5.I INTRODUCTION

The discussion in Chapter 4 concerned the market-area or supply-area patterns of activities in which there is strong spatial repulsion among the individual units. In sharp contrast, however, other activities show highly clustered patterns.

Cluster is, of course, the logical pattern for units of an output-oriented activity whose markets are concentrated at one or a few locations, and correspondingly for units of an activity oriented to inputs whose source locations are few. There is a high concentration of producers and suppliers of such theatrical inputs as actors, stage designers, and theatrical makeup specialists in Los Angeles and New York because so much movie making and theater activity is concentrated there. The making of vintage wines is confined to the relatively few areas where the right kinds of grapes will flourish.

There are other situations, however, where the basis for clustering is the mutual attraction among the competing units of a particular activity, and this attraction outweighs any repulsion that might arise from their rivalry. Thus a frequent practice of chain-store firms is to locate branch stores as close as possible to a competitor’s branch store. A tendency toward agglomeration is unmistakable in the juxtaposition of car sales-rooms along "automobile rows" and in the formation of financial districts, nightlife districts, civic centers, produce markets, and high-class shopping areas in cities. The larger the city, the more specialized and numerous are such neighborhood agglomerations. In New York, large advertising agencies are so clustered along a section of Madison Avenue that the street has given its name to the industry. Similarly, a section of Seventh Avenue is preempted by the garment trades, part of Forty-seventh Street by diamond merchants, and so on for many other specialties. The common feature of all such clusterings is that each unit finds the location good because of the presence of the others. There is a positive mutual attraction rather than a repulsion. The explanation of such mutual-attraction clusters lies in special characteristics of the activity itself, its markets, or its suppliers.

5.2 EXTERNAL ECONOMIES: OUTPUT VARIETY AND MARKET ATTRACTION

In some activities, the basic reason for the agglomerative tendency is that the outputs of individual units are not standardized; they are not perfect substitutes for one another, and moreover, they differ in such manifold and changing ways that they cannot be satisfactorily compared by the buyer without actual inspection. The locational significance of this characteristic can best be seen by a pair of contrasting examples.

A manufacturing firm buying sheet steel simply decides on its specifications and then finds out which steel producer will give the best price and fastest delivery. A visit to warehouses or rolling mills to look over the sheets and make a selection is unnecessary, because the specifications themselves (plus conceivably a sample sent for testing in the buyer’s plant or laboratory) fully identify the characteristics of the steel. Consequently, the transfer costs involved are those of shipping the steel from producer to user, and there is nothing in the situation that would make it desirable or convenient for the rival sheet steel producers to be concentrated in one place.

Contrast this with a man or woman buying a car or a new hat, a department store selecting its line of fall fashions, or a fashion designer searching for something simply devastating in novelty buttons. In any of these cases, the buyer does not know exactly what will be purchased. He or she will be selecting one item (in the case of the car) or maybe more (in the case of the hat) or a very large number (in the case of the department store’s fall line). The items cannot be adequately described in a catalog, and it would be much too expensive and time consuming for the producers to supply each prospective buyer with a full set of samples. Under these circumstances, the "demand" is not so much demand for specific items as it is demand for a varied display of products; and the wider the variety presented at a particular location, the more demand that location will attract.

Therefore the buyer makes a shopping trip, preferring the largest display center accessible to him. The more he is prepared to spend, the farther he will be prepared to go in the interest of variety. Thus most of us would be willing to journey farther out of our way to select a camera than a necktie; still farther to select a new car; and still farther to select a job with career possibilities.

It is clear that the activity that is presenting the displays will tend to adopt a clustered pattern, with its units positively attracting one another. A newcomer to the cluster may even be welcomed, because that seller will enrich the variety and draw still more demand to the location.

It should be noted also that where comparison shopping is important, the significant transfer costs are borne by the buyer, and the major element in transfer costs is personal travel time. The transfer of the goods bought may be handled by the buyer himself (he may drive his new car home or carry his other purchases). In any event, however, the transfer cost is not enough to counteract the advantage (to both buyers and sellers) of having the selling units agglomerated.

When the purchases are transferred separately, it is of course feasible to separate production or delivery, or both, from display. Thus new car dealers sometimes have to order from the nearest assembly plant after the buyer has made his choice; and in recent years more and more garment producers have moved their factories out of the city in order to reduce production costs, and maintain in the city only the functions of display and associated entertainment for the out-of-town buyers.

