Ann Reg Sci (2015) 54:797–817 DOI 10.1007/s00168-015-0686-9 ORIGINAL PAPER
The city and the region as contrasts in spatial organization John B. Parr1
Received: 24 October 2014 / Accepted: 30 July 2015 / Published online: 11 August 2015 © Springer-Verlag Berlin Heidelberg 2015
Abstract Within a number of disciplines, the terms “city” and “region” are frequently referred to in combination, raising the obvious question as to the relationship between two. The central focus of the paper involves an attempt to identify the more significant differences between the city and the region in terms of their respective modes of spatial organization. This is undertaken from three broad perspectives. The first compares the individual city and the individual region as independent entities, while the second perspective considers the city in relation to the region in which it is located. A third perspective is concerned with a system of cities in comparison with a system of regions. The latter part of the discussion examines alternative definitions of the city, and the extent to which these may be regarded as satisfactory. JEL Classification
R10 · R11 · R12
1 Introduction For many years, the terms “urban” and “rural” were commonly used in various branches of the social sciences. This continues to be the case, particularly in fields such as demography and the analysis of economic growth and development. Over recent decades, however, the non-dichotomous categories of “city” and “region” (and their associated adjectives “urban” and “regional”) have come into prominence and are often employed together. This combined usage of these terms appears in official publications as well as in the language of the media and is also to be seen in academic and professional contexts. Within universities, for example, it occurs in the names of
B 1
John B. Parr
[email protected] University of Glasgow, Glasgow, UK
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subject divisions such as the Department of City and Regional Planning at the University of Pennsylvania, and the Centre for Urban and Regional Development Studies at Newcastle University, and it is found in the titles of various serials, e.g., Regional Science and Urban Economics, International Journal of Urban and Regional Research, and European Urban and Regional Studies. The reasons for this combined usage of terms are not entirely obvious. One plausible explanation is that in both urban analysis and regional analysis, which have emerged as important specializations in several disciplines, use is made of closely related theoretical frameworks, methodologies, and analytical techniques. In any event, this joint usage of terms raises a number of questions. For example, is it simply acknowledging the fact that the city and the region represent two valid scales in the analysis of spatial phenomena? Does it imply that the city must necessarily be viewed in terms of the region to which it belongs? Might it be referring to important interrelationships between the city and its region? The question to be considered in the following discussion, however, concerns the extent to which the city and the region represent distinct entities. This question will be approached by comparing the spatial organization of the city with that of the region, primarily from an economic (rather than social or cultural) viewpoint. It is somewhat surprising that such a basic question not been directly addressed before, particularly since it has a relevance in a number of contexts. These include the selection of units in the collection of statistical data, the formulation of hypotheses in the analysis of these data, and the design and implementation of particular areas of public policy, to name but a few. To appreciate the city and the economic region in terms of spatial organization, it is important to recognize that both have been influenced over many decades by decision making on the part of firms, public agencies, and households in such areas as production, investment, housing, and consumption. The processes involved, which were mediated though various market systems and public allocation mechanisms, were highly interrelated and ultimately affected the long-run evolution of both the city and the region. Rather than attempting to unravel such complex, interacting processes, attention will be focused on their outcomes and in particular, on the forms of urban and regional spatial structure, to which these processes have given rise. For related reasons, no consideration will be given to the spectacular growth of some cities and the decline of others, nor to the differential economic performance of regions, nor to the various economic, social, and governance issues that have arisen in both contexts, important as all of these aspects undoubtedly are. In coming to grips with the spatial organization of cities and regions, three perspectives are adopted, each within the overall context of a nation. The first compares the city and the region independently of each other, and the second is concerned with the individual city within its region. The third perspective examines cities and regions as elements of wider systems, so that the system of cities is seen in relation to the system of regions. Consideration is subsequently given to various alternative perceptions of the city and to the validity of these.
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2 Preliminary definitions Comparison of spatial organization is only practical if there is adequate specification of the terms “city” and “region.” To this end, two key definitions are introduced. The first involves the city, which is taken to be the “built city.” This refers to the wider urban area or the physical extent of continuous or near-continuous tracts of land devoted to housing, industrial building, offices, commercial premises, public institutions, areas of outdoor amenity, etc. By this definition, Evanston, for example, would be regarded as part of the built city of Chicago, while Versailles would be included within the built city of Paris. With certain important exceptions, the built city corresponds approximately to the “Urbanized Area,” as employed by the Bureau of the Census in the USA, and also to the “Built-up Area,” used by the Office for National Statistics in the UK. Depending on the prevailing structure of political organization, the built city may contain several (and sometimes numerous) jurisdictions. The outer extent of the built city is usually defined as the location where some minimum level of population density is encountered. It is sometimes defined as the location at which a lower limit on the spacing of physical structures such as residences or commercial buildings is reached. Only built cities with populations in excess of around 200,000 are considered here, although adjustments to this minimum-population level may be necessary, depending on the size of the nation.1 The imposed values for both the edge density of the built city and its minimum population are unavoidably arbitrary. In a later section of the paper, alternative definitions of the city are considered, but for the time being reliance is placed on the built city. The second key definition, which relates to the region as a whole, requires greater elaboration. Whereas the city represents an observable phenomenon (if only in physical terms), the region is in the nature of a mental construct or technical device, though no less significant for that. Moreover, while in certain respects the boundary of a city is distinct, the boundary of the region is less clear and open to varying demarcation. In a widely cited review article, Meyer (1963) identified three broad types of economic region. The emphasis here will be on the nodal region, the other two types being the homogeneous region and the programming or planning region. Since the primary concern is with spatial structure, no consideration will be given to the homogeneous region (perhaps the most common view of the region), which by its nature is more concerned with uniformity of conditions rather than with internal organization. Other types of region such as the “river-basin region” (Barrow 1998) and the “polycentric urban region” (Kloosterman and Musterd 2001; Davoudi 2003; Meijers et al. 2003) are not considered.2 The undesirability of excluding these other forms of region is recognized, particularly in view of recent concerns with the environment and the 1 For nations with populations of less than around 50 m (particularly if these are also territorially extensive) a minimum built-city population below the 200,000 level would be more realistic, while a value greater than 200,000 might be more appropriate for nations with populations in excess of 50 m. On particular occasions it has been found desirable to allow the minimum population of the built city to vary according to the overall population density within different geographical sections of a nation (Bogue 1950, p. 16). 2 In contrast to the nodal region, a region based on a river basin is frequently not organized around a particular city or node, while the polycentric urban region has no single city occupying a position of clear dominance.
