Media Briefings

THE HIERARCHY OF CITIES: A new explanation for the human landscape

  • Published Date: September 2012

Stock exchanges and symphony orchestras are found only in the biggest cities of the world while petrol stations and convenience stores are found almost everywhere. This seemingly simple insight into contrasts in the economies of scale of different industries is key to understanding the hierarchy of city sizes, which displays remarkable regularity over time and across countries.

Writing in the September 2012 issue of the Economic Journal, Professor Wen-Tai Hsu provides a new explanation for the phenomenon known as the power law of city size distribution. His study shows how industries matter in shaping the hierarchy of cities – and why the human landscape can be viewed as a ‘fractal structure’, in which smaller parts of the hierarchy are similar to the whole.

The distribution of city sizes is highly skewed: there are many more small cities than large cities. This distribution can be approximated by the power law: if all cities are ranked in terms of their sizes – so that the largest city has the rank of 1, the second largest city has the rank of 2 and so on – the rank of a city is inversely proportional to a power of its size.

It turns out that the power law of city size distribution is highly stable over time and across countries. Such striking robustness has aroused a tremendous amount of curiosity among social scientists to find the underlying mechanism that generates such regularity.

A popular explanation has been to derive the distribution of city sizes from a process in which cities grow at a random growth rate (which can possibly be negative). In a random growth process, large cities arise because of their long histories of favourable events – but since the probabilities of such events are low, there are not many large cities, leading to a skewed distribution.

Various scholars have specified conditions under which such a skewed distribution will follow the power law. But one criticism of this explanation is that cities are not spatially related in these theories, which suggests that geography does not matter. In other words, cities are not placed in a geographical space and hence the distances between cities are indefinite and do not factor in the explanation.

Since cities are concentrations of economic activities and populations in a geographical space and since there are differently sized cities distributed across the entire geographical space, the very notion that geography does not matter in generating the empirical regularity of city size distribution has puzzled some social scientists.

Wen-Tai Hsu’s study provides a new explanation of the power law based on an economic theory in which spatial relations among cities matter. It turns out that the power law is a mathematical property of a roughly 80-year-old theory called ‘central place theory’.

The idea underlying this theory is that industries differ in their degrees of scale economies. Industries with substantial economies of scale – such as stock exchanges and symphony orchestras – will be found in only a few locations, whereas those with few economies of scale – such as petrol stations and convenience stores – will be found in many locations.

Moreover, large cities tend to have a wide range of goods whereas small cities provide only those with a low degree of scale economies. In central place theory, larger cities provide all the goods that smaller cities provide. This set-up clearly implies a skewed distribution of city sizes.

The intuition for why the power law emerges from such a hierarchy of cities is that the hierarchy exhibits a pattern of spacings in which larger cities are wider apart with the immediate next smaller city located roughly in the middle between the two neighbouring larger cities. Such a regular pattern produces a spatial ‘fractal structure’, in which the smaller part of the hierarchy is similar to the larger one.

As the power law is also found in various phenomena in the natural sciences, there have been explanations of the power law based on fractal structures in these disciplines. But the main contribution of this study is that it explains why the human landscape can indeed be viewed as a fractal structure.

The findings in this research not only solve a puzzle by explaining the distribution of city sizes via a geographical/spatial angle; they also have implications for how cities and the human landscape should be perceived and for how industries matter in shaping the hierarchy of cities.

ENDS

Notes for editors: ‘Central Place Theory and City Size Distribution’ by Wen-Tai Hsu is published in the September 2012 issue of the Economic Journal.

Wen-Tai Hsu is at the National University of Singapore.

For further information: contact Romesh Vaitilingam on +44-7768-661095 (email: romesh@vaitilingam.com); or Wen-Tai Hsu via email: ecswhth@nus.edu.sg