These examples illustrate one important kind of external economy of agglomeration of an activity—"external" to the individual unit involved because the advantages depend on how many other units of its type are joining it to make a cluster that attracts demand.¹

5.3 EXTERNAL ECONOMIES: CHARACTERISTICS OF THE PRODUCTION PROCESS

5.3.1 Introduction

The externalities associated with the size of a cluster are by no means limited to those that enhance demand as a result of the characteristics of shopping behavior. Some closely analogous external economies of agglomeration involve cost and supply considerations, and these tend to affect many of the same activities.

If products are complexly differentiated and changeable from one day or week to the next, the chances are that at least some of the inputs also share those characteristics. Thus a fashion garment shop will have a constantly changing need for different fabrics, thread, buttons, zippers, and the like. With the nature of the output continually changing, manpower needs can vary unpredictably and suddenly; with speedy delivery at a premium and production scheduling intricate, equipment repairs and parts must be quickly available. Since perhaps the most important task of the manager is to estimate what the buyers will want and what his or her rivals will offer, a crucial input is fresh information, gathered largely by mixing with the right people and keeping the eyes and ears open.

Every one of these input requirements, plus others, is best satisfied in a tight cluster. The basic reason can be made clear by the following example. Suppose we have a small plant that manufactures ladies’ coats. A long sequence of separate operations is involved, including such operations as cutting and binding the buttonholes. Specialized equipment exists for making buttonholes rapidly and cheaply in large quantities, but it represents a sizable investment. Individual coat manufacturers would not find it worthwhile to invest in such a machine, since they could not keep it busy all the time; they have to resort to making their buttonholes in a slower way, involving greater labor cost. However, if they locate in a cluster with enough other clothing manufacturers, their combined need for buttonholes may suffice to keep at least one of the specialized buttonhole machines reasonably busy. Then a separate firm specializing in buttonhole making joins the cluster. The clothing manufacturers contract that operation out to that firm, to the advantage of all concerned, including the customer who gets the coat cheaper.

This example can be extended to embrace dozens of other individual operations that likewise can be delegated to specialized firms when there is a cluster, enabling a sufficient number of firms using the specialized service to enjoy convenient access to the specialist.

5.3.2 External Economies and Scale

Some highly significant facts emerge from this discussion. First, we have explained an external economy for the clothing manufacturers in terms of the internal economies entailed in specialized operations (the buttonhole-making establishment and other such auxiliary suppliers must have at least a certain minimum amount of business or they cannot cover their fixed costs). Second, the result of the mutually beneficial symbiosis of the garment makers and the buttonhole maker is that the former are now also more specialized. They are confining themselves to a narrower range of operations, and for any given level of output of coats they will have smaller plants and fewer employees; that is, the productivity of inputs will be enhanced. There is another advantage in this. The principal constraint on the size of their plants is the complexity of management decision making in an industry where the products are continually changing (in response to or in anticipation of a volatile demand), orders are small, and the production cycle is of extremely short duration; specialization should enhance efficiency here as well. A further constraint, in many cases, is the supply of capital for the individual entrepreneur.

For a given establishment or firm, these gains in production efficiency may be illustrated graphically by reference to Figure 5-1. If, as the result of specialization, the location unit within an activity cluster can take advantage of internal economies of scale, subsequent increases in productivity will move the unit down along its average total cost curve. Thus in panel (a) of Figure 5-1, location within the cluster has made it possible to increase the rate of output from Q₀, to Q₁, with a consequent decrease in average total costs from ATC₍₎to ATC₁.

The increased efficiency in production that results from the cluster of activity may show up also as a decrease in average total costs at each rate of output. As shown in panel (b) of Figure 5-1, this would imply a downward shift in costs from ATC to ATC’. Such a change could stem from several sources. For example, if scale economies are achieved by members of the cluster, the products and services they produce will be available to all buyers at lower cost. Hence the per unit cost of inputs will fall for any buyer using their outputs, including those buyers who are also members of the cluster. Similarly, any savings in transfer costs realized by members of the cluster would have the effect of lowering average total costs. Other such sources of economies might include the ability of group members to maintain smaller inventories in the face of demand or supply uncertainties, increases in labor productivity resulting from specialization in the work place, or increased efficiency in management and organization.

It is also important to note that in an industry where these agglomeration economies are realized, there is little or no rationale for the development of multiplant firms. As we have pointed out, the economic size of the individual plant in such industries is effectively limited by the problems faced by management. There is no point in the firm’s establishing branch plants; all the activity is at one location, and the management must constantly give close attention to what is going on inside the plant. This situation contrasts sharply with that of a business such as food retailing, where the constraint upon the size of an individual store is the maximum size of its market area (reflecting transfer costs). The multistore firm enjoys great advantages in mass purchasing, advertising, research, financing, and management; the optimum firm size far exceeds optimum store size.