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emergence of multidisciplinary research. In addition, no attention is given to transnational regions such as Cascadia in the western part of North America and the Blue Banana in Western Europe, which have been proposed by journalists and writers, largely because such regions tend to be poorly specified with little discussion of the criteria used in their definition. The nodal region can be identified at widely differing scales, but for the purposes of this discussion, it is assumed to be at the scale of the “metropolitan region,” a concept used by Duncan et al. (1960, pp. 82–104). This is closely related to the “city-region” (Dickinson 1947; Parr 2005; Scott 2001), the “metropolitan community” (Bogue 1950), the “polarized region” (Boudeville 1966), and differs from these mainly in matters of emphasis. Examples of the metropolitan region would include economic regions based on Boston, Buffalo, Denver, and Vancouver in North America, and Barcelona, Bordeaux, Milan, and Munich in Europe. Following Bogue (1950) and others, it is assumed that the metropolitan region in question is one of a space-filling set, i.e., a set that exhausts the national space. A hallmark of the metropolitan region is the readily identifiable core-hinterland structure, and the accompanying high levels of interaction between the two parts. The core is represented by its largest city (in our case a built city with a population greater than 200,000), while the hinterland contains a rural population and a population located in a network of urban centers of varying size, some of which may be substantial, but with populations below the minimum level. This core-hinterland structure is discussed further in Sect. 5. For most nations of the developed world, the metropolitan region represents a distinguishing feature of their respective space economies. The term “metropolitan region” is not to be confused with the metropolitan area, defined above as the built city. The metropolitan region typically covers a territory considerably greater than that of the metropolitan area. Unfortunately, the term “metropolitan region” (or city-region in Europe) is sometimes used to refer simply to a major metropolitan area or built city, a tendency which can be the source of confusion.
3 Similarities and parallels in spatial organization In order to bring into relief the differences in the internal structure of the city and the region, we briefly consider particular features that are shared by both. Some of these are obvious; others are less so. It is clear that the city and the region are both subnational in character, except in the case of a city-state such as Singapore or Monaco. The city and the region each represent a small, open economy. Here, “small” refers to size relative to the national economy, while “open” draws attention to the virtual absence of non-economic impediments to trade and factor movement within a nation. As in national accounts, income or economic welfare of both the city and the region can be measured in terms of either gross domestic product of the city (region) or the gross urban (regional) product. The gross domestic product of the city (region) is the value of goods and services produced within it. The gross urban (regional) product also takes account of external payments both received by the city (region) and made by the city (region). These include property payments (such as dividends, profits, royalties) and the wages and salaries of commuters. The two measures are linked in the following
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manner: Gross urban (regional) product is equal to the gross domestic product of the city (region) plus net external payments (which may be positive or negative). Related to these measures is the balance of payments of the city and the region. This indicates the levels of inward and outward monetary flows with respect to trade, capital movements, factor payments (including those associated with commuting), and fiscal transfers managed by a central or federal government. While the categories will be the same for the city and the region, their relative proportions are likely to vary, particularly in the case of commuting. Although the city is a relatively compact unit and the region a more extensive one, there is an interesting spatial structure parallel between the two, inasmuch as the city and the region can each be viewed as a network of points, with one point tending to dominate. In the case of the city, the dominant element is the central business district (CBD). Definition of the extent of the CBD is usually undertaken, using of such criteria as the density of employment (especially in commercial, retailing, and other service activity), the level of non-residential use, and the height of buildings. The CBD is surrounded at varying distances by a hierarchical system of subcenters, mostly involved with retail and other service activity (Beavon 1977), with some based on manufacturing. In other words, the city has a multiple-nuclei structure, a phenomenon observed by Harris and Ullman (1945) over 70 years ago, and periodically rediscovered since then. For large cities, there may be more than one dominant element, e.g., Downtown Manhattan (the district that includes Wall Street) and Midtown in New York City, and the “City” (the financial center) and the West End in London. A particular case of more than one dominant element also occurs when the built city contains the CBDs of “twin cities,” as in the cases of Minneapolis and St Paul in the USA or Mainz and Wiesbaden in Germany. In the case of the region, the parallel network consists of a dominant core or node and a set of subordinate urban centers in the hinterland, undertaking economic functions relating to service provision as well as manufacturing. And by the same token that the city may have more than a single dominant element, it is possible for a region to possess more than one core, although this is rare, e.g., Calgary and Edmonton in Alberta, or Cologne and Düsseldorf in North Rhine-Westphalia. For both the city and the region, the spatial structure of centers (particularly their size, spacing, frequency, and functional composition) is amenable to analysis in terms of the theoretical frameworks proposed by Christaller (1933/1966), Lösch (1944/1954), Tinbergen (1961). Although recent decades have seen the emergence of complexities in patterns of private and public service provision that reach beyond the scope of such frameworks, these continue to represent useful points of reference.
