand or backward linkage”). Since migration is driven by real wage differentials, however, falling prices of manufactures lower the costs of living and thus encourage further migration. This process continues until nominal wages adjust to equalise real wages internationally (or across regions). The result is the emergence of a “cost or forward linkage”, which shifts the manufacturing firms’ average and marginal cost curves downwards. As the authors show, allowing for inter-industry linkages by introducing “intermediate goods” provides another channel for agglomeration forces, which also establish “forward” and “backward” linkages, that is, external economies which are transmitted through the price mechanism. With “intermediate inputs”, the link between increasing returns which are internal to the firm and pecuniary externalities is established through the following channel: if one firm raises its production level, this increases its demand for inputs, which are (partly) produced by some other firm. The second firm records the higher price it can obtain for its product and takes this as a signal to increase its own production. By so doing, because of firm-level increasing returns, the second firm’s average costs decrease, leading to a lowering of the price. Thus the production decision of the first firm has the external effect, transmitted through the price mechanism, of decreasing the second firm’s costs; and thus ‘a modelling tool that allows firm-level increasing returns also allows the representation in general equilibrium of economy-wide pecuniary externalities’ (Meardon, 2001, 230).37

5. Concluding remarks

67This paper has reviewed the contributions of three authors, Viner, Chipman, and Krugman, in order to trace inter-connections, differences, similarities, and incompatibilities in their formal treatment of the Marshallian concept of “external economies”. It was shown that Viner’s graphical representation of net external economies was originally conducted in a “Ricardo-Marshall framework” with perfectly elastic factor supplies (apart from land inputs), and that Viner invoked pecuniary external economies in the derivation of a negatively inclined long-run industry supply curve, because he considered the concept of technological external economies to be empirically vacuous. It was then argued that Chipman’s concept of “parametric external economies” concentrated instead on the formalization of technological external economies, and that in the specific general equilibrium model adopted by Chipman, with a single primary factor in inelastic supply and no inter-industry linkages, pecuniary external economies in Viner’s sense cannot possibly occur. Consequently, Chipman’s formulation did not provide a rehabilitation of Marshall’s partial analysis of a competitive equilibrium with external economies. Finally, it was shown that there exists a close connection, at the analytical level, between Krugman’s and Viner’s conceptualization of external economies. From early on, but particularly in his later models, Krugman invoked pecuniary external economies, which arise from introducing either inter-industry linkages through bringing in “intermediate inputs” or, alternatively, labour migration (or, more generally, international or inter-regional factor mobility) into a general equilibrium model of monopolistic competition with firm-internal increasing returns. The assumption that the supply of labour (or, more generally, the supply of all original factors) in each region is perfectly elastic amounts, in effect, to re-introducing the “peculiar” Ricardo-Marshall assumptions regarding factor supplies to which Jacob Viner in his original 1931 article had still adhered.

An earlier version of this paper was presented at the annual conference of the European Society for the History of Economic Thought in Thessaloniki, Greece, 23-26 May 2009. Valuable comments from the discussant and the session participants as well as from Arrigo Opocher, Heinz D. Kurz and two anonymous referees of this journal are gratefully acknowledged.

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1 See, in particular, Marshall (1920, Bk. IV, Ch. XIII, Bk. V, Ch. XII, and Appendix H).

2 The paper thus takes up a theme that was recently also studied, from a somewhat different angle, by Bobulescu (2002, 2007).

3 For summary accounts of these contributions, see Chipman (1965, 736-749) and Opocher and Steedman (2008a, 253-259).

4 See Freni (2001, 365), who noted that this was ‘the Marshallian framework commonly employed before the 1930s’; it was also the framework adopted by Sraffa (1998 [1925]).

5 See Opocher and Steedman (2008a, 260).

6 It is noteworthy that Viner, in a different context, also dismissed Frank Graham’s argument for protection on the ground that ‘it seems difficult even to suggest plausible hypothetical cases of the existence of genuine technological external economies’ (1975 [1937], 480-481).

