INCREASING RETURNS AND MARSHALL’S THEORY OF VALUE*

NEIL HART

University of Western Sydney, Macarthur

I. INTRODUCTION

Marshall’s claim to the position as an important co-founder of the marginalist approach to economic theory is most often associated with his development of analytical tools of particular relevance to the partial equilibrium framework. However, Marshall perceived serious logical difficulties associated with this analysis;

The statical theory of equilibrium is only an introduction to economic studies; and it is barely even an introduction to the study of the progress and development of industries which show a tendency to increasing return. Its limitations are so constantly overlooked, especially by those who approach it from an abstract point of view, that there is a danger in throwing it into definite form at all.

(Principles, p.461) ’ Marshall viewed the requirement to incorporate the pervasive effects of increasing returns

as the most serious threat to the theoretical structure he was attempting to construct. These difficulties, which came to be known as Marshall’s reconciliation pmblem, were also the subject of the important value theory debates of the late 1920s. And as Hahn (1973, 1984) and Arrow (1985) have conceded, the inability to adequately represent increasing returns continues to challenge the efforts of subsequent equilibrium theorists.

Not surprisingly therefore, Marshall’s reconciliation problem continues to attract a deal of attention in the literature. However, it is argued in this paper that the precise nature of Marshall’s reconciliation problem, together with his proposed ’solutions’, appears to have been seriously misunderstood by many of Marshall’s immediate followers and subsequent readers of his Principles. In Section I1 of the paper it is argued that the widespread association of Marshall’s reconciliation exercise with an attempt to reconcile increasing returns with the existence of pure (or perfect) competition is both mistaken and misleading. Such an interpretation owes its origins to the simplified Marshallism of the decades subsequent to the publication of Principles. In Section 111 the persistent belief that Marshall’s solution rested

* I am grateful to Peter Kriesler, Tony Aspromourgos and an anonymous referee for comments on an earlier version of this paper.

’ Unless otherwise noted, all references to Marshall’s Principles of Economics refer to the Eighth Edition as published by Macmillan in 1920 (1947 reprint).

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with the treatment of increasing returns as externalities, is shown to lack compelling support in Marshall’s own writings. In Section IV it is established that it was through his appeal to biological analogies and the associated representative firm concept that Marshall attempted to entrap the dynamic increasing returns process within a static equilibrium framework. In Section V Marshall’s often overlooked concern with dynamics, and its relation to the reconciliation problem is highlighted. The central conclusions of the paper are restated in Section VI.

11. THE NATURE OF MARSHALL’S RECONCILIATION PROBLEM

The following passage from Principles most clearly represents Marshall’s assessment of the logical difficulties associated with reconciling the existence of increasing returns with the attainment of equilibrium in the context of normal supply and demand conditions:

Some, among whom Cournot himself is to be counted, have before them what is in effect the supply schedule of an individual firm; representing that an increase in its output gives it command over so great internal economies as much to diminish its expenses of production; and they follow their mathematics boldly, but apparently without noticing that their premises lead inevitably to the conclusion that, whatever firm gets a good start will obtain a monopoly of the whole business of its trade in its district. While others avoiding his horn of the dilemma, maintain that there is no equilibrium at all for commodities which obey the law of increasing return; and some again have called into question the validity of any supply schedule which represents prices diminishing as the amount produced increases. (Principles, p.459)

Quite clearly therefore, Marshall’s reconciliation problem was the construction of a supply schedule in the presence of increasing returns internal to the firm, and incorporating the ’market imperfections’ which inevitably accompany such returns. However, to many of the critics of his value theory, Marshall’s reconciliation problem came to be associated with the construction of industry supply schedules under conditions resembling pure competition. This interpretation emerges from the value theory debates in the decades following Principles, and is evidenced most clearly in Sraffa’s (1926) destructive contribution where competitive conditions are frequently referred to. The widespread acceptance of this interpretation is further highlighted in Schumpeter’s (1942, p.78) claim that ‘he [Marshall] as well as Wicksell framed his general conclusions on the pattern of perfect competition so as to suggest, much as the classics did, that perfect competition was the rule’ (emphasis added).