4 The city and the region as unrelated entities With this initial perspective on spatial organization, attention is focused on those features which differentiate a representative city from a representative region. In other words, the concern is not with a city located in a particular region, but with cities in general and regions in general.
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4.1 Competition for space Cities, when defined in the broad terms of the built city, are nearly always located sufficiently far apart that the physical expansion of one does not affect the physical expansion of the other, so that there is no competition for physical space.3 In other words, neighboring built cities can expand without merging, although the past expansion of a given city may have involved the absorption of small urban centers in its immediate vicinity. Historically, the reason for the spacing of cities (often much smaller than the 200,000 lower limit imposed here) was that the enterprises located therein required a minimum level of separation to be efficiently located or at least economically viable. This was certainly the case where the city needed to be centrally located with respect to its market, or similarly located in terms of the supply of inputs for goods produced within the city. On other occasions, however, when these requirements were not decisive, cities may have been located in relatively close proximity to each other, but still far enough apart not to compete for space.4 This was common for cities based on textile and mineral production. Unlike the situation with respect to cities, competition for space among regions is unavoidable. As will be recalled, the concern is with space-filling regions, so that the enlargement of one region necessarily involves contraction of one or more neighboring regions. It will be argued in a later section that this difference relating to the absence or presence of competition for physical space helps to explain some of the contrasts in spatial organization between the city and the region. There is a further aspect of this difference. Whereas economic development of the city typically involves its physical expansion, economic development of the region is accommodated internally by the intensification of economic activity at one or more locations, with the region’s boundaries remaining intact. In contrast to the boundaries of a city, regional boundaries, once in existence, tend to change at a very gradual pace. 4.2 Patterns of population density The internal structure of the city and that of the region may be compared in terms of their differing population distributions, as revealed in their respective density functions.5 Each is a summary of the manner in which density declines with distance from a central location. In the case of the city, the pattern of density decline from the center 3 In other respects, cities can be said to be in competition, since firms in different cities compete for markets,
skilled labor, capital, entrepreneurial talent, etc. Within the individual city, competition for land among the various users is obviously present. 4 There were, of course, exceptions to this spacing of cities, and mention has already been made of the twin-city phenomenon. In other instances, the expansion of a group of neighboring independent cities (and smaller urban centers) eventually coalesced to form of a single urban concentration such as Boston in the USA and Birmingham in the UK. 5 As used in this subsection (and as commonly employed in the literature), the term “density function” refers exclusively to marginal density, i.e., the density at distance x from the center of the city or the region. By contrast, average density is the population density within the area extending from a central location to a perimeter at distance x. The relationship between the two types of function (marginal and average) is discussed by Holden and Parr (2013).
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Fig. 1 Density functions for the city and the region
of the city is approximated by the negative exponential function (Clark 1951). This has been shown to have an economic rationale based on the trade-off between household preferences for accessibility to the center and the availability of space (Alonso 1964; Evans 1973). In the negative exponential function, the logarithm of density decreases with distance from the center of the city at a constant rate and is of the form ln M (x) = ln C − bx
b > 0; 0 ≤ x ≤ x
(1)
where M(x) is density of population at distance x, and C or M(0) is the extrapolated value of density at the center, while b is the slope of the function, indicating the degree of urban centralization or suburbanization. The graph of the negative exponential function is shown in Fig. 1a, where distance x represents the edge of the city, i.e., the distance at which some minimum urban density M(x ) is reached (see Sect. 2). This function is an obvious simplification, since it fails to reflect the density crater near the city center. Such a phenomenon results from the fact that near the center of the city, land uses are primarily of a non-residential nature, being concerned with retail facilities, offices, and other commercial establishments. The quadratic exponential function proposed by Newling (1969) is able to accommodate the presence of such a density crater. In the case of a region, the pattern of population density can be accurately described by the lognormal function (Nairn and O’Neill 1988). This is expressed as ln M (x) = ln N + a (ln x) − g (ln x)2 (g > 0)
(2)
where M(x) is the density at distance x, and N or M(1) represents the density at one unit of distance from the center of the region (and therefore the center of the core city). The parameter a determines the location of maximum density (if a = 0, the maximum density occurs at one unit of distance and is equal to N ). The remaining parameter g may be viewed as an approximation of the slope of the function over distances beyond the maximum density and reflects the extent of regional concentration. The
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graph of the lognormal function is shown in Fig. 1b, where the distance x refers to the extent of the city within the entire region and G is a given distance from the center of the region beyond distance x . N.B. The city in Fig. 1b is not intended to refer to the same city indicated in Fig. 1a. In addition to showing the density crater near the city center, the lognormal function approximates the negative exponential pattern of densities over the rest of the city, so that the logarithm of density decreases with distance at a roughly constant rate. The lognormal function also describes the pattern of density decline across the hinterland. Over this range, the function resembles the inverse power function, with the logarithm density decreasing with the logarithm of distance at a constant rate, so that the logarithm of density decreases with distance at a decreasing rate, as in Fig. 1b. It is speculated that this departure from the negative exponential form may be related to the presence of urban centers of varying size across the hinterland of the region.6 4.3 Internal circulation and interaction The concern here is with three types of spatial interaction: the trade among