7 The example suggested by Viner to illustrate pecuniary external economies which are not generated by (internal or external) economies in some other industry is so exceedingly fanciful that it seems to have been deliberately chosen in order to highlight the irrelevance of such cases: ‘But cases are theoretically conceivable where pecuniary external economies to industry A may not be economies to any other industry, as, for instance, if laborers should have a preference, rational or irrational, for working in an important rather than in a minor industry, and should therefore be willing to accept lower wages as the industry expands’ (1953 [1931], 218).

8 As Chipman (1965, 738-739) pointed out, the idea of firm’s average and marginal cost curves shifting downward as the industry expands can be traced back to Cunynghame (1892) and Edgeworth (1905, 66-67; 1925, III, 140-141).

9 Interestingly, Sraffa did not find it necessary to introduce Viner’s restrictive assumption: In his 1925 paper he suggested that when the industry expands the firm’s average and marginal cost curves ‘would be completely altered’, so that ‘the point of maximum economy [i.e., the point of minimum average costs] could be moved in any direction because of the change’ in industry output (1998 [1925], 352).

10 In the introduction of his essay, Viner pointed out that the differences between the Austrian school, which ‘tacitly assumes that the supplies of all the elementary factors of production are given and independent of their rates of remuneration’, and the English school, which emphasises ‘the dependence of the amounts of certain of the elementary factors, notably labor and waiting, on their rates of remuneration’, are unimportant. This is because in ‘the present analysis … it is assumed either that the prices of the elementary factors remain unaltered or that they undergo changes of a kind consistent with the basic assumptions of either school’ (1953 [1931], 200).

11 Viner also discussed cases in which factors are in imperfectly elastic supply; see Viner (1953 [1950], 229-231).

12 Viner noted, however, that the “law” will operate unambiguously ‘only after the expanding industry has reached the stage beyond which there are no net technological or efficiency advantages of increasing the scale of plants in order to increase output of the particular commodities concerned as compared to increasing the number of plants, i.e., where there are no “net technological economies of large-scale production.’ (1953 [1950], 232)

13 See Freni (2001, 364-367).

14 The former distinction concerns differences in the assumptions that are made about the elasticity of factor supplies within a partial equilibrium framework. It may also be noted here that a serious criticism of partial equilibrium analyses was recently put forward by Opocher and Steedman (2008b): They show that neither Viner nor anybody else has as yet provided a solution to the problem that whether the resulting industry supply curve is rising or falling depends on the arbitrary choice of the numéraire.

15 See Mishan (1960, 6).

16 On the development of the notion of “externalities”, see Lagueux (1998).

17 Note that Ellis and Fellner, unlike later authors, did not abandon the notion of “pecuniary externalities”. On the contrary, they pointed out that “external pecuniary diseconomies” are bound to arise from “rising transfer costs”. On the other hand, however, they also noted that these do not give rise to any divergences between “private” and “social marginal costs”, thus anticipating the later classification of pecuniary externalities as “non-Pareto-relevant externalities”.

18 As we shall see in Section 4 below, the argument that pecuniary external economies cannot arise from firm-internal economies in supplying industries cannot in general be sustained.

19 Both traditions are still present in reputable contemporary microeconomics textbooks.

20 According to Coase (1988, 23, note 35), the term “externality” was first used by Paul A. Samuelson in a 1958 book review.

21 On definitions of “externalities”, and on the existing confusions in the literature concerning “externalities”, see Hausman (1992) and Sturn (1998).

22 For the profession at large this shift must probably be dated much later, considering that an author such as Mishan, as late as 1971, could still write: ‘The analysis of external effects has always been conducted within a partial equilibrium framework’ (1971, 8).

23 Compare, for instance, the following statement by Mishan: ‘The term external pecuniary diseconomies was proposed to cover the case of a rising supply price that is the result solely of changes in relative factor prices as output expands. But in the complete absence of external effects, rising supply price is an implication of any interdependent economic model having such familiar features as production functions homogenous of degree one, imperfectly elastic factor supplies, and factor proportions differing from one product to another. … Therefore to invoke the term pecuniary external diseconomies to “explain” supply curves that are in fact already explained by this familiar interdependent economic system simply in order to distinguish them from external diseconomies proper … strikes one today as, perhaps, a verbal extravagance.’ (Mishan, 1960, 6; emphasis added) It should be emphasized, however, that Mishan’s dismissal of Viner’s term “pecuniary (dis)economies” as ‘a verbal extravagance’ should be taken seriously, because no microeconomic argument can rest on any kind of monetary, nominal effect. In fact, there is nothing inherently “pecuniary” in Viner’s “pecuniary externalities” What is relevant to his argument is in fact that the minimum average cost and the output price in one industry increases or decreases relative to the output prices in other industries.