However a closer reading of Principles clearly demonstrates that Marshall did not intend his supply schedule to be confined to the analysis of ‘competitive’ markets. Indeed solutions which attempted to imprison the analysis within such assumptions can be shown to be inconsistent with Marshall’s own writings.

In Marshall’s Principles it is essential to distinguish between the type of market structure being discussed during the first few chapters of Book V and the later discussion of manufacturing industries. In Chapter Three of Book V Marshall makes what he terms a provisional assumption of ’much free competition’in which the forces of demand and supply have free play amongst independently acting buyers and sellers. All participants have sufficient knowledge of what others are doing to prevent them from taking a lower or paying a higher

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price than others are doing. As a result of these assumptions ’there is only one price in the market at one and the same time’ (Principles, pp.341-342). This type of model is applied to his simple example of a fishing industry undergoing a once-and-for-all change in demand.

Marshall emphasises clearly that such assumptions must be seen to be only provisional; c ’we will have to inquire further, how far these assumptions are in accordance with the actual

facts of life’ (Principles, p.341). In his subsequent discussion of manufacturing and large scale production in Principles, Marshall plainly encompasses a market structure more complex than that described in these provisional assumptions. Here Marshall’s analysis draws heavily on a distinction between what could be termed general and particular markets;

This may be expressed by saying that when we are considering an individual producer, we must couple his supply curve - not with the general demand curve for his commodity in a wide market, but - with the particular demand curve of his own special market. And this particular demand curve will generally be very steep; perhaps as steep as his own supply curve is likely to be, even when an increased output will give him an important increase of internal economies.

(Principles, p.458, emphasis added)

It can be seen quite clearly here that once Marshall’s analysis escapes from the provisional assumptions of ‘free’ competition it makes no sense at all to speak of the forces of demand and supply achieving an industry equilibrium characterised by the existence of only one price in the market at one and the same time. Firms can no longer be assumed to be passive price takers with perfectly elastic demand curves. It is this context, and not under the provisional assumptions of free competition, that Marshall attempted to construct his industry supply schedule. This schedule was meant to capture, within a static equilibrium framework, the presence of the ’market imperfections’ corresponding to the dynamic increasing returns process. In short, the nature of the reconciliation exercise implicit in critics such as Sraffa and Schumpeter is at once more precise, but less meaningful, than that posed initially by Marshall.

111. THE ROLE OF EXTERNAL ECONOMIES

A reasonably well developed discussion of the now familiar distinction between internal and external economies of scale can be found in Marshall’s privately circulated Pure Theory of Domestic Values (Marshall, 1975b, pp.195-198). By the publication of Principles, this distinction had been further clarified. External economies are defined as those dependent on the general development of the industry, while internal economies are dependent on the resources of the individual houses of business engaged in it, on their organisation and the efficiency of their management. Three major classes of internal economies are isolated - those generated through increased subdivision of labour; increased specialisation of the managerial function and those arising as a result of creative innovations in the organisational and mechanical aspects of production. External economies are treated less precisely by Marshall. However, it is possible to isolate two general types. Economies arising from ’the use of specialised skill and machinery’ depending on ‘the aggregate volume of production in the neighbourhood’ are one type. The other involves ‘especially those connected with the growth of knowledge and the progress of the arts’ and which depend on the ‘aggregate volume of production in the whole civilised world’ (Principles, pp.265-266).

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The precise role of external economies in Marshall’s writings has been the subject of some debate As writers such as Arndt (1955) have emphasised, both external and internal economies represent one of the major sources of growth in Marshall’s scheme. On the other hand if economies were not firm specific, but instead available to all competitors in the industry, Marshall’s reconciliation problem would appear to be negotiated. Such economies would tend to preserve competition by counteracting the tendency towards monopoly.

