Alfred Marshall's Mecca: Reconciling the Theories of Value and Development*

(i) Market Order and the Particular Expenses Curve

By arranging the given set of firms in terms of ascending levels of unit cost we can draw the long period particular expenses curve represented by the array E–E in Figure 1(a).⁹ The differences between the ‘steps’ signify the degree of unit cost variation in the population and the lengths of the ‘steps’ signify the interfirm differences in installed capacity.¹⁰ The curve is a product of the industry's history, of the pattern of accumulation and of many of the creative forces that we have provisionally locked in the pound, ceteris paribus, particularly innovations in organisation and technique, entry and exit. Of course, its ‘position and shape’ are transient and one of the strongest of the consequences of competitive evolution is to narrow the gap between the least efficient active firm and the most efficient, or best practice, firm.

Since we are assuming a perfect market, a demand curve such as D–D may be imposed on the diagram and the resultant point of coordination defines the normal long period, market clearing price and identifies the ‘marginal firm’, should one exist. It is firm m with demand curve D–D, and this firm exactly breaks even taking account of prime and supplementary costs. However, with demand curve D′–D′ no firm is marginal although firm f is the closest to a state of marginality. Any firm with unit costs higher than the ruling normal price is deemed to be non-viable, to have ceased production and to have scrapped its capacity – hence, the dashed form of the curve beyond D′–D′. Thus, there are two possible configurations of a market order to contend with, and the differences between them play an important role in the analysis of industry evolution. Case I corresponds to curve D′–D′ in which long period market coordination is maintained through price adjustment. It is the flex price case. Case II corresponds to the demand curve D–D in which long period market coordination is maintained through quantity adjustment, that is to say, by changes in utilisation of the capacity of marginal firms selling at a price equal to their long period average costs. This is the fixed price case. The long period order captured in Figure 1(a) is the story Marshall tells in book V. The marginal firm, if it exists, just breaks even and all the other active firms earn surplus profits or composite, long period rents on their past investment in technique, organisation and knowledge. It is the surplus profits earned by the inframarginal firms that play the central role in the following account of Marshallian long period competition.

How does this relate to the representative firm? Not at all, if the purpose of the analysis is solely to characterise a given long period, normal market order. To give purpose to the representative firm we must investigate the transient nature of the particular expenses curve as it is reshaped by the investment strategies of the active firms, and how these strategies interact with the distribution of composite quasi-rents. This requires a theory of the growth of the firm, the purpose of which is to link value theory to the development of the industry.

We capture firm dynamics by a simple rule, a classical rule that links investment in new capacity to profitability but which allows for idiosyncratic variations in strategy. This rule is as follows. If the operating return is greater than a particular cut-off value, the firm expands at a rate determined by the finance it can raise. If the rate of return is less than the cut-off value, the firm does not invest, it is stationary although it may still be profitable. If the rate of return drops below zero, the no longer viable firm exits the industry.

To formalise this, let g_i be the firm's growth rate of capacity and output, and let the accumulation rule be expressed as¹¹

(2)

The ratio φ_i/µ defines for each firm its critical investment margin, equivalent to Marshall's ‘outer limit, or margin, of profitableness’ (P, V, 4, p. 356). The coefficient φ_i is interpreted as a strategic investment parameter, a measure of a firm's willingness to invest at a given rate of return and the coefficient µ, common to all firms, we call the investment coefficient. The smaller is φ_i, the more expansive is the investment strategy. We assume that each firm distributes profits to the owners and draws investment funds from the ‘capital market’ at a rate that depends on its profitability. Finance constrains growth, and the fact that µ is the same for all firms means that the capital market is not discriminating between firms with the same operating profit.¹² We should notice immediately the asymmetrical nature of this investment strategy rule. The growing firm obeys (2) but the declining firm obeys a quite different set of rules in relation to the utilisation of existing capacity and the decision to scrap capacity that is underutilised. This is a crucial Marshallian distinction, the economics of decline are not the economics of expansion in reverse and this asymmetry plays an important role in the following analysis.¹³

In Figure 1(a) we can incorporate this new dimension of firm behaviour if we add the dotted, stepped line, labelled h*, lying above the particular expenses curve to show the normal price for each firm that corresponds to its critical investment margin. In the case of firm f and demand curve D′–D′ we see that this firm is profitable but that the prevailing long period price is below the critical value required to justify investment. Consequently, firm f is a profitable firm but it is also a stationary firm. It seems intuitively clear from Figure 1(a) that the relation between profitability and expansion in the aggregate depends on the joint distribution across the population of the two characteristics φ and h_ẇ, and so it will turn out to be. The significance of allowing the firms to differ in investment strategy, as well as in their unit costs, is that two firms with the same unit costs and profit margin may grow at very different rates in terms of capacity and market shares. While real world competition is certainly many dimensional, a framework with just two of many possible dimensions of interfirm variety is sufficient to provide the richness we need to explore and develop Marshall's linking of value to costs in the representative firm.

