Urban Hierarchy
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The urban hierarchy ranks each
city A city is a human settlement of notable size.Goodall, B. (1987) ''The Penguin Dictionary of Human Geography''. London: Penguin.Kuper, A. and Kuper, J., eds (1996) ''The Social Science Encyclopedia''. 2nd edition. London: Routledge. It can be def ...
based on the size of population residing within the nationally defined statistical urban area. Because urban population depends on how governments define their
metropolitan area A metropolitan area or metro is a region that consists of a densely populated urban agglomeration and its surrounding territories sharing industries, commercial areas, transport network, infrastructures and housing. A metro area usually com ...
s, urban hierarchies are conventionally ranked at the national level; however, the ranking can be extended globally to include all cities. Urban hierarchies tell us about the general organization of cities and yield some important insights. First, it tells us that within a system of cities, some cities will grow to be very large, but that number will be small relative to the universe of cities. Second, it refutes the expectation of an optimally sized city. Lastly, it establishes cities as belonging to an inter-related network where one city's growth affects others'.


Theoretical distribution

The hierarchy is usually related to the empirical regularity with which cities are distributed. The pattern has been formulated in a number of ways, but usually as a variation of the
power law In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, inde ...
. Formally, it is a frequency distribution of rank data where the frequency is inversely proportional to rank such that cities with population larger than ''S'' are approximately proportional to ''S−a'', where ''a'' is normally close to 1. There are no good explanations for the exponent consistently being close to 1. This is problematic because an exponent of 1 in the power law implies an infinite population.
Paul Krugman Paul Robin Krugman ( ; born February 28, 1953) is an American economist, who is Distinguished Professor of Economics at the Graduate Center of the City University of New York, and a columnist for ''The New York Times''. In 2008, Krugman was th ...
proposes that, in the case of cities, the power law operates according to the
percolation theory In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected ...
. This relaxes the condition on the exponent approaching the value of 1 and breaking down the model. Importantly, the application of a percolation model leads to one of the key insights regarding city sizes: geography and economic conditions give cities advantages that allow them to grow more than cities with a relative scarcity of these benefits. A simpler formulation of the relationship between rank and frequency is expressed with reference to Zipf's Law. The law applied to cities states that "if cities are ranked in decreasing population size, then the rank of a given city will be inversely proportional to its population." According to this intuitive formulation, in a country where the largest city has a population of 10 million, the second largest will have population size of 5 million, the third largest 3.33 million, etc.


Empirical evidence

The urban hierarchy has been described in detail in the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
where the power law has held consistently for over a century. In 1991, there were 40 U.S.
Metropolitan Areas A metropolitan area or metro is a region that consists of a densely populated urban agglomeration and its surrounding territories sharing industries, commercial areas, transport network, infrastructures and housing. A metro area usually com ...
with population above 1 million, 20 above 2 million, and 9 with more than 4 million. Recent advances in data collection have allowed researchers to test the theoretical distribution against global data. Shlomo Angel finds that the pattern holds remarkably well for a global sample of 3,646 cities. The predicted distribution based on Zipf's law and the actual distribution are virtually identical. The most common size ranges from 100,000 to 200,000 and constitutes about half of the entire sample. The distribution extends to the largest cities with population over 2.5 million.


Explanation

While the frequency distribution of urban hierarchies is empirically simple, the set of factors that create it are complex and no individual explanation can account for the distribution. The unequal distribution of city sizes and lack of convergence on one equilibrium size are relatively well understood. Henderson's model of urban system relies on three sets of factors that influence the size of cities: land inputs, labor, and capital. The model formally relates the benefits of
economies of agglomeration One of the major subfields of urban economics, economies of agglomeration (or agglomeration effects) describes, in broad terms, how urban agglomeration occurs in locations where cost savings can naturally arise. Most often discussed in terms of ...
and congestion cost. Cities benefit from
economies of scale In microeconomics, economies of scale are the cost advantages that enterprises obtain due to their scale of operation, and are typically measured by the amount of output produced per unit of time. A decrease in cost per unit of output enables ...
that attract firms and workers, making them larger. But, the limited supply of land means that the price of locating near the center of production increases as the population size increases. Eventually, the greater costs lead to
diminishing return In economics, diminishing returns are the decrease in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal ( ceteris parib ...
s to scale and cities tend towards an optimal equilibrium size, assuming they all share the same attributes. Henderson relaxed the assumption of identical cities to explore the implications of a diversified economy of traded goods. The extension of the model underlies the urban system literature and gives rise to the finding that cities will differ in size to account for the factor rewards associated with traded goods of varying degrees of return to scale and intensity of land use.


Alternative hierarchy

While the pattern of urban hierarchy tends to conform to the power law, it is not universal. Especially at the country level, significant deviations from the theoretical distribution are observed. Countries with a
primate city A primate city is a city that is the largest in its country, province, Federated state, state, or region, and disproportionately larger than any others in the urban hierarchy. A ''primate city distribution'' is a rank-size distribution that has on ...
, a city that dominates in population size and, usually, economically, have a deficit of intermediate size cities. Examples of primate cities include
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...
in France,
London London is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea, and has been a majo ...
in the United Kingdom, and
Tokyo Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, with an estimated 37.468 ...
in Japan. The history of these countries play a large role in the persistence of their primate city. Particularly, the concentration of political power in one city early on has a large degree of
path dependency Path dependence is a concept in economics and the social sciences, referring to processes where past events or decisions constrain later events or decisions. It can be used to refer to outcomes at a single point in time or to long-run equilibria ...
.


References

{{Reflist Urban planning Urban economics Urban sociology