In summary, we can distinguish three levels at which economies of size appear in respect to any particular activity.² These are (1) economies associated with size of the individual location unit (plant, store, or the like); (2) economies associated with the size of the individual firm; and (3) economies associated with the size of the agglomeration of that activity at a location. We can refer to these, for brevity’s sake, as unit, firm, and cluster³ economies, and the size at which each of these economies peaks can be thought of as the optimum unit size, the optimum firm size, and the optimum cluster size.⁴

These optima are determined by the characteristics of the activity, including its locational sensitivity to transfer costs and other locational factors. When firm optimum is larger than unit optimum, there are multiunit firms with operating branches, ordinarily in different locations, as in retail chains and some kinds of manufacturing. Otherwise, the single-unit firm is the norm. When cluster optimum exceeds the optimum for units or firms, there are multiunit and/or multifirm clusters of the activity; otherwise, separate locations are the norm, as is illustrated by primary processing plants for farm or forest products.

5.3.3 Lichtenberg’s Study of "External-Economy Industries"

The classic analysis of the clustering of certain manufacturing industries on the basis of agglomeration economies external to the individual location unit and firm was made in the late 1950s by Robert M. Lichtenberg for the New York Metropolitan Region Study. Table 5-1 (below) lists the 87 industries that he identified as dominated by external-economy factors of Location and that are relatively concentrated in the New York metropolitan region.

*Approximate figure estimated by Lichtenberg: exact figures unavailable because of Census disclosure rules.

⁺n.e.c.: not elsewhere classified.

Source Robert M. Lichtenberg, One-Tenth of a Nation (Cambridge, Mass.: Harvard University Press, 1960), pp. 265-268; based on data from U.S. Census of Manufactures, 1954.

"Relatively concentrated" means that the region’s share of national employment in the industry exceeded 10.4 percent—which was the region’s share of total national employment and accounts for the title of Lichtenberg’s book.⁵

Lichtenberg’s study provides documentation and illustration on some of the points we developed earlier. Table 5-2 sums up some salient characteristics of those manufacturing industries that he rated as least affected by transport orientation. It covers, in his words, "all industries for which the dominant locational factor is inertia, Labor, or external economies, and those for which no dominant locational factor could be assigned." It is clear from this tabulation that prevalence of single-unit firms (which we previously noted as a characteristic of industries clustered because of external economies) is associated with small size of plant, high labor intensity (as suggested by small energy use per worker), and (for consumer goods industries) small inventories implying fast turnover.

Table 5-3 examines the relation between degree of concentration in New York and proportion of single-plant firms, in the same set of industries as in the preceding table. Industries most heavily clustered in the New York metropolitan region are consistently characterized by a prevalence of single-plant firms. In other words, New York as the chief metropolis of the nation appears to have strong special attractions for industries of the single-plant type, which, as Table 5-2 showed, are characterized by small units and high labor intensity.

Table 5-4 compares average plant size (number of employees per establishment) in the New York metropolitan region and in the United States as a whole, for different classes of industries. In transport-sensitive industries selling to national markets (the first row of figures in the table), the situation is roughly as follows: New York plants are larger than plants elsewhere in industries that show a definite tendency to concentrate in New York (that is, the region has more than 20 percent of national employment). This relationship seems to make sense. In a market-oriented industry, we should expect that the main centers of the industry would have the largest plants, since they are the locations with best access to markets, and the economic size of plants in such industries is constrained primarily by the added transport costs involved in serving a wider market area. In addition, at least four of the transport-sensitive national-market industries⁶ most heavily concentrated in New York (chewing gum, rattan and willow ware, copper refining, and cork products) use imported materials, and New York’s status as a major port of entry helps to explain its advantage.

The external-economy industries, which are nearly all rather highly concentrated in the New York region, show a significantly contrasting size relationship. Despite the great prominence of New York as a location for such industries, the plants there are smaller than those elsewhere. This should be expected according to the considerations already discussed. A plant of an external-economy industry located in New York is in a position to contract out more operations to specialists, such as our buttonhole maker. Within any Census industry classification, those firms and plants that to the greatest degree share the special characteristics of clustered external-economy activities (such as variable demand and product, rapid production cycle, and low degree of mechanization) will be the ones most likely to find the New York location attractive; and those characteristics are, as we have seen, strongly associated with small plant size. Plants in the same Census industry located elsewhere are more likely to be turning out a less variable kind of product, and their optimum plant size is somewhat larger.