The final element we need relates to the dynamics of demand. The implication of (1) is that the rate of growth of demand for any firm depends on the growth of the overall number of customers, N, the change in the firm's share of this total number of customers, d_w, and the change in the intensity of their demand, η(p), which depends in turn on the rate of change of the long period normal price. The first of these we can treat as an exogenous growth rate, the natural market growth rate, g_N, under the supposition that new entrant or exiting customers are distributed across the existing firms in proportion to their current share of the total number of customers in the market. The last we treat by assuming that the elasticity of the intensity of demand, α, is the same for all customers.¹⁴ It is the second element, the shares of each firm in the total market that requires more elucidation. Here a perfect market provides a great simplification since customers are indifferent as to whom they buy from. Consequently, in long period normal conditions, the shares of each firm in total demand are determined by their shares of industry capacity, and it is the evolution of the capacity share that drives the corresponding share of market demand. In this way the evolution of the industry structure is tied to the prevailing long period market order, for how the shares in capacity evolve depends directly on the distribution of profit margins in relation to the distribution of investment strategies. Order results in the revision of order that is the implication contained in (1) and (2). What characteristics does the process of evolution have? The answer is that it has to have characteristics appropriate to a variation selection dynamic, or, as Marshall put it, a principle of substitution in which the processes of accumulation and market growth are mutually determining for the industry and for the differentiated firms.

The immediate consequence of combining the organisation of firm and market in this way is to highlight the possibility that a particular active firm can occupy one of several different, mutually exclusive categories according to its characteristics and the prevailing environment and, moreover, it can change the category it is located in. There are three possibilities:¹⁵

Of these three groups it is the dynamic group that drives the evolutionary process of Marshallian adaptation and it is this group that is the focus of the long period method.¹⁶ The stationary group may account for a large share of the total market but they do not impose development on the industry. For the marginal firms too, investment strategy is of no relevance; rather, their problem will be how to manage the relation between reductions in output and reductions in capacity.

To identify how the population of firms is distributed across the three groups, we introduce the device of a selection set and the operation of partitioning that set. The selection set is simply another way of representing the data from Figure 1(a) in relation to the particular expenses curve and the threshold prices that determine investment behaviour. Partitioning is the way that we introduce Marshall's flux into the depiction of evolution. In developing this evolutionary toolkit, we will uncover the significance of the representative firm, establish its relation to the marginal firm, and see how it is an essential element in the dynamic processes that Marshall sought to describe.

(ii) Finding the Representative Firm, Partitioning the Selection Set

The selection set is a primitive concept in this evolutionary framework. It is defined by the whole population of firms that are subjected to the same causal forces defined by relations (1) and (2). In principle, it may have any number of dimensions but in our terms it is defined by the two variational characteristics, φ_ẇ and h_ẇ. We represent this in Figure 1(b) by the convex space defined by the set of points {s} and the linear boundaries that connect them.¹⁷ Any firm that has existed in this population since the foundation of the industry is represented by a point in this space, the boundary and interior of which may be sparsely or densely populated. In fact, only two firms are required to define a meaningful selection set. Over time, the nature of the set will change as new firms enter, possibly redefining the boundary, and as existing, active firms innovate by changing unit costs or investment strategy. For the moment let us hold all such changes in abeyance and explain the idea of an evolutionary partitioning while holding constant the number of firms.

Despite Marshall's emphasis on interfirm variety within an industry, it was tempting for post-Marshallians to take an essentialist position and argue, as Pigou (1928) did, that all this talk of differentiated firms and their ‘rising and falling’ was an inessential aspect of the working of the market process.¹⁸ Order could be understood without Marshall's resort to variation, its description could be rendered impervious to flux. Unfortunately, the central notion that variation leads to the transformation of order was lost in this approach and with it Marshall's evolutionary intentions. For adaptation and flux is latent in the variety contained in the selection set but how the three broad classes of firms mutually influence each other's differential growth, decline and survival requires some careful elucidation.