The notion that external economies may have been the vessel through which Marshall ’solved’ his reconciliation problem has been advocated strongly in Stigler’s influential assessments. Stigler (1941) argues specifically that it is the existence of external economies, and not, as others had suggested, that of the representative firm following the life cycle pattern, which permits reconciliation of competition and decreasing long-run average costs;

Marshall’s chief purpose in creating this category [external economies] . . . . . was to explain the great historical reduction in production costs, which were associated with increases of output, size of plant, and size of firm, and which to a large extent were not accompanied by monopolisation.

(Stigler, 1941, p.76)

Supporters of Stigler’s interpretation2 are able to point to passages in Principles which, when considered in isolation, would appear to offer verification. Stigler’s emphasis on the priority of external economies finds some justification through Marshall’s remark that, when considering economies resulting from a high industrial organisation, internal economies ‘are frequently very small’ relative to external economies resulting from the general progress of the industrial environment (Principles, p.441). In a later passage, Marshall noted that such economies may lead to the situation where ’the prices of the products will keep to a level which yields only a normal rate of profits to that class of industry’ (Principles, p.318).

However apart from these isolated instances, there is little in Principles to substantiate Stigler’s thesis. Significantly, in his conclusion to Book IV of Principles Marshall implies that the existence of external economies does not in fact limit firm size or the extent to which internal economies may be realised;

The general argument of the present Book shows that an increase in the aggregate volume of production of anything will generally increase the size, and therefore the internal economies possessed by such a representative firm; that it will always increase the external economies to which the firm has access; and thus will enable it to manufacture at a less proportionate cost of labour and sacrifice than before.

(Principles, p.318)

Marshall’s most direct analysis of the dilemma presented by increasing returns to the theory of long-period normal equilibrium is to be found in Chapter XI1 of Book V and Appendix H. Once again it is significant to note that this analysis did not include any reference to the

* See for example Jenner (1964-5). and more recently Thirlwall (1987, p.324) and Harris (1988). External economies are also listed in Levine’s (1980) account of the ‘consensual’ view of Marshall’s reconciliation exercise.

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notion that the solution to the reconciliation problem could be uncovered through the existence of external economies. This is not surprising, once it is accepted that the object of Marshall’s reconciliation exercise was not the preservation of pure competition.

The notion that Marshall’s dilemma could be resolved through an appeal to external economies in fact was popularised largely by Pigou and his supporters? Pigou (1913, p.22) for example concluded that the ‘apparent conflict between mathematical analysis and experience’ was basically to be resolved by the proposition that each individual firm was operating under increasing costs, while the industry as a whole was operating under decreasing costs, therefore reflecting economies external to the firms in the industry. This had followed on from Pigou (1910, 1912) where external economies were implied in his analysis of long- period supply. While there is some evidence to suggest that Marshall himself disapproved of Pigou’s arguments, Pigou’s method of interpreting returns to scale remained largely unchallenged for over a decade in the published literature, gaining the support of influential writers such as Edgeworth? Therefore Sraffa’s (1926) demonstration of the serious limitations of such an approach was not so much an attack on Marshall’s analysis, but rather on the theoretical apparatus being constructed by those who sought to circumvent the dilemma Marshall had posed and attempted to resolve. To argue as Harris (1988, p.164) recently has that Marshall sought to get around the problem ‘by assuming, for no good reason, that increasing returns are external to the firm and internal to the industry’ detracts attention away from the important analytical issues which Marshall’s biological analogies were specifically devised to confront.

IV. BIOLDGICAL ANALOGIES AND THE REPRESENTATIVE FIRM

It is not surprising that Marshall should have turned to biological analogies in his attempts to incorporate the operation of returns to scale into his theoretical system. In Appendix B of Principles Marshall discusses the significance of the great stride forward in the speculations of biology to the growth of economic science, while in the Preface Marshall presents his now famous claim that the Mecca of the economist lies in economic biology rather than in economic dynamics (Principles, p.xiv).