firms in different sectors; the trade between firms and the consumers of goods and services; and interactions relating to the labor market. For the purpose of comparison, the city is divided into zones, and the region is treated as a set of points, representing urban centers, including the core city of the region. In the case of trade among firms, it is not easy to generalize about differences between the city and the region; such is the extent of variation in each case. A clearer picture emerges in the case of trade between firms and households. Trade of this type necessarily involves the journey to consume (better known as the “shopping trip”), which results from the separation of the location of residence and the location of expenditure. Naturally, this is of little relevance in the case of those types of shopping that do not require travel on the part of the consuming household, e.g., mail-order, telephone, and Internet purchases. Within cities, the relative ease of movement, together with consumers’ desire for variety (reflected in the extent of product differentiation) causes a willingness to travel long distances, whether to specialized retail centers or to the CBD, in order to visit museums, concert halls, sports venues, etc. This results in a high level of interzonal interaction, so that the propensity to consume locally (i.e., within the same zone as the residence) is fairly low (Hewings and Parr 2007). Different conditions obtain within the region, where the travel times between centers are invariably longer than those between the zones of a city, and the influence of product differentiation on shopping patterns is less pronounced. Consequently, the level of shopping beyond the nearest relevant center tends to be low, causing the propensity to consume locally to be relatively high. 6 It might be supposed that the existence of an urban center in the hinterland at a particular distance from the core city of the region would cause a secondary peak in distance–density plot. This tends not to be the case, however. Each point on a distance–density plot (from which the best-fitting function is derived) refers to the mean density throughout the relevant concentric ring. This has the effect of smoothing the form of plot, usually leading to a suppression of a local peak. In the Bogue (1950) study, the vast majority of the regional distance–density plots did not display secondary peaks.
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In a third type of interaction, the concern is with commuting. Here, the urban labor market (seen in terms of daily movement) differs in a number of respects from its regional counterpart. In the city, the distances between zones of residence and zones of potential employment are, on average, relatively short, so that there is a tendency for the journey to work to involve interzonal travel and, increasingly, not simply from the outer zones to the central zone or CBD. At the regional scale, the distance between the center of residence and the nearest center of potential employment is relatively long, with the result that the extent of intercenter commuting is constrained, though still present to some degree. In general, therefore, the proportion of the workforce able (and electing) to commute to other zones in the city is greater than the comparable proportion commuting from one center to another center in the region. This has implications for structural adjustment within the labor market. For the city, changes in the location of employment, with the location of residence remaining unchanged, are responded to relatively easily by modified patterns of commuting. Similar changes across the region as a whole are less likely, and adjustment usually involves the costlier expedient of intraregional migration.
5 The city and its region In the second perspective, we move beyond the comparison of the city and the region, when these were considered independently of each other. It is sometimes the case that differences between the city and the region may become apparent if a city is examined within the context of its region. The comparison is now between the core city and its host region, i.e., the region of which the core city is the focus. Attention is initially given to the internal functioning of the region, particularly the relationships between its two constituent parts. 5.1 The core-hinterland structure The dominant position of the core city is reflected in its role as a command-andcontrol center for the entire metropolitan region. The core is often a central place (or at least has significant central functions), being a location for the distribution of highlevel goods and services (to households as well as firms) throughout a hinterland, which represents the largest market area of the core. In other situations, the core may function primarily as a collection and/or processing center, drawing on the raw materials and semi-manufactured goods produced by hinterland in its role of a supply area for the core. On particular occasions, the core may act in both capacities. These supply and demand complementarities between the core and the hinterland underlie the substantial trade between the two parts of the region. Other important elements of interaction include commuting, capital movements, substantial two-way migration streams, as well as information and related flows (Hall 1991; Hall and Pain 2006). Despite the very strong internal linkages between the core and the hinterland, the economy of the region is not a closed one. The core may harbor particular economic activities (such as manufacturing and the provision of specialized services) that are largely unrelated to the hinterland and serve extraregional markets. In addition, certain
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activities undertaken in the urban centers and rural areas of the hinterland may not be oriented to the core city, but are dependent on the demands exerted by other regions. Furthermore, each part of the region may be reliant on capital, raw materials, and/or manufactured inputs from sources external to the region. Patterns such as these are a clear reflection of the openness of the regional economy, referred to earlier. 5.2 Sectoral structures Regarding the overall economic composition of the core city and that of the entire region, certain underlying differences can be expected. The economy of the core city consists largely of secondary-sector and tertiary-sector activities, i.e., manufacturing (processing as well as fabricative) and the provision of services (consumer-based activities, together with intermediate or producer-oriented services, sometimes referred to as “quaternary-sector” activities). The widespread trend of deindustrialization over the last 40 years has caused the manufacturing component in the sectoral profile of many cities to become significantly reduced, in both absolute and relative terms. In the case of the region as a whole, all of these “city” activities will necessarily be present, in addition to such primary-sector activities as agriculture, forestry, mineral exploitation, and (increasingly) the provision of recreational services and retirement-related amenities, each of which tends to be of a space-consuming character and is located mainly in the hinterland, i.e., outside the core city. It follows that the sectoral structure of the core city is likely to have a lower level of diversification than that of the entire region. This also tends to be the case if the comparison involves the respective export bases of the core city and the region. 