Urban-Rent Theory, Time Series and Morphogenesis: An Example of Eclecticism in Geographical Research

Urban-Rent Theory, Time Series and Morphogenesis: An Example of Eclecticism inGeographical ResearchAuthor(s): J. W. R. WhitehandSource: Area, Vol. 4, No. 4 (1972), pp. 215-222Published by: The Royal Geographical Society (with the Institute of British Geographers)Stable URL: http://www.jstor.org/stable/20000692 .

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Urban-rent theory, time series and morphogenesis: an example of eclecticism in geographical research J. W. R. Whitehand, University of Birmingham

Summary. Ideas derived from urban-rent theory and the analysis of building cycles are examined in relation to morphogenetic concepts concerning the development of urban land-use patterns. A tentative schema, which recognizes consistencies between the results of these previously unrelated types of research, is outlined.

Urban-rent theory and morphogenesis, though enjoying less popularity now than in the past, have by no means exhausted their potentialities, and the

implications of time series for geography have never been widely appreciated.

The object of this paper is to exemplify possible insights that might be derived from the integration of certain aspects of these lines of research. This is done

by abstracting essentially morphogenetic and economic concepts from their accepted frames of reference and showing that, if inter-related, they provide a

basis for explaining certain aspects of the development of urban land-use

patterns. The concepts borrowed from existing studies have been in currency

for more than a decade and some familiarity with them in their traditional

contexts is therefore assumed.

Bid rents and land uses

Certain essentially economic or economico-geographical assumptions provide

the starting point for the argument. These, together with a simple deduction

from them, may be listed as follows:

(1) The bid-rent curve of users with high accessibility costs per unit of land

tends to be steeper than that of users with low accessibility costs per unit of land.1

(2) The relative amounts of development involving low and high capital

investment per unit of land are partly a function of the availability of

capital. (3) Uses with high accessibility costs per unit of land tend to involve high

capital investment per unit of land. Thus, a reduction in the availability of capital is likely to cause a relatively larger overall reduction in the bid

rent of high accessibility cost users than in the bid rent of low accessibility cost users.

These grossly simplified relationships can be shown in diagrammatic form.

Figure 1A shows during an economic boom bid-rent curves of high and low

accessibility-cost users per unit of land and a resulting two-use landscape. Linear relationships are assumed for the present purpose. Figure lB depicts the situation during an economic slump-here the curve of one of the uses falls

entirely below that of the other and a single-use landscape therefore results.

Since it is assumed that for both uses costs of accessibility remain a constant

215



216 Urban-rent theory, time series and morphogenesis

proportion of total costs, the gradients remain unchanged. Various situations intermediate between lA and IB, or more extreme than either of them, can of

course be envisaged. Such notions have far-reaching implications for the composition of the

urban land-use pattern. A recent paper2 has directed attention to some of these implications in relation to an important land-use change, namely the change from rural use to that by housing and institutions.3 In that paper a model where by land at the urban fringe is assigned to housing or institutional use is derived, assuming that these two uses are representative of ' a' and ' b ' in Figure 1 and that the building cycle is partly a function of the availability of credit.4

oa _

C

a

C C_ U) I

Distance Distance

Figure 1. Hypothetical bid-rent curves and resulting landscapes, (A) during an economic boom, (B) during an economic slump.

Assignment to sites is based on the assumption that the ratio of new institutional to new housing development is related to the differences between the bid rents

of these two uses. Thus during a boom in housing construction there is a high probability of housing being assigned to sites close to the edge of the built-up area and institutions to more distant sites: during a housing slump there is a high probability of institutions being assigned to sites close to the built-up area. Iterations of long-period booms and slumps create a series of zones characterized by different proportions of housing and institutions.

A study of north-west Glasgow has revealed that the pattern of development in that area is in many respects consistent with this model. Furthermore, the resulting land-use pattern at the urban fringe is broadly in accord with the find ings of morphogenetic work on the early stages in the development of urban fringe belts. The essentially annular pattern of growth with alternating zones

with different proportions of institutions and housing conforms closely to M. R. G. Conzen's alternating fringe belts and zones of residential accretion, although the former are characterized by various uses in addition to institu tions.5 However, the model assumes constant bid-rent gradients over time and, although this is a convenient simplification when studying the relatively short periods involved in the process whereby land is converted from rural to urban use, it becomes increasingly unsatisfactory when the urban land-use pattern is examined in greater historical depth; for example, in relation to changes experienced by former fringe uses as they become embedded within the built-up area. Attention is drawn to this insufficiency if comparison is made with the results of morphogenetic work on long-term changes in land-use patterns.