It is the prevailing long period normal price taken from Figure 1(a) that provides the first step in the partitioning, for it separates the viable from the non-viable firms. By erecting the locus AV at p on the unit cost axis we deem all the firms located to the right of this locus to be inactive. Cases I and II differ only in respect of the fact that, in the latter, some active, marginal firms are positioned on the AV locus. To the left of AV will lie the dynamic and stationary firms. It is the former that will drive the adaptive process, since it is only this group that invest and in so doing reshape the particular expenses curve and, depending on the co-movements of the demand curve, redefine the long period normal price. Any changes in this price will change the nature of the partitioning and transfer firms between the different possible categories. It is in this way that the evolutionary dynamics is premised on the prevailing market order; hence, Figure 1 is interconnected and our next task is to exploit this fact and further refine the partitioning and separate the dynamic from the stationary firms.

To do so we need the following measures of the population structure. Let s_i be the share of dynamic firm i in the total output of the dynamic group of firms, with s_j and s_k defined as the corresponding shares for a stationary firm and a marginal firm in their respective groups. Let e be the share of the non-dynamic firms in total output, and f be the share of marginal firms in the output of the non-dynamic firms.¹⁹ It follows that we can define the growth rates for each class as g_s =∑ s_ig_i; g_c = ∑ s_jg_j; and g_m = ∑  s_kg_k. Since the growth rate of the stationary firms is by definition equal to zero, we can write the aggregate growth rate of the industry's output as²⁰

In normal conditions this must be equal to the rate of growth of total market demand which is given, from Equation 1, by,

where g_p is the rate of growth of the long period normal price, g_N is the rate of growth of the number of customers in this market, and α is the elasticity of market demand. Relations (3) and (4) capture the fundamental features of the evolution of the industry in which either the rate of change of the normal price or the rate of change of capacity in marginal firms maintains order over time. The distinction between the two cases of market order now becomes important.

(iii) Case I

To identify the boundary between stationary and dynamic firms, we need only equate the growth rate to zero in (2) to define the locus A–A in Figure 1(b), which cuts the horizontal axis at a value equal to the prevailing long period normal price, and has a slope of –µ. By construction, any firm located on or above this locus is stationary although it will be profitable. All the dynamic firms are located below this locus. Thus, a knowledge of the normal price provides the basic partitioning of the industry into non-viable firms in area N, marginal firms on the locus AV, stationary firms in the area C and on the locus AA, and dynamic firms in the areas D. Now that we have identified the subpopulation of dynamic firms, we can use the output shares s_i to define the average values of unit costs and the propensity to accumulate as and , respectively.

Because the stationary and marginal firms have no active role in the accumulation process, we can focus on the dynamic firms, and if we aggregate (2) across this group, using the weights, s_i, we find that their average growth rate is given by

(5)

By using (5) to eliminate p from (2), the growth rate of each dynamic firm, in normal conditions, can be expressed in terms of the deviations of φ_i and h_i from their corresponding dynamic group population averages; thus

(6)

Equation 6 is fundamental to the evolutionary interpretation of Marshall's theory, since it captures the different contribution that each dynamic firm makes to the reshaping of the particular expenses curve and to changing the structure of the industry. It also embodies a distance from mean dynamic or replicator principle that is the signature of a variation cum selection-based evolutionary processes. The expansion of any one firm relative to the growth of capacity as a whole depends on how its characteristics compare to the population averages: a higher than average efficiency and a greater than average propensity to invest support growth at a rate greater than the group average.²¹ The relative rising and falling of firms also captures Marshall's principle of substitution in which the growth rate of each firm is mutually determined with the growth rates of its rivals. The growth rate diversity that ensues is the clue to Marshall's evolutionary dynamics.

By equating (6) to zero we can derive an alternative expression for the locus A–A in terms of the characteristics of the dynamic firms and their deviations from average behaviour in the dynamic group. Taking account of (3) we can write the stationary–dynamic boundary as

(7)

There is one further element in the partitioning to be uncovered, that which separates rising from falling firms, and this is where the representative firm makes its first appearance.

(iv) The Representative Firm

Where in the selection set can we locate the representative firm? To answer this question we have to deal with two problems. The first problem relates to the fact that the firms are differentiated in two dimensions, creating the possibility that representative behaviour serves only to define a trade-off between unit costs and investment strategies. The second problem is deeper, and connects to the very idea of Marshall's industries as populations of firms. By a population, we simply mean a set of entities constituting an ensemble. By an evolutionary population, we mean a set of entities whose changing relative importance in the set, however measured, is the caused outcome of specific selection and other causal processes operating equivalently on all the members of that population. Marshall's industries in this view are evolutionary populations unified by the action of common market forces. Hence, the problem: a representative firm is only representative relative to some evolutionary population, and if we change the population in terms of its constituent firms or the causal processes acting on them, then we change necessarily what we mean by representative.