5.3 Externalities and agglomeration economies It has frequently been argued that external economies or “externalities” exert an important influence on the economic performance of both the city and its region. Broadly speaking, externalities refer to those cost savings to the firm (but sometimes other advantages), over which the individual firm has no direct control. An important subset of external economies, which is spatially constrained or contingent on the spatial concentration of the relevant activity at one or more locations, is known as agglomeration economies (Rosenthal and Strange 2003; Storper 1995, 2010). Mention is made of a wholly different group of agglomeration economies which is internal to the firm, but this is not considered here. Externality-based agglomeration economies are generally viewed as contributing to improved productivity and innovation and can be divided into three broad types (each spatially constrained): “localization economies” or external economies of scale (involving firms in the same industry); “urbanization economies” or external economies of scope (relating to firms in different industries that are not directly dependent on each other); and “activity complex economies” or external economies of complexity (concerned with firms in different industries that have strong input–output linkages). It is important to recognize that agglomeration diseconomies may also be present. These are associated with such phenomena as high location rents and additional pollution costs, increased factor costs, more expensive
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transaction costs. The term “agglomeration economies” is therefore used as a shorthand expression for “net agglomeration economies.” For firms located in the core city, many of the externalities are rightly regarded as agglomeration economies. However, to suggest or to imply, as is sometimes done, that agglomeration economies exist (i.e., are available to firms) throughout the region, is to introduce something of a contradiction. It is true that certain firms, regardless of their location with respect to the core city, are able to avail themselves of particular economic advantages associated with the core, e.g., access to communications, as well as to production inputs, including financial, technical, marketing, and specialized management services. Such advantages are more accurately described as “regional externalities,” with the term “agglomeration economies” referring to core-city firms for which the need for concentration or juxtaposition is especially strong.7 There exists a further class of regional externalities which is not specifically associated with the core city, but which is region-wide in scope, e.g., regional externalities relating to efficient transportation and public-utility systems, specialized occupational skills, technical education, legal and regulatory frameworks, trade associations, cooperative traditions.
6 A system-wide perspective In this third perspective on spatial organization, the city and the region are each considered within the broader context of a national system: the system of cities and the system of regions. Here, reliance is placed on cross-sectional analysis, so that the spatial organization of cities and regions is being considered for a particular point in time. 6.1 Density functions across cities and regions We return to the population density functions considered in Sect. 4.2. Evidence from North America and Europe points to relationships between the parameters of the density functions and the populations of cities and regions. Across cities, Weiss (1961) and Berry and Horton (1970) demonstrated that in the negative exponential function of Eq. (1), the central density C increases with city population, whereas the slope b decreases. The situation is different for regions. The distance–density displays presented by Bogue (1950, p. 33) are in the form of an inverse power function, which may be regarded as a two-parameter approximation of the lognormal function of Eq. (2); see Sect. 4.2. If described in terms of a lognormal function, Bogue’s results are such that across regions N , the density near the center of the region (as well as the maximum level of density) increases with the population of the core city on which the region is based, as does g, the slope of the function beyond the maximum level of density. Since, generally speaking, the larger the population of the core city, the larger 7 The argument here does not refer to those agglomeration economies (usually of urbanization type) which are enjoyed by firms in non-core cities of the region. These are appropriately termed “local agglomeration economies.”
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will be the regional population, it follows that both N and g increase with regional population. It is clear that the central densities of the density functions for cities and those for regions both increase with population, as is to be expected. However, there is a significant difference between the two in the variation of slopes with population level (decreasing in the case cities and increasing for regions). This difference is related to the question of competition for space, as discussed in Sect. 4.1. Among cities, competition for space is absent, so that enlargement of a particular city is not constrained by the existence of a neighboring city. Increases in population across cities involve physical expansion and would be reflected in Eq. (1) by progressively higher values for C, the central density, and progressively lower values for b, the slope. The lower values for b point to the influence of relatively efficient systems of surface transportation, without which the values for b would probably remain constant or even rise with city population. Across regions, however, competition for space is present, in the sense that a given region is bounded by adjacent regions. It has already been mentioned that N and the maximum level of density both increase with regional population. Therefore, in the case of two adjoining regions having substantially unequal populations, the difference in their values for N (i.e., the difference in the density levels near their respective centers) will be relatively high, as will the difference in their maximum levels of density. However, at the common boundary of the two regions the difference in density levels will be low or even zero (Bogue 1950, p. 33). As a consequence g, the slope of the density function beyond the distance where density is at a maximum will be greater for the larger or more populous region. This is necessarily true if the boundary is located at the halfway point between the core cities of the two regions, and also true up to a limit, if (as is likely) the boundary is displaced beyond the halfway point toward the core city of the smaller region (Parr and Holden 2015). Generalizing from this two-region example, it becomes apparent that for a system of regions, g increases with regional population, unlike b which decreases with city population.