The specific task Marshall allocates to his biological analogy in Principles is basically one of illustrating how internal economies may not be fully exploited by an individual firm because of limits to its productive life span. According to Marshall;

Nature still presses on the private business by limiting the length of the life of its original founders, and by limiting even more narrowly the part of their lives in which their faculties retain full vigour. And so, after a while, the guidance of

Whitaker (1982) provides a detailed account of the external economy approach adopted by many of Marshall’s contemporaries and immediate followers.

Marshall’s manuscript notes on his copy of Pigou (1912), reproduced with insightful commentary in Bharadwaj (1972), suggests that Marshall had serious reservations of Pigou’s work. In other unpublished correspondences, Marshall (1961, pp.800-819) is also critical of the approaches adopted by Cunynghhame and Edgeworth. Robertson (1924) and Young (1913, p.678) provide notable criticisms of the external economy approach.

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the business falls into the hands of people with less energy and less creative genius, if not with less active interest in its prosperity. (Principles, p.316)

As a result Marshall concludes that the full life of a firm seldom lasts very long, as the firm is likely to ‘ere long quickly to decay’ having lost the exceptional energy which enabled it to rise (principles, p.287). The process is further illustrated in Marshall’s famous analogy, where the growth of business is likened to the growth of trees in a forest;

But here we may read a lesson from the young trees of the forest as they struggle upwards through the benumbing shade of their older rivals. Many succumb on the way, and a few only survive; those few become stronger every year, they get a larger share of light and air with every increase of their height, and at last in their turn they tower above their neighbours, and seem as though they would grow on for ever . . . but they do not. One tree will last longer in full vigour and attain a greater size than another ; but sooner or later age tells on them all. Though the taller ones have a better access to light and air than their rivals, they gradually lose vitality; and one after another they give their place to others . . .

(Principles, pp.315-316)

If accepted, Marshall’s life cycle theory of firms clearly implied that a position of long- period equilibrium for an industry coincided with a situation in which individual firms are at dkequilibrium. In Marshall’s terminology, some businesses will be rising and others falling. In this context the notion of the ’marginal firm’can have no operational role for the derivation of long-period normal supply conditions, and Marshall replaced it with the theoretical construct of the representative firm. The representative firm is ’representative’of an industry in the sense that it has ’normal access to the economies, external and internal, which belong to the aggregate volume of production’ (Principles, p.317). It can be seen as corresponding to the miniature of an industry, and it is its marginal costs that are used when the long-period supply price is being discussed (Principles, p.460). The representative firm therefore can be seen as a device which selects the appropriate tree to illustrate the general conditions of the forest, and ceases to perform the role allocated to it by Marshall if the biological analogy is rejected.

It has been argued that in the later editions of Principles Marshall’s reliance on his biological analogy in the reconciliation exercise was substantially reduced. Levine (1980, pp.269-70) for example argues that Marshall did not intend the ‘biological folklore which is the life cycle of the firm’ to serve as a vehicle for effecting ‘competitive dispensation’. Certainly, from the sixth edition of Principres in 1910, Marshall did add a significant qualification to the trees in the forest analogy by acknowledging the growing importance of joint-stock companies. Marshall conceded that because of the great recent development of vast joint-stock companies, his ‘general rule’ of eventual stagnation ‘is far from universal’. As a result such an organisation could under ‘favourable circumstances secure a permanent and prominent place in the work of production’ (Principles, p.316). However, in his Principles, Marshall did not consider that this qualification substantially altered his general proposition, as he considered it likely’that joint-stock companies would eventually lose much of its progressive force such that ’the advantages are no longer exclusively on its side in its competition with younger and smaller rivals’. Similarly in Appendix H he concluded that in the case where ’these businesses are fused in a trust . . . the use of the term “normal” is less inappropriate than seemed probable a priori’ (Principles, p.805).