Recall the definition above, a representative firm is some average firm that maintains constant its share in the output of the relevant population. From this we see immediately that two notions of representativeness come to the fore. One is Marshall's representative firm that grows as quickly as the total market, a definition that makes no distinction between the different categories of active firm, whether dynamic, stationary and marginal. Marshall's representative firm maintains constant its share in total market capacity and demand for the industry. The other is a dynamically representative firm, one that grows as quickly as the population of dynamic firms in the population. The dynamically representative firm maintains constant its share in the total output of the dynamic group. The two notions of what it is to be a representative firm are quite different and only equate to one another when the only active firms are in the dynamic category. One can see immediately, that, in general, the dynamically representative firm must expand more rapidly than Marshall's representative firm, which, of course, is growing at the same rate as the industry as a whole.

To locate the dynamically representative firm we proceed as follows. We have already identified the relevant population as the subset of firms located below the locus A–A in Figure 1(b). However, this ensemble of dynamic firms consists of two subgroups, occupying the regions labelled D₁ and D₂, according to whether the firms in question are rising or falling in terms of their relative outputs. To separate these two groups is to identify the dynamically representative firm. Because such a firm is growing at the average rate for the dynamic subpopulation, we set g_i = g_D/(1 – e) in (6), to define a locus labelled R–R in Figure 1(b). This locus passes through the point of population means for the dynamic subpopulation so that dynamically representative behaviour is described in terms of the capacity share weighted average characteristics of the firms in the dynamic group. This result is not arbitrary but flows from the underlying theory. The position of this locus is independent of the market growth rate and the structure of the active population, and it is given by

(8)

It also has a slope of –µ, and it stands vertically below A–A by a distance that measures g_s, the growth rate of the dynamic group. Like A–A, the locus R–R is a statistical construction, a demarcation, in this case, between two classes of dynamic firms. Any actual firm whose unit costs and strategic investment stance place it on this locus will be growing at the same rate as the dynamic group as a whole, and so may be labelled dynamically representative. Either side of the R–R locus we find Marshall's flux. Any firm in the region D₁ between this locus and A–A is expanding absolutely but declining relatively to the output of the dynamic group as a whole. Any firm below R–R in the region D₂ is expanding absolutely and relatively to the dynamic group.²² However, pace Marshall, ‘representativeness’ does not define a single firm but rather a whole possible family of them, in fact those hypothetical firms that lie on the locus R–R.²³ Of course, no actual firm need lie on this locus at any one time, nor does our account require that there is such a firm. This locus simply defines the possibility that any firms that should happen to be on it will be growing absolutely but neither rising nor falling relatively in the dynamic group. This is the dynamic significance of the representative firm, a significance that is entirely lost in a static treatment of competition as a state rather than as a process.

If A–A identifies the stationary–dynamic boundary and locates the zero growth firms, we might now enquire which of the firms in the selection set will have the highest long period growth rate. Since growth rates increase as we move towards the origin from A–A, it follows immediately that it is firm b on the south-west boundary of the selection set that is the fastest growing, and is thus the dynamic firm on which the output of the industry is concentrating. Given the shape of the selection set, the location of this firm depends only on the investment coefficient, µ, that is to say on the assumed characteristics of the capital market and the investment requirements for expansion of the firms. It is immediately apparent that, in general, the fastest growing firm is not the least cost firm in the selection set, for this is firm a in Figure 1(b). As in any variation cum selection analysis, the competitive dynamic selects for the characteristics that maximise expansion (fitness), not the characteristics that only maximise efficiency. Indeed, only if all firms followed the same investment strategy would efficiency be maximised in this adaptive process.²⁴

We have already indicated that our dynamically representative firm is not, in general, Marshall's representative firm. Where now do we locate Marshall's representative firm, that firm that maintains its share in the total market rather than any one submarket? Necessarily it too must be a dynamic firm, for it must be growing if the market is growing, although it is necessarily growing less rapidly than the dynamic representative firm we have just identified. To identify its properties we set g_i = g_D in (6) to define the locus labelled M–M in Figure 1(b). This locus is given by the equation

(9)

This locus lies in region D₁ above the locus R–R and below the locus A–A, its position depending on the share of non-dynamic firms in the overall population of active firms, and on the overall growth rate of market demand. Any firm on this locus is maintaining a constant share in total industry capacity and thus market demand but has a falling share of the capacity within the dynamic group of firms. Where this locus cuts the unit cost axis is defined by the point h̃* in Figure 1(b).²⁵ Around Marshall's representative firm there is flux too, not in terms of shares of output in the dynamic subpopulation, but in terms of changing shares of total industry output. It should now be clear why it is only in an industry consisting entirely of dynamic firms that the two concepts of the representative firm coincide. As soon as we allow for non-dynamic firms they diverge, and it is the notion of the dynamic representative firm that we must give primary attention to for it is the dynamic firms that are the carriers of long period adaptive forces. The dynamically representative firm therefore acts as the fulcrum around which the industry is evolving and around which all of the flux in the industry can be rendered intelligible.

