Settlement Geography II: Urban Systems, Central Place Theory, Models of Urban Land Use, Global and Edge Cities, Segregation and Urban Poverty

The second settlement chapter covers the city as a system and as a structure. The document lists urban systems (the law of the primate city and the rank-size rule); the central place theories of Christaller and Lösch (it writes "Losch"); the internal structure of the city and the models of urban land use of Burgess, Harris and Ullman, and Hoyt; the concepts of megacities, global cities and edge cities; changing urban forms (peri-urban areas, the rural–urban fringe, suburban, ring and satellite towns); social segregation; urban social area analysis; and the manifestation of poverty in the city (slums, informal-sector growth, crime and social exclusion). Christaller's k-values and the rank-size rule are worked numerically, as NET sets them.

1. Urban systems: the primate city and the rank-size rule

Mark Jefferson's "law of the primate city" (1939) observed that in many countries the largest city is disproportionately large — commonly more than twice the size of the second — and supereminent in national economic, political and cultural life. Primacy is measured by the two-city index (P1 ÷ P2) or the four-city index (P1 ÷ [P2 + P3 + P4]); Bangkok, Lima, Dhaka and, historically, Paris and London are standard examples. The rank-size rule, anticipated by Felix Auerbach (1913) and formalised by G.K. Zipf (1949), states that the population of the city of rank n is the population of the largest city divided by n: Pn = P1 ÷ n. If the largest city has 12 million people, the second should have 6 million, the third 4 million and the fourth 3 million; plotted on double-logarithmic paper, a rank-size system is a straight line with a slope of −1.

Brian Berry (1961) compared the city-size distributions of 38 countries and found no simple link to level of development; rank-size (log-normal) distributions were associated with large countries with a long urban history and complex economies, primate distributions with small countries, simple economies or a colonial or political concentration of functions. India as a whole approximates a rank-size system with several large metropolises and no single primate city, but primacy is strong within some states — Kolkata in West Bengal is the classic case.

2. Central place theories: Christaller and Lösch

Walter Christaller's Die zentralen Orte in Süddeutschland (1933) asked why settlements that supply goods and services to a surrounding area are of particular sizes and spacings. He assumed an isotropic plain — uniform in fertility, population density and purchasing power, with transport equally easy in every direction and cost proportional to distance — and consumers who buy from the nearest centre. Two concepts do the work. The threshold is the minimum population or purchasing power needed to keep a good or service in business; the range is the maximum distance people will travel to obtain it. Low-order goods (bread, vegetables) have small thresholds and short ranges; high-order goods (jewellery, specialist hospitals) have large thresholds and long ranges. Circular market areas would leave gaps or overlap, so competition packs them into hexagons, the shape nearest the circle that fills a plane completely. The result is a hierarchy: higher-order centres are fewer, larger and farther apart, and supply all lower-order goods as well — Christaller identified seven orders in southern Germany, from the Marktort up to the Landeshauptstadt.

PrinciplekHow lower-order centres are placedMarket areas per order
Marketing (supply)3At the corners of the higher-order hexagon, each shared by three higher-order centres: 1 + 6 × 1/3 = 31, 3, 9, 27, 81 …
Traffic (transport)4At the midpoints of the sides, on the straight routes between higher centres, each shared by two: 1 + 6 × 1/2 = 41, 4, 16, 64 …
Administrative (separation)7Wholly inside the higher-order hexagon, so each is controlled by one centre: 1 + 6 = 71, 7, 49, 343 …

August Lösch, in Die räumliche Ordnung der Wirtschaft (1940; English translation The Economics of Location, 1954), derived the hexagon from the economics of demand: sales fall with distance as delivered price rises, generating a demand cone, and free entry squeezes market areas into hexagons. Unlike Christaller, Lösch did not fix one k for the whole system. Each good has its own threshold and so its own net of hexagons; he took the smallest possible networks (k = 3, 4, 7, 9, 12, 13, 16, 19, 21, 25 and so on), superimposed them on a single metropolis and rotated them to make as many centres coincide as possible. The result is a landscape of six city-rich and six city-poor sectors radiating from the metropolis, and a more continuous hierarchy in which centres of the same size need not offer the same functions. Christaller's model is a deductive hierarchy of fixed levels; Lösch's is a profit-maximising general equilibrium of overlapping nets.

🧠 Deriving k in one line
Count the higher-order centre's own lower-order area as 1, then add the share of each of the six surrounding lower-order areas it serves: one-third each at the corners (k = 3), one-half each at the midpoints of the sides (k = 4), the whole of each when they lie inside its boundary (k = 7). The number of market areas n levels down is kⁿ.