Thus industries of the clustered type have, as a class, the peculiar characteristic of operating in smaller units (in terms of both plant and firm) in locations of major concentration than they do elsewhere.

5.4 SINGLE-ACTIVITY CLUSTERS AND URBANIZATION

5.4.1 Introduction

The advantages of a clustered location pattern for certain types of activities are now apparent. But what does such a cluster contain besides the major beneficiary of those advantages?

There are certainly some types of clusters that need contain nothing else—for example, "automobile rows." Here the mere juxtaposition of a number of salesrooms makes the area attractive to prospective buyers, and that is the basis of the agglomeration tendency. The same is true for many other types of single-activity neighborhood cluster in cities, such as art shops, antique stores, secondhand bookstores, wholesale and retail produce markets, and the like.

But in each of those cases, what really draws the buyers is variety. There would be no advantage in agglomeration (so far as buyers are concerned) if the wares of the different sellers were identical. Accordingly, still other product lines or activities may contribute to the advantage of the cluster, provided they offer something that the same buyers might want to pick up on the same trip. In this way, the attractions of a cluster of high-fashion dress shops may well be enhanced by the addition of a shop specializing in high-fashion shoes or jewelry, or even a travel agency catering to high-income travelers. At a more plebeian level, the familiar suburban shopping center includes a wide assortment of retail trade and service activities. The developers of the center usually plan rather closely in advance the kinds of businesses to be included and take pains to pin down at least some of the key tenants (such as a department store branch, a bank, or a movie theater) even before ground is broken. Other relatively broad and diverse clusters based on the attraction of a common demand are recreation centers and cultural centers.⁷

Just as externalities associated with shopping behavior imply advantages for clusters of closely related activities, a cluster in which availability of common inputs plays an important role (such as in the external-economy industries analyzed by Lichtenberg) is also more likely to be a complex of closely related activities than just a clump of units of one activity. Thus an essential part of a cluster that is advantageous to garment manufacturers is a variety of such related activities as machine rental and repair; designing; provision of special components such as buttonholes, fasteners, and ornaments; trucking services; and so on. Indeed, the Lichtenberg list includes such ancillary activities indiscriminately along with the producers of garments and other final products; this is quite fitting, since it is the tightly knit complex of activities that yields the external economies that help motivate the cluster.

5.4.2 Urbanization Economies

Our examples suggest that the process of identifying an activity cluster is somewhat more complicated than might first appear. Detailed examination of a large activity cluster discloses that while some constituent activities (such as buttonhole making) are so specialized that they are locationally associated with just one line of activity, others (such as trucking or forwarding services, entertainment facilities for visiting buyers, and a variety of business services) are not so restricted. They are essentially elements of a large urban agglomeration. Their presence, and the quality and variety of the services they offer, depend more on the size of the city than on the size of the local concentration of any of the activities they serve.

Economies generated by activities and services of this sort are external to any single-activity cluster, but they are internal to the urban area. There is a parallel to be drawn here to the relationship between a single-activity cluster and its constituent units. In that instance, economies were realized by the units as the size of the cluster increased; thus economies are internal to the cluster but external to the unit. In the case of urbanization economies, we recognize that economies accrue to constituent clusters as the size of the urban area increases. Thus some of the advantages that a particular activity gets by concentrating in New York could not be duplicated by simply having an equal amount of that activity clustered in, say, Columbus, Ohio—though, of course, it is possible that Columbus might offer some compensating attractions of a different nature.

There have been, and still are, some noteworthy multifirm clusters of single activities in relatively small places (historic examples are glove making in Gloversville, New York; hat making in Danbury, Connecticut; and furniture making in Grand Rapids, Michigan). But it is apparent that this type of single-activity cluster (in which the bulk of an activity is found in a few "one-industry towns") has rather gone out of style since F. S. Hall proclaimed its heyday in 1900.⁸ Such concentrations depended heavily on the external economies of a pool of specialized labor skilled in operations peculiar to one industry, and often predominantly of one nationality group;⁹ on a reservoir and tradition of entrepreneurship similarly specialized; and on the inertial factor of acquired reputation. Technological changes and enhancement of the mobility of labor and entrepreneurship explain why such local specialization has become increasingly rare. By contrast, external economies on the broader basis of urban size and diversity have remained a powerful locational force.