The idea of a representative firm, in either form, is derived from the idea of a long period partitioning of the selection set. Partitioning provides a complete characterisation of the rising and falling of firms, their viability and non-viability. Indeed, Figure 1a and 1b are complementary ways of representing the relation between a market order and its self-transformation. Partitioning is also the way we give content to the idea of economic structure not only in terms of relative scale but also in terms of dynamic characteristics of different firms and groups of firms. This is Marshall's point, the industry is always coordinated but the firms are all different, in terms of growth or decline and whether they are dynamic, stationary or marginal. It is from this heterogeneity that the progress of the industry is derived. Before we turn to the question of the necessary restless nature of this partitioning it will be useful to introduce a simplifying analytical device.

(v) A Simplifying Device

The simplifying device is as follows. For any dynamic firm we identify a hypothetical shadow firm, its identical twin we shall call it, which always has the same growth rate when faced with the same long period normal price. Consequently, every statement made for the original firm can be rendered equivalently in terms of its twin. Each twin firm, however, is defined only in terms of a corresponding hypothetical unit cost level and can thus be located on the ordinate axis in Figure 1(b). To define each twin firm we set a zero value to the strategy parameter φ_i and compensate for the effects on its growth rate by assigning to it a hypothetical unit cost level denoted by , where²⁶

((10a))

It follows that we can define the dynamically representative twin in equivalent fashion as one with average, twin unit costs equal to

((10b))

This particular value denotes the point at which R–R cuts the unit cost axis in Figure 1(b). Any dynamically representative firm, positioned on R–R, is dynamically equivalent to the twin firm defined by h*, while Marshall's representative firm, positioned on M–M, is dynamically equivalent to the twin firm defined by the hypothetical cost value, h̃*, where

((10c))

This simplifying device will help greatly in the following exposition and to illustrate this claim we use it to explore case II.

(vi) Case II

Very briefly, we must outline the case when some marginal firms are active and the demand curve is positioned as is curve D–D in Figure 1(a). This is the regime of quantity adjustment referred to above, in which the unit cost level in the active, marginal firms measures the long period normal price. It is not as straightforward a case as it might seem, and I will have to suppress many difficulties by sticking with the long period normal assumption that when output contracts absolutely, capacity contracts in step. On this assumption, marginal firms exit the industry when their output has contacted to zero, when their economic weight has disappeared. To state the method so boldly is simply to highlight its deficiencies, and to mask the importance of the processes associated with the demise of firms to the course of industry evolution. Accepting the magnitude of this unfinished business, we can still make some progress using the selection set and its partitioning.

All that changes in terms of Figure 1(b) is that we ‘lock’ the price at the unit cost level in the marginal firms to set p = h_m, and since the locus A–V is now populated by these firms, their share in total output, f, is rendered positive. On the demand side there is a further consequence of the ‘locked’ price, namely, that g_N = g_D, and the rate at which the demand curve is being displaced, the natural growth rate of the market, is an important determinant of the fortunes of the marginal producers. What determines their aggregate growth rate? Since they are not investing, their problem is one of capacity utilisation and, since the price is ‘locked’, we can use (6b), (3) and (4) together with the twin cost values to determine their collective growth rate, which is given by

((11a))

As illustrated in Figure 1(b), this growth rate is negative, that is to say, the long period normal price supports a growth rate of the dynamic firms consistent with the decline of marginal producers.²⁷ Since g_N = g_D, it follows that the vertical distance between A–A and M–M now measures the natural market growth rate and any Marshallian representative firm located on M–M will be growing at the rate g_N. Let the twin unit costs corresponding to this case be signified by h̃**. It follows that the value of h̃**, where M–M now cuts the unit cost axis in Figure 1(b), is equal to

((11b))

By setting g_N = g_D in (10c) we can also express this in terms of the twin costs of the dynamic representative firm rather than the costs of the marginal firm; thus²⁸

((11c))

For completeness, we can also represent the growth rate of the marginal firms entirely in terms of the various, twin cost values using (11b) as

((11d))

How the market order evolves in the presence of marginal firms thus depends on the relation between their twin unit cost level, the natural growth rate of the market and the structure of the industry, as expressed in the output share of the non-dynamic firms. As this process evolves, we reach a point in time when all the marginal capacity has been eliminated and the order reverts to case I as described above. It will not be lost on the reader that a dynamically representative firm even plays a role in the fate of the marginal firms, a hint of its acting as a fundamental determinant of the industry's dynamics.