3. Internal structure of the city: the models of Burgess, Hoyt, and Harris and Ullman

ModelAuthor, year, basisStructure
Concentric zoneErnest W. Burgess, 1925; Chicago; human-ecological processes of invasion and successionFive rings: I central business district (the Loop); II zone in transition (decaying housing, light industry, new immigrants); III zone of working-men's homes; IV residential zone of the middle class; V commuters' zone
SectorHomer Hoyt, 1939; residential rents in 142 American citiesWedge-shaped sectors radiating from the CBD; high-rent residential sectors grow outward along transport routes, high ground and away from industry, while low-rent sectors adjoin factories and railways
Multiple nucleiChauncy D. Harris and Edward L. Ullman, 1945Several separate nuclei — CBD, wholesale and light manufacturing, heavy industry, residential districts, outlying business districts, suburbs — because some activities need special facilities, like activities cluster, unlike activities repel, and some cannot afford the best sites

All three are Western, industrial-city models. Their economic logic is formalised in William Alonso's bid-rent theory (1964): each land use bids a rent that falls with distance from the centre, and the use with the highest bid at each distance occupies it, producing rings. The pre-industrial city described by Gideon Sjoberg (1960) reversed the gradient, with the elite at the centre and the poor at the edge. Indian cities are usually read as dual or composite: a dense old core (walled city, bazaar and temple or mosque), a colonial layer of civil lines, cantonment and railway colony, and post-independence planned sectors, industrial estates and peripheral informal settlements.

⚠️ Zone II is the zone in transition, not the working-class zone
In Burgess's scheme the ring immediately around the CBD is the zone in transition, invaded by business and light industry and occupied by the poorest newcomers; the zone of working-men's homes is the third ring, housing workers who have escaped it but need to live close to their jobs.

4. New urban forms, segregation, social area analysis and urban poverty

A megacity is, in UN usage, an urban agglomeration of 10 million or more. A global (world) city is defined by function, not size: John Friedmann's world city hypothesis (1986) ranked cities as control points of the world economy, and Saskia Sassen's The Global City (1991) argued that New York, London and Tokyo had become command centres where advanced producer services — finance, law, accounting, advertising — coordinate a dispersed global production system. An edge city, in Joel Garreau's Edge City (1991), is a new concentration of offices and retail on the periphery of a metropolis: at least five million square feet of office space, more jobs than bedrooms, perceived as one place, and nothing like a city thirty years earlier — Gurugram beside Delhi is often cited as an Indian case. Around cities, the rural–urban fringe mixes farmland with urban uses; the wider peri-urban zone is functionally tied to the city while administratively rural. Suburbs are residential extensions dependent on the core; ring towns form a circle of settlements around a metropolis; satellite towns are planned, partly self-contained towns with their own employment, set beyond a green belt — the idea descends from Ebenezer Howard's garden city (1898).

Social segregation is the spatial separation of groups by class, caste, ethnicity or religion; it is measured by the index of dissimilarity, D = ½ Σ |aᵢ/A − bᵢ/B| × 100, the percentage of one group that would have to move for the two to be evenly distributed. Urban social area analysis was developed by Eshref Shevky with Marilyn Williams (1949, Los Angeles) and Wendell Bell (1955, San Francisco). From census tract data it built three indices — social rank (economic status: occupation and education), urbanisation (family status: fertility, women in the labour force, single-family dwellings) and segregation (ethnic status). Later factorial ecology derived the dimensions statistically, and Robert Murdie (1969) showed that they map onto the classical models: economic status varies by sectors (Hoyt), family status by concentric zones (Burgess), and ethnic status in clusters (multiple nuclei).

Poverty in the city takes four forms named in the document. Slums — the 2011 census counted about 65 million people in slums, in statutory towns that reported them. The informal sector — a term popularised by Keith Hart's study of Accra (1973) and the ILO's Kenya mission report (1972) — covers unregistered, unprotected work such as street vending, domestic service and home-based manufacture, and employs the majority of urban workers in India. Crime tends to concentrate where poverty, overcrowding and weak institutions coincide. Social exclusion is the denial of full participation in society through lack of housing tenure, identity documents, services and voice; Oscar Lewis's idea of a self-perpetuating "culture of poverty" (1959, 1966) has been widely criticised for blaming the poor for structural conditions.

Key takeaways

  • Jefferson (1939): the primate city is disproportionately large; Zipf (1949): Pn = P1 ÷ n, a straight line of slope −1 on log–log paper; Berry linked rank-size to large, complex, long-urbanised economies.
  • Christaller (1933): threshold and range, hexagonal market areas, k = 3 marketing (1, 3, 9, 27), k = 4 traffic (1, 4, 16), k = 7 administrative (1, 7, 49).
  • Lösch (1940): demand cones, variable k, nets rotated around a metropolis into six city-rich and six city-poor sectors.
  • Burgess (1925) five concentric zones with the zone in transition second; Hoyt (1939) sectors along routes; Harris and Ullman (1945) multiple nuclei; Alonso's bid-rent explains the gradients.
  • Megacity ≥ 10 million; global city (Friedmann 1986, Sassen 1991); edge city (Garreau 1991); Shevky–Bell: social rank, urbanisation, segregation — sectors, zones and clusters in Murdie; slums, informal sector (Hart), crime and exclusion express urban poverty.