5.4.3 Measuring Urbanization Economies

The symbiotic relationships within single-activity clusters or more complex clusters reflecting urbanization economies have important implications, both for constituent activities and for the regional economy as a whole. As a consequence, much effort has been devoted to understanding and measuring agglomeration economies. Many people concerned with the growth and development of specific regions have examined the advantages inherent in urban concentrations, in an effort to understand the factors most relevant to their region’s prosperity and problems.

Our examination of agglomerative forces suggests that they may affect an individual location unit either through market demand considerations or through modifications of the production process that enhance efficiency. The evaluation of either or both of these effects entails some challenging difficulties.

Recent efforts to measure the extent of urbanization economies have focused on estimates of the productivity gain accruing to activities that are located in larger urban areas. They proceed by treating production in urban areas as being representative of the aggregate production of component activities. For example, if one were to estimate the aggregate demand for labor in Boston or Detroit, one would assume that the behavior of this aggregate reflects a weighted average of labor demand curves associated with all activities in the city.

Measurements of this sort rest on the belief that the demand for factors of production is determined by the value of their marginal product, that is, marginal physical product multiplied by the price of the good or service being produced. Because of this, the demand for inputs, including labor, would reflect the advantages of agglomeration economies. Whether the source of these economies is due to the size of the location unit, firm, cluster, or urban area, any associated increase in factor productivity would show up in the urban area’s demand for labor. With this in mind, researchers interested in measuring agglomeration economies have reasoned that by the comparison of labor markets associated with cities of different size, it might be possible to isolate the contribution of urbanization economies to labor productivity. Further, if it were possible to isolate a measure of aggregate efficiency in production due to these forces, we would also have a measure of their average effect on the activities that make up the urban areas in question.¹⁰

Reference to Figure 5-2 will help to explain and reinforce these ideas. The lines D_a and D_brepresent estimates of the aggregate demand for labor in two different urban areas, (a) and (b). D_bis that associated with the larger of the two. It is drawn to the right of D_a in order to reflect the fact that for any given level of employment, the value of labor’s marginal product is greater in the larger urban area. This productivity difference remains even after one accounts for differences in the size of the capital stock and the "quality" of labor between these areas.

If the two urban areas faced the same labor supply function, S_l, equilibrium employment in each would be given by E_aand E_b; labor is hired up to the point where the value of its marginal product (given by D_aand D_b) is equal to the wage rate. Because of this, the total value of goods and services produced in either urban area is given by the area under its respective labor demand curve, up to the level of equilibrium employment. Therefore, the shaded area, E_aE_bcdef is the increase in factor productivity associated with larger urban size.¹¹

Estimates of this measure of urbanization economies have varied from study to study, and a consensus is not easily drawn. The findings of two early research efforts have gained wide recognition, however, and will serve to illustrate the kind of results obtained.¹²

David Segal obtained estimates of aggregate production functions along with their implied labor demand functions for 58 metropolitan areas, using 1967 data. A simplified version of the functional form he uses is given by

where Q is output, K is capital stock, and L is employment (quality adjusted) in city i.¹³ Technical efficiency is characterized by the multiplicative constant AS^c, where S is a dummy variable denoting size, and A and c are parameters. Segal finds constant returns to scale in aggregate production (a + b=1), and estimates of c are of the order of .08 for cities with populations of 2 to 3 million. This translates to an 8 percent productivity gain (the shaded area in Figure 5-2) for metropolitan areas when this population threshold is reached.

In a study of fourteen industries also based on 1967 data, Leo Sveikauskas finds that an average productivity gain of about 6 percent can be expected with each doubling of city size. He reaches this conclusion by regressing the logarithm of output per worker (productivity) in a given industry on the logarithm of population and on an index of labor quality across a large sample of cities. Sveikauskas recognizes that these productivity differences may be due to differences in capital intensity across cities; if the ratio of capital to labor (K/L) is large, output per worker will also be large. However, upon investigation he finds that the variation in capital intensity is not sufficient to account for the observed productivity differences.

Productivity advantages of this magnitude can mean a substantial competitive edge. They can be a powerful locational incentive and may well have played an important role in encouraging shifts in the spatial distribution of economic activity toward urban areas during much of the postwar period.¹⁴

Many problems confront efforts to measure external economies accruing to activities in urban areas, and it is important to keep the limitations of related research in mind. Some types of externalities associated with clusters are not necessarily related to urban size and are therefore omitted from measurements of the sort described here. Others are not manifest in productivity differences at all; rather, they are reflected in demand considerations. Further, because of data constraints, measurement efforts have been limited to highly aggregate analysis, whereas many of the most interesting aspects of agglomeration economies can be appreciated only at a much more micro level. The method described in this section is nevertheless representative of the kind of systematic effort that is required to address these and other issues related to the measurement of this important phenomenon.