The point that we have attempted to establish so far is that Marshall's framework of industry analysis was designed to identify the evolutionary consequences of interfirm heterogeneity in behaviour. It is a rich framework, by no means limited to two dimensions of firm variation, and it is indeed a pity that Marshall is usually misinterpreted as conceiving of his firms in terms of cost differences alone. This is why we have added the second dimension of investment strategy to demonstrate Marshallian variation in relation to the long period forces of investment. There need be no limit to this process of generalisation; we can accommodate as many dimensions of interfirm variation as we wish, provided that they are relevant to the process of competition. Indeed, variations in product type and quality would be of prime importance in this regard.²⁹ This is the great virtue of a Marshallian approach to economic evolution: the greater the variety. the more we are likely to explain about real world competitive processes. Variation is not the nuisance that the essentialists would have us believe, it is the route to understanding why the economic world changes in the way that it does. Marshall clearly sensed this fundamental fact and its relation to the ceaseless development of the system (Shackle, 1965, p. 42). But further elaboration of the framework is not our task here; rather, we must recognise that the market order and its partitioning is an evolving order. It is this elemental fact that raises so many potential difficulties in comprehending the nature of the representative firm, for it means that the representative firm is always changing its character. How is this evolution to be understood?

(i) Normal Value

How does normal value evolve? From Figure 1(a) it does so in a fashion that depends on the relative rates of change of the market demand curve and the particular expenses curve but how the later evolves depends on the changing nature of the partitioning in Figure 1(b). If we provisionally hold constant the structure of the industry, then we can obtain a partial grasp on the immediate evolution of long period normal value. Again the distinction between our two cases of market adjustment matters.

The fixed price case, II, with normal value locked by the cost structures of active, marginal firms is easily treated. As long as these firms are viable, the long period price is fixed by their costs and, consequently, no question of convergence to costs in the representative firm or any other firm for that matter can arise. This is the quantity adjustment case, and it continues to hold until we re-establish the conditions for case I. This later is more challenging, for now the process of investment in the dynamic subpopulation of firms redefines the particular expenses curve and changes the long period price, in a way that also depends on the rate at which the demand curve is changing. Thus, the rate of change of the long period normal price serves to maintain the market order by matching the rate of growth of total capacity with the rate of growth of demand. The combination of cases II and II in fact leads to a very clear outcome. Phases in which long period normal value is changing (case I) are punctuated by periods when it is stationary (case II). Consequently, the normal case, in which successive groups of marginal producers are eliminated, entails that the long period price follows a series of downward steps over time. Between the steps it varies at a rate determined by the relation between the growth of capacity and demand.³⁰

How the long period, normal price evolves in case I is readily established. On equating (3) and (4), and noting that g = (1 – e)g_s > g_N, we derive the following logistic differential equation to capture its evolution.³¹

((12a))

where h** is the twin cost value defined by

((12b))

This twin cost value stands above unit costs in the dynamically representative firm by an amount that is greater the greater the natural growth rate of the market and the smaller is the share of the dynamic firms in the total output of the industry.³² This is the sense in which unit cost in the dynamically representative firm serves as the anchor for the system of price adjustment.

What can we say in the light of these results about Marshall's connection between long period value and the costs of the representative firm? Since p > h**, the normal price declines over time, and h** acts as its attractor; and, moreover, the system is globally stable for given values of g_N and e.³³ The rate of convergence to h** increases with the share of the dynamic firms in total capacity, it increases with the investment rate parameter, and it is smaller for larger values of the elasticity of demand. All this fits with the economic logic of long period evolution.

The wider significance of this formulation is that it is the dynamically representative firm, rather than Marshall's representative firm, which underpins the attractor for long period normal value. This attractor corresponds to a price, and a profit margin, that would enable a representative firm to grow at the same rate as the natural market growth rate, g_N.³⁴ This is the sense in which Marshall's theory correctly interpreted the evolutionary dynamic of the competitive process, yet there are important differences that we have uncovered between the different notions of a representative firm. Most importantly, the long period normal price converges on h** > h̃* > h* > h̄_s and it is not attracted to costs in the twin representative firm except when the natural market growth rate is zero. Here again, Marshall's intuition was sound, when the market is stationary, the long period normal value is attracted to costs in the (dynamically) representative firm h*. However, it is the twin cost values not the actual costs that define the attractor, and the fact that twin and actual costs diverge is the direct consequence of allowing firms to have investment strategies, as they do in Marshall. Only if the strategic investment parameters, φ_i, are zero for each dynamic firm, will true unit cost in the dynamically representative firm be the attractor for long period normal value.