6.2 Size distributions of population for cities and regions In comparing the size distributions of a system of cities with that of a system of regions, the following common notation is used. The term PR is the population or size of a unit (a city or a region) of rank R, where rank or cumulative frequency refers to the number of units with populations greater than or equal to PR , while P1 is the population of the unit of rank 1 (the unit with the highest population). In a system of cities, the size distribution commonly adheres to the rank-size function, a particular form of the Pareto function. With the rank-size function, the logarithm of population decreases with the logarithm of rank at a constant rate, so that the graph of this function is linear and downward sloping, as in Fig. 2a. The form of the rank-size function was expressed by Lotka (1925) and Vining (1955) as follows: ln PR = ln P1 − q (ln R) (q > 0)
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Fig. 2 Size distributions for cities and regions
where P1 and q are constants, q being the slope of the function and indicating the extent of interurban concentration. The rank-size function holds for cities above the level of ph , the minimum population of 200,000 assumed here, but frequently also for cities below this level, as indicated in Fig. 2a. For a system of regions, generalization is more difficult than with the system of cities, largely because published data on regions may be based on political or administrative areas, which do not necessarily correspond to metropolitan regions assumed here. Nevertheless, for many nations the size distribution of regions appears to resemble a cumulative lognormal function. This is generally defined in terms of μ, the mean of the distribution, and σ , its standard deviation (Aitchison and Brown 1957). To permit comparison with the rank-size function of Eq. (3), the cumulative form of the lognormal function is expressed as the following approximation: ln PR = ln P1 − k (ln R)t
(k, t > 0)
(4)
where k and t are constants, k indicating the extent of interregional population inequality. When plotted on logarithmic axes of rank and size, the cumulative lognormal function appears as in Fig. 2b, which refers to the same nation as in Fig. 2a. It can be seen that for the upper part of this function, the logarithm of population size tends to decrease with the logarithm of rank at an approximately constant rate (as in the ranksize function), but thereafter decreases with the logarithm of rank at an increasing rate. In certain cases, the lognormal function is of a truncated form, so that the slope of the lower part of the function does not approach the vertical. The form of each size distribution is usually explained (or rather rationalized) by treating an existing distribution as the steady-state outcome of a growth process, involving the “law of proportionate effect.” This states that the population growth rate of a unit (a city or a region) over an interval is independent of its size at the beginning of the interval (Gibrat 1931; Steindl 1965; Levy 2009; Portnov 2012). If the law holds, and if over time the net entry of units into a growing system at some threshold
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level accounts for a constant proportion of growth, the steady-state distribution tends toward a rank-size function. N.B. This threshold is typically below ph , the minimum population of the core city, assumed here to be 200,000. If, however, the law holds, but the number of units remains fixed, the steady-state outcome is of a cumulative lognormal (or truncated lognormal) form. Thus, in the case of cities, where net entry into the system (i.e., cities attaining some threshold size) can be expected to occur, the rank-size function describes the steady-state distribution. For regions such net entry into the system is unlikely, and as a result the steady-state distribution tends toward the cumulative lognormal.8 6.3 Population–area and density–area relationships There exists a further contrast between a system of cities and a system of regions. This is concerned with the relationship between the population of a unit (a city or a region) and the area of that unit. For cities in the USA as well as in England and Wales, Stewart and Warntz (1958) found that the relationship between population and area (expressed in common logarithms) could be described as follows: log Ai = log Wc + wc (log Pi ) (0 < wc < 1)
(5)
where Ai is the area of city i, and Pi is its population, with Wc and wc as constants, wc representing the slope of the function or the rate of change of the logarithm of population of the city with the logarithm of area of that city. This regularity was also observed by Vining and Louw (1978) for systems of cities in a number of other nations. The relationship is positive, so that, unsurprisingly perhaps, the greater the population of a city, the greater is its area (the curve Pc in Fig. 3a).9 For regions, however, the relationship between population and area, which was briefly considered by Vining et al. (1979), would be of the form log Ai = log Wr − wr (log Pi ) (wr > 0)
(6)
where Wr and wr are constants. Here, the relationship is negative, so that the greater the population of a region, the smaller will be its area (the curve Pr in Fig. 3b). A closely related regularity focuses on the average density of a unit (again a city or a region) and the area of that unit. For a given unit i, its population Pi and its average density Di are linked by the equation Pi = Di Ai , where Ai is the area of unit i. Substituting for Pi in (5), the relationship for cities would be as follows: log Ai = log Vc +
wc (log Di ) 1 − wc
(7)
8 If the focus is on all urban centers, which would include those well below the minimum level for the built city of 200,000 ( ph in Fig. 2a), net entry of centers into the system over a given interval would be negligible or nonexistent. As a consequence and assuming the law of proportionate effect to be in operation, the steady-state distribution would tend to the cumulative lognormal, as in the case of regions. 9 In Fig. 3a (and also Fig. 3b), the right section of the x axis refers to the population–area relation, while the left section refers to the density–area relation (considered shortly).