5.5 MIXED SITUATIONS

In order to bring out certain controlling factors, we have been considering sharply contrasting types of activity location patterns. We have distinguished patterns dominated by mutual repulsion from those dominated by mutual attraction. We have also distinguished patterns involving market areas from patterns involving supply areas.

It is now time to recognize that in the real world there are various intermediate stages between the extreme cases described. In one and the same activity, it is not uncommon to find (1) dispersive forces dominant at one level of spatial detail and agglomerative forces dominant at another level, or (2) coexistence of market-area and supply-area patterns. Let us take a brief look at each of these types of "mixed" situations.

5.5.1 Attraction plus Repulsion

In any given activity, the forces of repulsion and attraction among units are usually both present in some degree, even though one generally predominates. Thus in an activity characterized by a mosaic of market areas, some of the locations will have more than one plant, store, or other such unit. Though we think of retail grocery stores or gasoline stations as primarily mutually repulsive, it is not uncommon to find groupings of two or more adjacent competitors showing some degree of mutual attraction. Being at essentially the same location, these rival units are likely to share the same market area, though one might have a somewhat wider reach than another. If we think of them as simply sharing "the market area of that location," the statements made earlier about market-area determination and pricing policies are still largely valid, except that spatial pricing systems involving systematic transfer cost absorption become less feasible when the seller is not alone at its location.¹⁵

Similarly, an activity that we think of as basically clustered, such as the making of fashion garments, often has several widely separated clusters. Among the external-economy industries of New York enumerated in Table 5-1, it will be noted that only a few come close to being exclusively concentrated in the New York region. The rest are found also in substantial, lesser clusters in other large cities. One reason for replication of clusters is, of course, that over long distances transfer costs (in time if not in money) become a significant constraint on concentration relative to far-flung markets or input sources. Thus, when we look at the country as a whole, we see a pattern of market or supply areas showing some force of mutual repulsion among competing centers. If such an activity is concentrated primarily in, say, New York, Los Angeles, and Chicago, there will be three roughly demarcated market areas or supply areas, each shared by all the members of the corresponding cluster. In this connection, it is much more likely that market areas rather than supply areas will be involved, since most external-economy activities produce transferable outputs that need fast delivery to rather widespread markets, and their transferable inputs come from fewer sources and are of a more staple character.

5.5.2 Coexistence of Market Areas and Supply Areas, When Both Sellers and Buyers Are Dispersed

Somewhat different from the case just discussed is a not uncommon situation in which there are many selling locations and many markets, and not necessarily any significant clustering tendencies at all. Sales from one producing district are distributed over many market points, and at the same time any one market district buys from many supplying points. The situation does not lend itself to analysis purely in terms of a set of supply areas or a set of market areas. How, then, can we most effectively analyze such a pattern?

Except in the unlikely situation in which the patterns of supply and demand coincide (which would mean that no transfer is required and that each point is self-sufficient in this particular product), there will be surplus areas where local output exceeds local consumption, and deficit areas where the opposite situation prevails. The product will be transferred from surplus areas to deficit areas; and in order to motivate the flow, there must be a price differential corresponding to the costs of transfer along the paths of flow.

The relationship between price patterns and transfer can be demonstrated as follows. Suppose we were to map the spatial variations in the price of the good, depicting a price surface by plotting a set of contour lines, each connecting points at which the price is at some particular level. The iso price lines (isotims) corresponding to the highest prices would occur in the principal deficit areas, and those corresponding to the lowest prices would occur in the principal surplus areas. The price gradient along any path would be determined by the frequency with which we cross successive isoprice contours as we traverse that path. Shipments of the commodity would be most likely to occur along the paths with the steepest price gradients, and such paths would cross the isoprice lines at right angles. Actual shipments would occur wherever there is a price gradient at least as steep as the gradient of transfer costs; and in an equilibrium situation, we should expect that these shipments would result in no price gradient being substantially steeper than the transfer cost gradient.