There is yet a further complication to Marshall's desire to equate long period normal value with unit cost for the representative firm. It is that the process defined by (12) of convergence of value to ‘representative costs’ is itself a partial process; one that is continually being revised by the long period forces that evolve the particular expenses curve. These forces are repartitioning the selection set continuously, so redefining the representative firm, and revising the structure of the industry and with it the relative importance of its dynamic firms. Consequently, the values of h** and e in (12) evolve too, and they only stop evolving when all the variety has been driven out of the population, and the industry has converged on the most dynamically efficient of the firms, firm b in Figure 1(b). It is in this process of convergence that the dynamic representative firm plays its second role as the fulcrum around which the industry is continually restructured and, moreover, it is a fulcrum that is continually changing under the influence of Marshallian flux.

(ii) Marshallian Flux

We have seen how partitioning generates a snapshot picture of the evolutionary structure of the industry and how different firms may fall into very different economic categories, yet an evolving system is one in which this partitioning is always changing. Repartitioning is the consequence of Marshallian flux, the restless dynamics of an industry in which firms differ in efficiency and investment strategy, and these fundamental evolutionary processes are of three distinct kinds: those due to market selection and the implied differential growth of firms; those due to the transfer of firms between the dynamic, stationary and marginal categories; and those due to the differential growth of the different groups of firms as a whole, and the consequent restructuring of the industry between the dynamic, stationary, marginal and non-viable groups. Each one is a different reflection of the principle of substitution, and not one of these processes could arise in an essentialist world of identical firms. Moreover, each one reflects the fundamental evolutionary principle that variation drives change, and to illustrate this principle we take each dimension of flux in turn.

The Dynamics of the Selection Process: Fisher's Principle

It is not unrealistic to claim that Marshall was very close to formulating an explicit theory of market evolution as a variation cum selection process; he certainly understood the significance of firm heterogeneity in relation to his principle of substitution, the closest he came to articulating the concept of dynamic selection in the Principles and in Industry and Trade (1919). Unfortunately, as many have argued, he lacked the means to spell this out in any detail.³⁵ Yet within a decade of the publication of the last edition of the Principles, the biologist Fisher (1930) set out the necessary apparatus, an apparatus that became central to the subsequent development of evolutionary theory. Fisher's great contribution, judged with the benefit of hindsight, was to formulate evolutionary theory in terms of the distance from mean dynamics of the replicator principle. It is this crucial, conceptual innovation that immediately connects him to Marshall, the principle of substitution and the representative firm. At the centre of this scheme is a fundamental aspect of evolutionary dynamics; namely, that the evolution of the population depends on how the characteristics of its members are jointly distributed around the associated population means. From this it follows that the dynamic representative firm, far from being the fifth wheel of Marshall's analysis, is in fact the conceptual fulcrum around which an industry evolves. To establish this is straightforward. Beginning with our fundamental replicator relation (6a) we can rewrite this to express the evolution of the market shares of the dynamic firms as

((13a))

In terms of the twin equivalents this becomes

((13b))

This formulation makes the replicator dynamics of industry evolution particularly transparent, remembering that (13b) only holds for the dynamic firms satisfying p > . Thus, we see immediately in (13b) how the dynamically representative firm is the fulcrum around which the dynamic group of firms evolves, rising or falling relatively according to how each individual firm stands in relation to the said representative firm when both are expressed in twin terms.

The fact that the dynamic firms are rising and falling relatively around the dynamically representative firm, naturally implies that the value of h* = ∑ s_i is changing too, even when the individual values of are constant. That is to say, the measure of this dynamically representative firm is not constant but evolves according to

(14)

where V_s(h) is the variance of the hypothetical, twin cost values around h*.

This is an exact example of what biologists call Fisher's Fundamental Law of Selection, that the rate of evolution due to selection of some average population characteristic is proportional to the variation of that characteristic around the population average. In Marshallian terms, the dynamic representative firm evolves in a way that depends on the distribution of variety in firm's characteristics and on the economic significance of that variation for interfirm performance.³⁶ What (14) captures is the centrality of the dynamically representative firm to an understanding of a Marshallian theory of competition: not perfect competition but open competition, competition that is only possible because the firms are different in their business traits and competitive characteristics.³⁷

It also follows from (14) that the competitive process imparts a direction to the evolution of the industry. Indeed, competition serves to reduce h* over time, from which it follows that the locus R–R is always contracting towards the origin at a rate which is proportional to the variance of the twin cost values. The set of rising firms is being squeezed ever smaller by the competitive process as the industry concentrates on the dynamically fittest firm(s) in the selection set. Having established what happens in terms of the twin cost values, it is also of interest to enquire into the evolution of the true characteristic averages and , for it is clear from the definition of h* that the following conservation condition must hold; namely,