Changes over time in fringe belts

One of the most significant aspects of the development of urban fringe belts



Urban-rent theory, time series and morphogenesis 217

according to several studies6 is their perpetuation, in varying degrees of adapta tion and redevelopment, long after they cease to be at the urban fringe. This empirical fact, related by morphogenetic scholars to the continuing influence of the inheritance from past periods, appears to be inconsistent with fixed bid rent gradients of institutions and house-builders. Such fixed gradients would require that during a housing boom existing institutional sites would tend to fall to the bids of house-builders, the institutions themselves being displaced to sites farther out which were still of sub-marginal utility to the house-builder. Evidence from fringe-belt studies suggests that this is a quite inadequate explana tion of actual land-use changes.

Figure 2 summarizes for two adjacent areas in Glasgow (Hillhead and Maryhill) variations in land losses and gains by fringe-belt uses as they become

Passage of main t hhouse - building

2'0 v activity .C /lX

I I\ I 2

0 J

A n HILLHEAD

o -,HILHA

C

0-5

E

? .

,, 0 ; _ Sc

GLASGOW'S BUILDING CYCLE 4 L

PasIg of -on

a 0 50 . 5.,...0 ;;

58 77 93 1908 23 38 51 6a~3 t

10-~~~~~~~~~~~~ A- 4

Passage of main an house-building c

o activity 0 0 0 MARYHILL 0

0.5

JA4'0 185- 18I3 84 ;9 92 -1'9 92

58 77 93 1908 23 38 51 68

Figure 2. Percentage of fringe-belt sites incurring losses to and gains from

housing in two areas in north-west Glasgow, 1840-1968, compared with the

building cycle.

embedded within the built-up area.7 From this we may tentatively conclude that, during the time when the conversion of rural land to housing is at its maximum, a minority of fringe-belt sites are vulnerable to redevelopment for housing. This may be followed by a period after the- passage of the main house-building

activity when few fringe-belt sites are acquired by house-builders and there is




relatively little expansion of fringe-belt uses into adjoining areas. After this, and sometimes without such a period intervening, there is an increasing proba bility of fringe-belt uses actually expanding their site areas at the expense of adjacent housing areas by the conversion of existing buildings and/or redevelop

ment. The redevelopment of fringe-belt land for housing correlates positively with the building cycle but the subsequent expansion of surviving fringe-belt uses into adjoining housing areas occurs on a significant scale during both housing booms and slumps.

Changes over time in bid rents

This change over time in the behaviour of fringe-belt uses on established sites draws attention to the limitations of an assumption of fixed bid-rent gradients over time. If land users are studied over a period of not one but several building cycles, it is necessary to allow for changes that significantly affect their bid-rent gradients. During such a long period of time in a growing city a site is likely to be transformed from a peripheral location to one deeply embedded within the built-up area and the related increase in its land value is likely to be associated with considerable organizational changes in the activity located on the site. In order to justify the use of increasingly expensive land the accessibility costs of the user per unit of land must rise, involving a more inten sive use of the site. The gradients of the bid-rent curves of both housing and institutions will therefore steepen.8

For a number of reasons it is unlikely that the curve of housing will steepen as much as that of institutions. To appreciate this it is necessary to consider the different potentialities of housing and institutional sites for more intensive use which stem from the differences in the capital investment per unit of land involved in their original development. Even low-density housing sites will have less space for adding new accommodation than will the average institution,

which when first established will have devoted only a small fraction of its site area to buildings. In fact, if investment in additional buildings on housing and institutional sites is plotted over time, generalized curves approximating to those shown in Figure 3A might be expected to obtain. Direct empirical con firmation of this is not available, but Figure 3B shows the cumulative number of

major investments in additional buildings for seven institutions established in north-west Glasgow in the period 1840-77 and surviving on the same sites in the post-war period.9 The adding of new buildings took place throughout the 100 year period,10 although with slightly diminished intensity during housing slumps. By contrast, on housing sites in the same area there was scarcely any investment in additional buildings, although the population density increased appreciably in association with the subdivision of large dwellings.