Such a graphic analysis does not, however, explicitly recognize the relation between supply and demand patterns that creates the price differentials giving rise to shipments. William Warntz has suggested an empirically feasible shortcut method of measuring this supply-demand relation that utilizes the access potential index described later.¹⁶

For any given point i, we can construct an index of local and nearby supply, or "access to supply," by the following formula:

where s_j is the output at any supply location j, t_ij, is the transfer cost from that supply location j to the given point i, and x is an exponent empirically chosen to provide the best fit to the observed statistics. For the same point i, we can construct also an index of local and nearby demand, or access to market, by the analogous formula:

With both indices derived for each location, we can identify surplus areas as those where the supply index is greater than the demand index, and deficit areas as those for which the demand index is greater than the supply index. We should expect that spatial variations of the price of the good should be positively correlated with the demand index and negatively correlated with the supply index; this expectation was borne out in some of Warntz’s studies of the price patterns of agricultural commodities.

5.6 SUMMARY

Just as some activities are characterized by mutual repulsion among units, others are characterized by cohesive or clustering (agglomerative) forces. These forces may result from demand or production (supply) characteristics of the activity in question.

In some instances, each unit finds advantage in locating near others of the same kind primarily because the units are not exactly identical. This generally happens when the output is varied and changing somewhat unpredictably, so that buyers need to "shop"—that is, to compare various sellers’ offerings. Selling locations attract buyers according to how wide a choice they can offer; therefore, sellers gain by being part of a large cluster.

Further agglomerative forces arise from the external economies of a cluster large enough to support a variety of highly specialized suppliers of inputs: labor, components, services, and so forth. These clusters also are characteristic of activities dealing with nonstandardized and perishable outputs and inputs. In such activities the units are small and generally only one to a firm. Lichtenberg’s classic study of external-economy industries showed the nature of such clustering and its importance in the economy of a large metropolis such as New York.

As the size of an urban area increases, it becomes capable of supporting activities and services that are external to any cluster but that generate economies for a number of clusters. Urbanization economies of this sort imply important advantages for activities located in large metropolitan areas, where we observe complexes of interacting activities.

Although a contrast has been drawn between activities dominated by mutual repulsion of units and those dominated by mutual attraction (agglomeration), there are some elements of both mutual repulsion and attraction in many activities. There are also many situations in which sellers have market areas, and buyers at the same time have supply areas.

TECHNICAL TERMS INTRODUCED IN THIS CHAPTER

SELECTED READINGS

Brian J. L. Berry, Geography of Market Centers and Retail Distribution (Englewood Cliffs, N.J.: Prentice-Hall, 1967).

Stan Czamanski and Luiz Augusto de Q. Ablas, "Identification of Industrial Clusters and Complexes: A Comparison of Methods and Findings," Urban Studies, 16, 1 (February 1979), 61-80.

Robert M. Lichtenberg, One-Tenth of a Nation (Cambridge, Mass.: Harvard University Press, 1958).

Hugh 0. Nourse, Regional Economics (New York: McGraw-Hill, 1968), pp. 85-92.

Harry W. Richardson, Urban Economics (Hinsdale, Ill.: Dryden Press, 1978), Chapter 3.

David Segal, Urban Economics (Homewood, Ill.: Richard D. Irwin, 1977), Chapter 4.

ENDNOTES

1. B. Curtis Eaton and Richard G. Lipsey. "Comparison Shopping and the Clustering of Homogeneous Firms," Journal of Regional Science, 19, 4 (November 1979), 421-435, examine some locational implications of comparison shopping in a more theoretical context.

2. In Section 5.4 we shall distinguish yet another level at which economies of size may appear; there, we shall find that such economies are also associated with urbanization per se.

3. What are here identified as "cluster" economies are sometimes referred to as economies of localization. Alfred Marshall’s succinct characterization of the ‘economies of localized industries" is often quoted from his Principles of Economics, 8th ed. (London: Macmillan, 1925), Book IV, Chapter 10. F. S. Hall’s Census monograph, "The Localization of Industries" (U.S. Census of 1900, Manufactures, Part 1, pp. cxc—ccxiv), reported on the development of highly clustered patterns of individual manufacturing industries toward the end of the nineteenth century. Unfortunately, however, the term "localization" has also been used synonymously with "location" and even in the sense of "dispersion," so it is best avoided.

4. A thorough and original discussion of business organization and location in terms of these several optima appears in E. A. G. Robinson, The Structure of Competitive Industry, rev. ed. (Chicago: University of Chicago Press, 1958).

5. Robert M. Lichtenberg, One-Tenth of a Nation (Cambridge, Mass.: Harvard University Press, 1960). Lichtenberg’s list of "external-economy industries" includes five more, in which the region’s share was less than 10.4 percent: industrial patterns and molds, separate trousers, men’s dress shirts and nightwear, woolen and worsted fabrics, and special dies, tools, and metal-working machinery attachments. He does not explicitly categorize any nonmanufacturing activities as external-economy-oriented though he does discuss the heavy concentration of central offices of large industrial corporations in the New York metropolitan region Among the 500 largest such corporations as listed by Fortune magazine in 1959, 155 (31 percent) maintained their headquarters in the region. The region’s share was greater still for the largest corporations, rising to 44.2 percent of those with $750 million or more in assets (ibid., Chapter 5 and specifically Table .37, p. 155).