Practice questions (11)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. The "law of the primate city" was put forward in 1939 by:

    1. Brian Berry
    2. Mark Jefferson
    3. G.K. Zipf
    4. Walter Christaller
    Show answer

    Answer: B — Mark Jefferson

    Jefferson observed that a country's leading city is often disproportionately larger than the next and dominates national life. Zipf formalised the rank-size rule and Berry compared city-size distributions across countries.
  2. In a country that follows the rank-size rule, the largest city has 12 million people. What should be the population of the fourth-ranked city, in millions? Type a number.

    Numerical answer — type the value.

    Show answer

    Answer: 3

    Pn = P1 ÷ n, so P4 = 12 ÷ 4 = 3 million. The second city would have 6 million and the third 4 million.
  3. In central place theory, the "threshold" of a good is:

    1. The minimum population or purchasing power needed to support its supply
    2. The number of centres supplying it
    3. The price at the central place
    4. The maximum distance consumers will travel to buy it
    Show answer

    Answer: A — The minimum population or purchasing power needed to support its supply

    The threshold is the minimum demand that keeps a supplier in business; the range is the maximum distance people will travel for the good. A good can be offered at a centre only where its range exceeds its threshold.
  4. Christaller's k = 4 system, in which lower-order centres lie on the straight routes between higher-order centres, follows the:

    1. Agglomeration principle
    2. Administrative principle
    3. Marketing principle
    4. Traffic (transport) principle
    Show answer

    Answer: D — Traffic (transport) principle

    Placing lower-order centres at the midpoints of the hexagon's sides puts as many of them as possible on the main routes; each is shared by two higher-order centres, giving 1 + 6 × ½ = 4. Marketing gives k = 3 and administration k = 7.
  5. In Christaller's k = 7 (administrative) system, how many lowest-order market areas lie within the market area of a centre two orders higher? Type a number.

    Numerical answer — type the value.

    Show answer

    Answer: 49

    Each level multiplies the number of market areas by k, so two levels down there are k² = 7² = 49. The corresponding figures for k = 3 and k = 4 would be 9 and 16.
  6. A landscape of alternating "city-rich" and "city-poor" sectors around a metropolis is a feature of the central place model of:

    1. Homer Hoyt
    2. Johann Heinrich von Thünen
    3. August Lösch
    4. Walter Christaller
    Show answer

    Answer: C — August Lösch

    Lösch superimposed hexagonal nets of many different k values on a single metropolis and rotated them to maximise coinciding centres, producing six city-rich and six city-poor sectors. Christaller used one fixed k; Hoyt's sectors concern residential rent within a city.
  7. In Burgess's concentric zone model, the ring immediately surrounding the central business district is the:

    1. Zone in transition
    2. Zone of working-men's homes
    3. Residential zone
    4. Commuters' zone
    Show answer

    Answer: A — Zone in transition

    Zone II, the zone in transition, is being invaded by business and light industry and houses the poorest recent immigrants. Working-men's homes form zone III, the middle-class residential zone IV and the commuters' zone V.
  8. Which of the following did Harris and Ullman give as reasons for the formation of multiple nuclei in a city? Select all that apply.

    1. Some unlike activities are detrimental to each other
    2. Invasion and succession produce concentric rings
    3. High-rent residential sectors extend outward along transport routes
    4. Certain activities require specialised facilities
    Show answer

    Answer: A — Some unlike activities are detrimental to each other; D — Certain activities require specialised facilities

    Harris and Ullman gave four reasons: specialised facilities, the clustering of like activities, the mutual repulsion of unlike activities, and the inability of some uses to pay high rents. Sectors along routes are Hoyt's idea, and invasion–succession rings are Burgess's.
  9. Shevky and Bell's urban social area analysis used three constructs. They were:

    1. Threshold, range and hierarchy
    2. Social rank, urbanisation and segregation
    3. Invasion, succession and dominance
    4. Primacy, rank and size
    Show answer

    Answer: B — Social rank, urbanisation and segregation

    Social rank (economic status), urbanisation (family status) and segregation (ethnic status) were computed from census tract data. Threshold and range belong to central place theory, and invasion–succession to the Chicago school's ecology.
  10. The concept of the "edge city" — a new suburban concentration of offices and retail with more jobs than bedrooms — was introduced by:

    1. Saskia Sassen
    2. Jean Gottmann
    3. Ebenezer Howard
    4. Joel Garreau
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    Answer: D — Joel Garreau

    Garreau's Edge City: Life on the New Frontier (1991) defined the form. Sassen wrote The Global City (1991), Gottmann described Megalopolis (1961), and Howard proposed the garden city (1898).
  11. Assertion (A): Central place theory uses hexagonal rather than circular market areas. Reason (R): Hexagons fill a plane without gaps or overlaps while staying close to the circle's property of minimising distance to the centre. Choose the correct option.

    1. Both A and R are true, and R is the correct explanation of A
    2. Both A and R are true, but R is not the correct explanation of A
    3. A is true, but R is false
    4. A is false, but R is true
    Show answer

    Answer: A — Both A and R are true, and R is the correct explanation of A

    Both are true and R explains A. Circles would leave unserved gaps or, if enlarged, overlap; squares and triangles fill space but put some consumers much farther from the centre. The hexagon is the best compromise.