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Fig. 3 Population–area and density–area relationships (see footnote 9)
where Vc and wc are constants, and where wc >0 1 − wc Here, average density and area are positively related: the greater the average density of a city, the greater will be its area (curve Dc in Fig. 3a). In the case of regions, a similar substitution for Pi in Eq. (6) would yield log Ai = log Vr −
wr (log Di ) 1 + wr
(8)
where Vr and wr are constants, and where 0<
wr <1 1 + wr
In contrast to the situation across cities, there is a negative relationship across regions between average density and area: the greater the average density of a region, the smaller the area (the curve Dr in Fig. 3b). This was borne out in a study by Haggett (1965, pp. 53–54) for counties in Brazil, and later in the work of Stephan (1972), who showed that the relationship was present across areal units in 94 of the 98 nations studied. Using the Stephan data, Vining et al. (1979) demonstrated in the case of regions that the density–area relationship was more robust than the population–area relationship considered above. The two sets of regularities may now be compared. For cities, wc <
wc 1 − wc
(9)
indicating that the increase in area with population occurs at a lower rate than the increase in area with average density (Fig. 3a). For regions, however,
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wr >
wr 1 + wr
(10)
so that that the decrease in area with population is at a higher rate than the decrease in area with average density (Fig. 3b). These particular differences in system-wide regularities between cities and regions again appear to turn on the question of competition for space. This becomes clear in the relationships between average density and area. For individual cities, there is no effective competition for space. It can be shown that across cities of increasing radius, and therefore increasing area, the effect of increasing values of C and decreasing values of b (referred to in Sect. 6.1) necessarily causes the average density of a city to be positively related to its area (Parr 2012, pp. 295–297). In the case of regions, however, competition for space is present. This may be likened to the process of spatial competition among firms under conditions of free entry, with market areas for highorder goods becoming comparable to economic regions. By the zero-profit condition, a high level of average density of population results in a relatively small market area (region), while a low level of average density requires a relatively large market area (region). This regularity was explicit in the Lösch (1944/1954, pp. 105–108) analysis of market areas and was prominent in the Skinner (1964) study of market-area structure in China. The negative relationship between average density and area is reinforced by other factors, such as the organization of political or administrative structures (Stephan 1977).
7 Alternative definitions of the city Up to this point, it has been convenient to specify the city in terms of the built city, as defined in Sect. 2. Such a morphological view of the city draws attention to its overall importance as a concentration of production, employment, housing, etc. However, the built city does not reflect the fact that certain localities physically separated from the built city may have a strong dependence on it. Nor is the built city a satisfactory reflection of its dependence on localities beyond its boundary. In certain respects, therefore, the built city may not be an adequate representation of the city. Other definitions of the city are introduced shortly, and as will be argued, these involve the progressive areal enlargement of city, to the point where the term “city” may seem inappropriate. 7.1 The extended city We begin with what is referred to as the “extended city.” This has several versions, but in all cases, it includes a base (the built city), to which various contiguous or indirectly contiguous areas (comprising statistical units) are added according to particular criteria (Parr 2007). These units are assumed to be relatively small, being in the vicinity of 20–25 km2 . One version of the extended city is the “employment city.” This is composed of the built city together with any unit that has at least 50 % of its employed population directly or indirectly reliant on it. The indirect element is that part of the unit’s employed population which is dependent (via the local employment multiplier
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effect) on those directly employed in the built city. In the case of the “consumption city,” a unit is added to the built city if at least 50 % of its consumption expenditures are undertaken within any part of the built city. In the case of both the employment city and the consumption city, the added units, which may contain rural areas and free-standing urban centers, are now regarded in economic terms as part of the city. In each case, certain units may not satisfy the relevant criterion, but are surrounded by units that do. In order to assure continuity, it is convenient to regard these former units as belonging to the relevant extended city. A third version of the extended city, termed the “workforce city,” is concerned with the area on which the built city relies for its supply of labor. It consists of the built city, to which increasingly distant units are added, so as to account for the overwhelming bulk of the employed workforce of the built city, say around 95 %.10 Obviously, the higher the percentage selected, the larger will be the area of the workforce city. The remaining percentage would refer to those employed in the built city but residing beyond the workforce city. The workforce city, which tends to be the broadest version of the extended city, is the least satisfactory by virtue of the arbitrary nature of the cutoff percentage. However, each of the three versions of the extended city is still recognizable as a city, and the main contrasts between the city and the region (outlined in earlier sections) continue to be valid. 7.2 The functional urban area Another perception of the city reaching beyond the built city involves the “functional urban area” (Organization for Economic Co-operation and Development 2012). As will be seen, by the nature of its construction the functional urban area based on a given city will be larger than any of the form of the “extended city” considered above. At the same time, the functional urban area based on a given city will be smaller than the metropolitan region centered on that city, i.e., the type of region considered up to now. The functional urban area is thus intermediate in scale between the extended city and the metropolitan region. As a city-based territory, the functional urban area is frequently defined in labor-market terms, although a number of alternative definitions are possible. It is generally the case that the functional urban areas of a given nation do not comprise a space-filling set.11 In the USA, attempts to define the city more broadly can be traced back to the 1910 Census with the introduction of the Metropolitan District. The approach has been revised from time to time, and at present, the relevant unit is the “Metropolitan Statistical Area” (MSA) which typically displays the characteristics of a functional urban area. The MSA replaced the standard metropolitan statistical area (SMSA), 10 An upper limit below 100 % is necessary, in order to exclude the relatively few workers that are employed in the built city but who reside at particularly long distances from it. Without such a limit, the workforce city would become unrealistically large. 11 In a compact nation with a high population density, the various functional urban areas might form a space-filling set, as in the study of the Netherlands by Klaassen et al. (1981). Outcomes such as this may also be due to the selection of a relatively low minimum-population level for cities on which the functional urban areas are based.