6. Lichtenberg gives a full listing of industries by locational category in ibid., Appendix B.

7. For an empirical analysis of cluster tendencies involving related lines of retail trade, see Arthur Getis and Judith M. Getis, "Retail Store Spatial Affinities," Urban Studies, 5, 3 (November 1968), 317-322. For a sophisticated and challenging empirical analysis of which activities cluster with which, see Joel Bergsman, Peter Greenston, and Robert Healy, "The Agglomeration Process in Urban Growth," Urban Studies,9, 3 (October 1972), 263-288; and for a survey of related literature, see Stan Czamanski and Luiz Augusto de Q. Ablas, "Identification of Industrial Clusters and Complexes: A Comparison of Methods and Findings," Urban Studies, 16, 1 (February 1979), 61-80.

8. Hall’s 1900 Census monograph, previously cited, gives numerous further examples.

9. Economic historians have often noted the important role of the influx of Germans to the United States in the mid-nineteenth century in establishing concentrations of certain industries in which they had special skills, such as optical and other scientific instruments in Rochester, brewing in Milwaukee and St. Louis, and tanning and shoemaking in these and other Midwestern cities.

10. A second approach to this measurement problem entails the direct estimation of the returns to scale exhibited by activities in metropolitan areas. Gerald A. Carlino, "Increasing Returns to Scale in Metropolitan Manufacturing," Journal of Regional Science, 19, 3 (August 1979), 363-373, provides estimates of this sort and attempts to decompose them into economies related to the size of the unit, cluster, or urban area associated with a given activity.

11. The assumption that the same wage rate prevails in both cities implies that this productivity difference reflects a long-run equilibrium in which spatial factor price differentials have been eliminated. In fact, the labor supply curve may be positively inclined, indicating that higher wages must be paid to attract more workers. Indeed, it may even be necessary to pay workers higher wages in order to compensate for the "disamenities" of urban life. (On this point see Oded Izraeli, "Externalities and Intercity Wage and Price Differentials," in George S. Tolley, Philip E. Graves, and John L. Gardner (eds.), Urban Growth Policy in a Market Economy [New York: Academic Press, 1979], pp. 159-194.) Recognition of these labor supply conditions would imply that adjustments to the measure of productivity gain described above are required in order to "net-out" these effects and identify "real" productivity gains. The reader interested in these issues should see Michael S. Fogarty and Gasper Garofalo, "An Exploration of the Real Productivity Effects of Cities," Review of Regional Studies, 8,1 (Spring 1978), 65-82; and Fogarty and Garofalo, "Urban Size and the Amenity Structure of Cities," Journal of Urban Economics, 8,3 (November 1980), 350-361. Fogarty and Garofalo use the graphical analysis presented here to develop perspective on their related work and explore the concept of "real productivity" in some depth.

12. See David Segal, "Are There Returns to Scale in City Size?" Review of Economics and Statistics, 58, 3 (August 1976), 339-350; and Leo A. Sveikauskas, "The Productivity of Cities," Quarterly Journal of Economics, 89, 3 (August 1975), 392-413. For qualifications and extensions of the method and results presented by these authors, see the articles by Fogarty and Garofalo cited in the preceding footnote and Ronald L. Moomaw, "Productivity and City Size: A Critique of the Evidence," Quarterly Journal of Economics, 94, 4 (November 1981), 675-688.

13. Actually, Segal accounts for differences in labor quality among cities by setting b =_kß_kq_ikwhere q_ik reflects the city’s labor force composition by education, sex, race, and age. He also includes a vector of site characteristics (accounting for climate, natural resources, etc.) in the multiplicative constant.

14. In Chapter 8, we shall find that the growth rate of nonmetropolitan areas has exceeded that of metropolitan areas in recent years. Some researchers have speculated that this also may be due to the changing structure of agglomeration economies.

15. If there are many sellers of a standardized commodity at one location, so that they are in nearly perfect competition, any seller could dispose of its entire output while confining its sales to that part of the market providing the largest profit margin. Consequently, any attempt to establish a discriminatory pricing system would break down.

16. William Warntz, Toward a Geography of Price (Philadelphia: University of Pennsylvania Press, 1959).