It follows from our initial assumptions that, if the additional capital invest ment per unit of land in an institutional site is greater than that in a housing site, the institution will experience a relatively greater increase in accessibility costs per unit of land and therefore a greater steepening of its bid-rent curve. Clearly, for this reason alone, the bid rent of an institution for its own site will tend to increase more than that of house-builders. However, the greater capital investment in additional buildings by the institution will also tend to produce a relatively greater increase in its bid rent for its present site as compared with all other sites and create a local peak in its bid-rent curve. This relates to the fact that, unlike the case of the house plot, on which the largest structure is generally



Urban-rent theory, time series and morphogenesis 219

2 ~~~~~~~~~i 20 E

0 6~~~~~~~~~~0.1 L ~~~~~~EE

6~~~~~~~~~ ~ ~ ~ ~~~~~

E 5

c>c 1.59- 1878- 1895- 1909- 1924- 1939- 1952 Time 7 7 94 1908 23 38 51 68

Figure 3. Investment in additional buildings over time, (A) hypothetical trends for institutional and housing sites, (B) cumulative number of major investments in additional buildings on seven institutional sites in north-west Glasgow,

1859-1968.

the house built at the time of initial urban development, the majority of build ings may be much more recent. Expressed another way, the average age of build ings will tend to increase more slowly on an institutional site than on a house site (Fig. 4). This will be associated with a quite different phasing of building obsolescence in which it is unlikely that the whole building stock will become

n

(1 0

Time

Figure 4. Hypothetical trends in the average age of building stock over time.

obsolete at one time. Thus, for a bid by a house-builder for an institutional site to be successful, the value of the land to the house-builder must exceed the value

of the land and the buildings to the institution. It is probable that, once a normal pattern of periodic additional building has been established, the capital value of an institution's building stock as a whole is only rarely at a sufficient level of depreciation to make it economic for the institution to sell its site to a house builder and develop a cheaper site at the urban fringe. For similar reasons the redevelopment by an institution of its entire site at one time tends to be unecono

mic.

Building cycles and changes in bid rents

The role of the building cycle in relation to changes over time in the bid-rent gradients of users remains to be considered. If it is accepted that an institution on an internal site develops accessibility costs per unit of land that are as high as those of housing at a similar distance from the city centre, then the explana tion offered for differences between housing and institutions in their patterns



220 Urban-rent theory, time series and morphogeniesis

of investment at the urban fringe is not applicable to internal sites. Indeed, if the internal institutional site is developed as a higher accessibility cost use than neighbouring housing areas, then the excess of its bid rent over that of housing

might be thought of as actually diminishing during slump periods. Although there is no empirical evidence to support it, this supposition is made in Figure 5 in which the bid rent of an institution for its own site is compared over time

with that of house-builders.

Incorporated Expansion onto in fringe adjacent sites

belt commences Established Embedded on fringe in built-up

iite b rer

Thesre t.Heporhetical coniderantions are inotwithtout sorigsonificane fovr thme exason

phase in fringe-belt development that was noted in Figure 2. There does seem to be a point in time when site saturation is approaching and, perhaps for a combination of the reasons already outlined, the institution is prepared to bid higher for adjacent sites than existing or potential residential users. How ever, this method of acquiring additional space does not solve for an institution the problem of accommodating its low accessibility-cost facilities (for example, playing fields) which, rather than subsidize on expensive adjacent sites, it will normally re-locate on cheaper land at the urban fringe, which may by this time be a considerable distance away.

In relation to such locational decisions the building cycle would again appear on theoretical grounds to have significance. Once an institution has outgrown its site, but cannot afford expensive adjacent sites for those of its activities with low accessibility costs per unit of land, its locational decisions become more diverse in the sense that they involve the assignment to sites of both high and low accessibility-cost activities per unit of land. It may be predicted that in a

housing slump, when credit is short but land is cheap, an institution will tend to concentrate on acquiring new sites at the fringe for low accessibility-cost activities per unit of land, even allowing some of this land to remain temporarily in agriculture or undeveloped. During a housing boom, when high rents and prices can only be justified by intensive use of the land, capital will tend to be invested in the more concentrated development of sites already acquired. In this respect the locational decisions of a large institution may resemble those of



Urban-rent theory, time series morphogenesis 221

local government in that the sites for activities with a variety of accessibility costs per unit of land are being financed from a single budget.

It has proved convenient in this paper to categorize urban developments on a broad land-use basis, assuming that all land users within each category have bid-rent gradients that behave similarly over time. Thus important variations within categories in the adaptability to growth of both sites and activities are ignored. The over-simplifications inherent in such assumptions require emphasis. If from the beginning a site is small relative to the size of the institution occupy ing it, this is likely to limit the scope for adding buildings and increase the

probability of a stage being reached when the whole building stock is simul taneously in a condition of obsolescence. There is a greater chance that the bid rent of an institution for such a site will be exceeded by that of a house-builder. In the case of some types of institution, space for the intensifying of activities

may be strictly limited by the nature of the activity. Where land, rather than buildings, remains by far the main asset, as is normally the case with many types of sports grounds, the potential return on redevelopment for housing is likely rapidly to exceed the value of land and buildings to the existing user and such sites are especially likely to be redeveloped for housing.