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suggested modifications of which involved either smaller units (Fox and Kumar 1965; Fox and Ghosh 1980) or larger units (Berry et al. 1968). The base unit of the MSA is the county in which the central city (the legal or de jure city with a population in excess of 50,000) is located. To this base, one or more neighboring counties are added, if a minimum level of two-way commuting ties between a given county and the base county can be identified. The Bureau of Census designation “Combined Statistical Area” refers a grouping of adjacent MSAs that have certain links based on commuting. The concept of the functional urban area has also been employed in the spatial analysis of cities in various nations of Europe (van den Berg et al. 1982; Cheshire and Hay 1989; Hall and Hay 1980; Klaassen et al. 1981). Different definitional approaches have been utilized, but the base of the functional urban area is generally taken to be a “central city” (the legal city but sometimes a larger entity such as the built city), having a population or employment level above some minimum. Localities or local-government areas are then added to this base unit, according to whether a particular criterion is satisfied, the extent of commuting to the central city being the most common one. Thus, if more than a given percentage of the employed population of a locality works in the central city, it is treated as part of the functional urban area. This percentage may be as low as 10 % though generally no higher than 20 %. A recent publication by the Organization for Economic Co-operation and Development (2012) outlined a more sophisticated version of this method for defining the functional urban area.
7.3 The functional urban area as a city A worrying aspect of the city being defined as its functional urban area concerns the resulting physical extent. When considered in these terms, the “city” in both the USA and Europe can sometimes have a very large diameter, even in excess of 120 kms (Berry et al. 1968; Hall and Hay 1980), casting doubt as to whether such a territory can, in fact, be considered a city. In defining a city as its functional urban area, certain units (counties in the USA or local-government areas in Europe) may become added which are not strongly linked in economic terms to the base unit, as is illustrated in the following example. The concern is with an individual unit (a municipality or area) located 20 km beyond the boundary of a built city. It is assumed that: (1) 15 % of the employed population of the unit commutes to the built city; and (2) the local employment multiplier is 2; so that (3) the employment within the unit that is supported by this out-commuting employment amounts to an additional 15 % of the employed population. As a result, 30 % of the unit’s employment is directly or indirectly dependent on the built city. Under a criterion of 10 % of the employed population commuting to the built city, the unit would obviously be included as part of the functional urban area, since the level of commuting to the built city is 15 %. However, in this example as much as 70 % of the employed population would not be dependent on the built city for employment, either directly or indirectly. The argument would be similar if incomes received were used in place of employed population. By either measure, the case for regarding the functional economic area as a “city” is not a compelling one.
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Thus, what is intended to be a representation of the city emerges as a considerably broader entity, often containing separate urban centers.12 In fact, a city defined in this way begins to assume particular characteristics of the more extensive metropolitan region, referred to throughout this discussion. As a consequence, particular contrasts between the city and the metropolitan region become less clear, something that is apparent in the case of patterns of interaction, for example. The underlying reason for this awkward convergence appears to be the failure to admit to a difference between the city as a relatively localized entity, and the reach of a city (i.e., its immediate field of interaction or influence), which covers a more extensive area. These are different, though related, facets of spatial structure, and viewing a city as its functional urban area necessarily involves a conflation of the two. Furthermore, to define the city as its functional urban area is to lose sight of certain of the key characteristics of the city, namely its relatively compact nature and the associated high levels of population and employment density. These characteristics are rooted in the imperatives of concentration, stemming from the tendency toward agglomeration in the organization and location of production, the requirement of relative proximity between place of residence and place of employment, and the necessity of a focal point in the exchange of information and the provision of particular specialized services. Therefore, defining a city at the scale of the functional urban area has the effect of diverting attention away from those facets of the city that are part of its raison d’être. However, this is not to discard the concept of the functional urban area. Under other circumstances, it provides a practical unit for examining the spatial structure of trade and various aspects of economic interaction within a city-based territory, and it has been employed by planners and other policy analysts to good effect. The use of the functional urban area as a means of defining a city, however, may be called into question.
8 Closing comments The preceding discussion, which focused on conditions within economically developed nations, has attempted to draw together a number of reasonably well-established empirical regularities. In the extensive literature on spatial analysis, these regularities have invariably been explored either at the urban level or at the regional level. Here, an attempt has been made considering such regularities at both levels, as a means of identifying particular differences between the city and the region. To maintain definitional clarity, reliance was placed on the built city and the metropolitan region (a large-scale nodal region) as convenient benchmarks, although other conceptions of the city were considered. It would be difficult to deny the fact that as economic units, the city and the region share a number of common features. It would be no less difficult to reject the proposition that important differences exist between the city and the region. In each of the 12 The problem is exacerbated if the added units are of a relatively large areal extent, as tends to be the case for certain MSAs in the western states of the USA, where the “added” counties are especially large. This difficulty does not arise in the case of the various forms of the extended city considered in Sect. 7.1, where the areal extent of the added units is deliberately small.
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three perspectives adopted above, it was clear that the city and region displayed significantly different forms of spatial organization. From this standpoint, therefore, a city does not simply represent a scaled-down version of a region, any more than a region can be viewed as an enlargement of the city. And it seems reasonable to conclude that the case for maintaining a distinction between the city and the region remains a defensible one, although as was seen, this distinction may be weakened if certain definitions of the city are employed. Aside from being of theoretical interest, such a conclusion has a number of important implications. For example, it casts light on differences in the manner in which spatial structure and economic performance are interrelated at the city and the regional levels. It also has a bearing on the framing and implementation of policy in fields as diverse as the economic adjustment to exogenous change, transportation and infrastructure investment, the provision of public services, and rationalizing the structure of local government and administration. Within these contexts, among many others, differences between the city and the region as units of analysis are sufficiently important as to warrant further scrutiny. Acknowledgments The author is grateful to D. Holden and anonymous referees for suggesting a number of modifications and revisions. Thanks are also due to D. Adams, D. Houston, R. Paddison, N. Sprigings, and K. Swales, who provided valuable comments on earlier versions of the paper.
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