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In Industry and Trade, joint-stock companies command a much more significant role in Marshall’s scheme. Here Marshall (1920a, p.315) argues that joint stock control had become ‘general even in regard to manufacturing and other industries which have an urgent need for alert and versatile administration’. Because such entities tend not to materially dwindle with age, Marshall (1920a, pp.315-316) conceded that joint-stock companies do not face the same order of difficulties as the smaller nineteenth century firms did on the score of maintaining their vigour unimpaired. Nevertheless, costs of production continue to be aligned with the representative firm concept. Importantly, as the following passage indicates, in Industry and Pade, Marshall continues to disassociate himself with the notion that decreasing long-period costs of production could be rationalised simply by an appeal to external economies;

But with the growth of capital, the development of machinery, and the improvement of the means of communication, the importance of internal economies has increased steadily and fast, while some of the old external economies have declined in importance; and many of those which have risen in their place are national, or even cosmopolitan, rather than local.

(Marshall, 1920a, p.167)

There can be little doubt therefore that it was through his biological analogy and the representative firm concept that Marshall hoped to confront his reconciliation problem. In this respect it is essential to distinguish between Marshall’s representative firm and Pigou’s (1928) equilibrium firm, a distinction which some of Marshall’s strongest critics, together with subsequent textbook writers, have failed to recognise! Robbins’ (1928, p.387) claim, for example, that the two were almost identical concepts indicates his lack of understanding of both concepts. This failure can in turn be traced to Pigou’s (1927, p.195) contention that ’the representative firm must be conceived as one for which, under competitive conditions, there is, at each scale of aggregate output, a certain optimum size, trespass beyond which yields no further internal economies.’ Such an interpretation is clearly inconsistent with Marshall’s own description of the representative firm, as is Pigou’s (1928, p.239-240) later construction of the equilibrium firm which was assumed to be in equilibrium whenever the industry as a whole was in equilibrium. Clearly, the equilibrium firm, together with the associated ‘U’ shaped long-run cost curves, represent a significant point of departure from Marshall’s thinking?

V. INCREASING RETURNS, BIOLOGICAL ANALOGIES AND DYNAMICS

It is essential to recognise that Marshall intended his biological analogies to capture the effects of dynamic economic processes. Statical solutions derived from mechanical notions of equilibrium were seen as affording starting points in a rude and imperfect approach to dynamic solutions. The need to place the analysis of the laws of return into a dynamic setting was stated most forcefully in Marshall’s important methodological writings. Marshall (1898)

’ Whitaker (1989) provides a detailed account of some of the differences between the two concepts.

Therefore the following interpretation by Thirlwall (1987, p.324) needs to be strongly rejected; Marshall’s reaction was to take refuge in the short run assuming capacity to be given and to treat increasing returns as externalities, preserving the U-shaped cost curve and the notions of the optimum sizes firm and competitive equilibrium’.

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cautioned that dynamic analysis was required because when a force moves a thing on which it acts, it changes the force which that thing afterwards exercises. Given the existence of returns to scale, thus would imply that movements along long-period supply curves lack operational meaning, calling into question the mechanical notions of equilibrium Marshall was attempting to construct. These difficulties are discussed most directly in Appendix H of Principles where the reconciliationsproblem receives its most formal treatment;

It must however be admitted that this theory is out of touch with real conditions of life, in so far as it assumes that, if the normal production of a commodity increases and afterwards again diminishes to its old amount, the demand price and the supply price will return to their old positions for that amount . . . . . For, when any casual disturbance has caused a great increase in the production of any commodity, and thereby has led to the introduction of extensive economies, these economies are not readily lost. Developments of mechanical appliances, of division of labour and of the means of transport, and improved organisation of all kinds, when they have been once obtained are not readily abandoned.

(Principles, pp.807,808)

However, Marshall (1898) was to abandon the search for the, ‘higher level of analysis’ incorporating dynamic issues on the grounds that dynamic solutions of economic problems were ’unattainable’. Marshall believed that such analysis required the application of ’vast and subtle mathematical engines’ which had limited usefulness in representing the ‘endless complexities’ of economics. However Marshall (1898, p.318) argues that in the more advanced stages of economics, the balance, or equilibrium, of demand and supply obtains ever more of a biological tone;

Consider, for instance, the balancing of demand and supply. The words ‘balance’ and ‘equilibrium’ belong originally to the older science, physics; whence they have been taken over by biology. In the earlier stages of economics, we think of demand and supply as crude forces pressing against one another, and tending towards a mechanical equilibrium; but in the later stages, the balance or equilibrium is conceived not as between crude mechanical forces, but as between the organic forces of life and decay.