24 The scale effect can also be associated with the total output of the industry under consideration by supposing that Ki = μi yiηi, with –∞ < ηi < 1, where μi and ηi are given parameters. For ηi = 1 output is unbounded; for ηi = it is a constant.

25 See also Freni (2001, 371).

26 In his 1965 survey article Chipman had dismissed Viner’s concept of “pecuniary external economies” in the following terms: ‘Scitovsky (1954, p. 146) also considers another concept, which he borrowed from Viner (1931, p. 39), called “pecuniary external economies,” which refers to changes brought about via market prices. They arise, according to Scitovsky, “whenever the profits of one producer are affected by the actions of other producers.” It would be difficult indeed to imagine cases in which this was not the case. “Pecuniary economies” in this sense seem to be just another name for general equilibrium.’ (Chipman, 1965, 746)

27 Chipman’s concept was adopted, among others, by Panagariya (1980), Inoue (1981), Suzuki (1996), and Silvestre (1999), but it cannot be said to have triggered a particularly broad stream of literature. It was also mentioned, and immediately dismissed, in the opening paragraphs—that is, in the so-called “literature survey” —of Romer’s seminal contribution to the new growth theory: ‘Subsequent work demonstrated that it is possible to construct consistent, general equilibrium models with perfect competition, increasing returns, and externalities (see, e.g., Chipman, 1970). … Following Smith, Marshall, and Young, most authors justified the existence of increasing returns on the basis of increasing specialization and the division of labor. It is now clear that these changes in the organization of production cannot be rigorously treated as technological externalities. Formally, increased specialization opens new markets and introduces new goods. All producers in the industry may benefit from the introduction of these goods, but they are goods, not technological externalities.’ (Romer, 1986, 1005)

28 See Dixit and Stiglitz (1977).

29 This justification was also invoked by Ethier (1979, 4, 1982b, 1245) and Panagariya (1980, 502).

30 Krugman (1987c) presents a model with dynamic economies of scale in which cumulative past output determines current productivity. It is assumed that at any point in time there are constant returns to the production of each traded good, while there are dynamic increasing returns, taking the form of an industry learning curve. More specifically, in each industry the productivity of resources depends on an index of cumulative experience (into which both domestic and foreign production enters).

31 In another paper Krugman observed that earlier authors (the reference is to Ohlin) tended to ‘fuzz over the distinction between internal economies of scale and external increasing returns.’ Later theorists ‘finally managed to “tame” imperfect competition and hence to feel comfortable talking about internal scale economies’ (1999, 6, 7).

32 Chipman’s concept was explicitly adopted, however, by Panagariya (1980, 1981) and, in a slightly different formulation, by Helpman (1984). Bobulescu’s claim that it provided ‘the starting point for contemporary analyses (Krugman, Helpman, Ethier, Panagariya), which use parametric external economies as a logical continuation of the Marshallian tradition’ (2007, 368) nevertheless seems difficult to sustain, and particularly so with regard to Krugman’s contributions.

33 For a similar model, see also Krugman (1991c).

34 See Marshall (1920 [1890], Bk. V, Ch. XII).

35 However, this did not prevent him from adopting a pure “external economies” representation of Marshall’s argument in his textbook. Krugman and Obstfeld (2006, 136-139) list the same three sources of increasing returns at the industry level from a regional clustering of firms (labour market pooling, specialized suppliers, and knowledge spillovers), and then ‘represent external economies simply by assuming that an industry’s costs are lower, the larger the industry. If we ignore possible imperfections in competition, this means that the industry will have a forward-falling supply curve: The larger the industry’s output, the lower the price at which firms are willing to sell their output’ (ibid., 139; first emphasis added).

36 See, on this, also Neary (2000, 26).

37 For a critical summary assessment of the new economic geography model presented in Fujita, Krugman, and Venables (1999), see Neary (2001).

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