This paper deals with only a limited aspect of the process by which spatial patterns of urban land use develop over time. The concepts introduced should not be expected to provide anything approaching a complete explanation of such a complex process. Major aspects, including the subsidization, on social and other grounds, of locations that are no longer economic, have been com pletely ignored. Furthermore, if the ideas outlined here are to provide a sound foundation for a more elaborate conceptual framework, a rigorous examination of both their theoretical and empirical bases will be required.

Acknowledgements Of the many individuals and organizations that contributed to the compilation of the data

used in this paper, the author is particularly indebted to Mr. J. A. Fisher of the Mitchell Library,

Glasgow, and Mr. H. K. Mackay of Baillie's Institution, Glasgow. Mr R. G. Ford and Mr

M. J. Tricker kindly gave advice on a draft of this paper. The illustrations were drawn by Miss J. G. M. Boulton in the Department of Geography, University of Birmingham.

Notes and references 1. A ' bid-rent curve ' represents the price or rent per unit of land that a user is willing to

pay at varying distances from the city centre. For a discussion of this term see Alonso, W., 1960. A theory of the urban land market. Pap. Reg. Sci. Ass., 6, 149-57.

2. Whitehand, J. W. R., 1972. Building cycles and the spatial pattern of urban growth. Trans. Inst. Br. Geogr. 56, 39-55.

3. The following are the main categories of land use defined as institutional:- educational, medical, military, central and local government, research, recreational (including clubs and public open spaces) and religious (including burial grounds).

4. Short-term business cycles are ignored in this analysis. For their relationship to building cycles and other economic series in an American context, see Isard, W., 1942. A neglected cycle: the transport-building cycle. R. Econ. Statist. 24, 149-58. For the relationship of the building cycle to economic trends in Britain, see Lewis, J. Parry, 1965. Building Cycles and Britain's Growth.

5. Conzen, M. R. G., 1960. Alnwick, Northumberland; a study in town-plan analysis. Trans. Inst. Br. Geogr. 27, and idem. 1962. The plan analysis of an English city centre. Proceedings of the IGU Symposium in Urban Geography Lund, 1960, Lund, 383-414.

6. See, for example, Conzen M. P., 1968. Fringe location land uses: relict patterns in Madison Wisconsin. Unpublished paper, Annual Meeting, Ass. Am. Geogr. West Lakes Division, Madison, Wisconsin.




7. These data and those relating to Glasgow referred to later in this paper were obtained from a diversity of sources, including the histories and records of individual institutions, Dean of Guild Records, the Register of Sasines, Post Office and Kelly's Directories, Valuation Rolls and Ordnance Survey and other maps and plans.

8. It is assumed for this purpose that, for the community as a whole, accessibility costs per unit distance remain constaDt relative to other costs.

9. The seven institutions included one example of each of the following:- children's home, hospital, barracks, botanic gardens, college (later adapted for use by the BBC), university, school.

10. If amount of investment were substituted for number of investments, the relationship would be curvilinear since the size of investments (at constant prices) tends to increase over time.

Special Publications of the Institute

The following is a list of Special Publications now available from the Institute of British Geographers, 1 Kensington Gore, London, SW7 2AR. Members of the Insti tute can obtain copies at 200% discount.

SPEC. PUBL. No. 1 LAND USE AND RESOURCES: Dec. 1968 STUDIES IN APPLIED GEOGRAPHY

-the Memorial Volume to Sir Dudley Stamp. 17 papers reflecting his special interests including a bibliography of his published works Price ?350 ($8.75)

SPEC. PUBL. No. 2 POST-GLACIAL UPLIFT IN ARCTIC June 1970 CANADA a geomorphological study by

Dr J. T. Andrews, Associate Director of the Institute of Arctic & Alpine Research,

University of Colorado Price ?2 50 ($6.25)

SPEC. PUBL. No. 3 SLOPES-FORM AND PROCESS a Jan. 1971 collection of papers edited by D. Brunsden

for the British Geomorphological Research Group-a Study Group of the IBG Price ?300 ($7.50)

SPEC. PUBL. No. 4 POLAR GEOMORPHOLOGY-a July 1972 symposium compiled by R. J. Price &

D. E. Sugden of 14 papers read at the 1972 Annual Conference Price ?360 ($9.00)

Corrigendum In the article by Professor Lawton on ' Geographers and the Census ' (Area 4, 1972, p. 212) the address of the Office of Population Censuses and Surveys should have read Titchfield, Fareham, Hants.



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Urban-Rent Theory, Time Series and Morphogenesis: An Example of Eclecticism in Geographical Research