To Marshall a tendency towards monopolisation was inevitably the conclusion to emerge from an analysis of increasing returns founded purely on static equilibrium analysis. The limits to monopolisation were seemingly to be found in the organic process of life and decay. Moreover it was through his appeal to biological analogies that Marshall sort to legitimise his attempts at representing the outcomes of a dynamic process within a static equilibrium framework. The representative firm should therefore be seen as the proposed vehicle by which the biological notions of life and decay are captured at a point in time in Marshall’s mechanical representation of equilibrium.

It can be seen therefore that Marshall’s reconciliation problem arose largely from his recognition of the difficulties associated with comparative static analysis, based on logical time, coming to terms with dynamic processes proceeding in historical time. Such difficulties were largely disregarded in the value theory controversies of the 1920s, with the demise of Marshall’s biological analogies and the emergence of the equilibrium firm. As Loasby (1990,

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p.124) concludes, Pigou’s (1928) decision to replace Marshall’s representative firm with his equilibrium firm destroyed the link Marshall had attempted to construct between a process theory of the firm and an equilibrium theory of price. Robinson (1978, p.xi) states this conclusion more forcefully in arguing that Pigou had effectively ‘emptied history out of Marshall’and ‘flattened him out into a stationary state’. It had the effect of diverting attention away from the dynamic implications of increasing returns which Marshall had been attracted to from the writings of Adam Smith.

Amongst the contributors to the value theory controversies in the decades following Marshall’s Principles, the implications of the failure to address the problem Marshall had posed was fully recognised by Young (1928, p.533);

No analysis of the forces making for economic equilibrium, forces which we might say are tangential at any moment of time, will serve to illume this field, for movements away from equilibrium, departures from previous trends, are characteristic of it. Not much is to be gained by probing in to it to see how increasing returns show themselves in the costs of individual firms and in the prices at which they offer their products.

A satisfactory solution to Marshall’s reconciliation problem therefore requires more than the formal inclusion of market imperfections into more elaborate equilibrium frameworks. It instead calls for techniques whereby the effects of dynamic processes can be adequately considered.

VI. CONCLUDING COMMENTS

It would be difficult to concede that Marshall’s biological analogies and the representative firm concept succeeded in their intended purpose of bridging the gap between statical analysis and dynamics. The ‘immortality’ of the emerging joint stock company revealed that Marshall’s ‘general but not universal’ rule of eventual stagnation on the part of individual firms had come to represent the exception. However Marshall’s inability to provide a satisfactory mechanism through which increasing returns could be incorporated into a static equilibrium framework does not diminish the importance of the logical and methodological issues he had raised. Such issues could not be addressed through a simple appeal to external economies, nor were the questions pursued by Marshall restricted to the construction of an industry supply schedule under conditions of pure competition. What was ultimately at stake was the appropriateness of mechanical notions of equilibrium analysis to economic theory. It was Young (1928) alone amongst the participants of the 1920s value theory controversies who recognised this point, a realisation later to be shared by one of the architects of the imperfect competition ’revolution’, Joan Robinson (1978)! The difficulties associated with representing essentially dynamic processes such as increasing returns within a static equilibrium framework continue to frustrate attempts to develop an operational equilibrium framework. A clearer understanding of the precise nature of Marshall’s reconciliation problem may have seen the development of analytical frameworks more able to come to terms with these difficulties. Instead general equilibrium analysis in the Arrow-Debreu tradition has evolved to a system containing those defects which Marshall had attempted unsuccessfully to overcome.

’ Robinson (1978, pp.x-xi) conceded that her early work on imperfect competition was ‘all a deduction from Marshallian assumptions as interpreted by Pigou’.

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