(15)

We know that this expression is negative, but this does not tell us how the component averages on the right-hand side evolve individually. To illustrate the problem, we can focus on the evolution of average unit costs in the dynamic group.³⁸ By virtue of (6) we find that the evolution of average unit costs h̄_s is represented by

(16)

where C_s(g, h) is the covariance between unit costs and growth rates across the population of dynamic firms. This is, once again, Fisher's principle at work, the rate and direction of evolution depends on the co-distribution of variation across all the characteristics in the relevant population; that is to say, it depends on correlation of characteristics, not just upon variation of characteristics. The covariance defined in (16) is what we might call a secondary moment, because it is defined in respect of variables, the firm growth rates, which are also determined by the causal forces acting on the population. If we use (6) to eliminate the growth rates, then we find that

((17a))

where and are primary moments of the subpopulation of dynamic firms.³⁹ From relation (17a) it is not immediately apparent how the population average h̄_s evolves. The variance term is reducing the average but this effect can, in principle, be offset by a sufficiently large negative value for the covariance term. Thus, while h* is invariably declining under the forces of selection, no such simple rule applies to h̄_s. To make this finding even more precise, we can imagine the experiment of regressing the output share weighted values of s_iφ_i on the values of s_ih_i, within the dynamic portion of the selection set (the region below A–A in Figure 1b) at a particular moment in time. The resulting coefficient for the slope of the regression line at that moment is

and so we can rewrite (17a) as

((17b))

This is a much neater way to capture the force of Fisher's principle, and it follows that h̄_s is decreasing if β_s > –µ. Otherwise, it is increasing, and, on average, the industry would be growing less efficient at that moment.⁴⁰ Thus, we see how statistical dependence and variation combine together in Marshall's evolutionary dynamics to redefine continually the dynamically representative firm and its component characteristics. Not by variation alone but by variation and correlation. That is why it is a dynamic concept and can play no useful role in a static theory of a competitive industry.

Transfer Effects

The rise and fall of individual firms, whether relatively or absolutely, is the central form of economic flux that we find in Marshall's theory of industrial change. The logic of our argument, however, uncovers flux of different kinds that we may dwell on briefly. The most interesting are consequent on any change in the long period normal price, for we have seen how that will repartition the selection set and potentially transfer active firms between the dynamic, stationary and marginal groups. Thus, for example, a lower market price relocates the A–A locus to the left, potentially transferring dynamic firms into the stationary group and stationary firms into the marginal or non-viable groups, and, thereby, changing the associated statistical distributions of firm characteristics. This repartitioning adds a further source of change to the population averages over and above those created by Fisher's principle and we can illustrate this briefly by focusing again on average unit costs.

Suppose the transfer is from the dynamic to the stationary group. Let the firms transferring into the stationary group have an aggregate output rate of Q at the moment of transfer. This rate of transfer, when expressed as a proportion of the output of the dynamic group, we define by the rate x_s, and when expressed as a proportion of the output of the stationary group by the rate ϑ_c.⁴¹ Let h̄_Q be the average unit cost level for the group of transferring firms, constructed by weighting the unit cost levels by their output shares within the transferring group. The total change in the respective average unit cost levels in the dynamic and stationary groups is then given by the augmented Fisher rule

((18a))

for the dynamic group, and

((18b))

for the stationary group.⁴² How h̄_Q compares with the pretransfer averages in the two groups we cannot say because it depends on which firms make the transfer. There is certainly no presumption that they are the higher cost firms from the dynamic group, it all depends on the distribution within the selection set and the corresponding correlation of characteristics within the two groups before and after the transfer.⁴³

Structural Change Effects

Having dealt with selection and transfer effects, it remains to record how the overall shares of the different groups change as a result of the different growth rates in their respective outputs. To illustrate, let us focus on the evolution of e, the share of non-dynamic firms in industry output. If we limit ourselves to case I, then it follows that⁴⁴

or in continuous time⁴⁵

(19)

Similar expressions follow to capture the changes in the other measures of overall structure, as the reader may testify, but now it is appropriate to sum up.

The net outcome of the structural, transfer and selection effects is to repartition continually the selection set, to modify the process of convergence of p on h** and to evolve h** as indicated in (12). Thus, the establishment of order and the transformation of order are firmly intertwined. We can no more explain changes in the prevailing long period normal price without reference to the changing particular expenses curve than we can explain the changes in the particular expenses curve without reference to the changing normal price. This is the great virtue of Marshall's long period economics, transformation depends on order, the two notions are inseparable. It was the attempt to separate them in the hands of the post-Marshallians that effectively marginalised Marshall's economics and destroyed its links with evolutionary theory.