Many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Do these general relations apply to European cities with centuries of history stretching back to the middle ages, just as they do to younger urban areas in other parts of the world? This is the bold question that Luís Bettencourt and José Lobo address in a recent study⁽¹⁾.

Urban scaling theory predicts that land densities, socioeconomic productivity, or innovation per capita increase predictably with city size. In fact, the path to a richer nation overall depends on two important but uncorrelated dynamics: baseline productivity per capita and city sizes. Nations with a lower productivity can become wealthy by growing larger cities, whereas nations with higher productivity can be rich even with relatively small cities.

Most large urban systems in Western Europe approximately agree with theoretical expectations, especially France and the UK, though scaling relations become especially clear at the pan-European level. But Luís and José also find some interesting deviations and derive some intriguing—but expected—conclusions.

The strongest deviations from scaling for GDP are observed for Naples and Berlin. In both cases, these cities are either too large in population for their economic performance, or have economies that are too small for their populations. Madrid, in Spain would also be too large.

The Netherlands and Switzerland use urbanization much more efficiently than Germany. They require smaller cities to achieve the same economic performance. Spain or Poland have large cities but could do better by increasing their baseline productivity. Switzerland or The Netherlands could become even richer simply by growing their cities further.

As a thought experiment, Luis and Jose extrapolated the expectations of Zipf’s law for the size of the largest cities in the EU and they find a city with population above 50 million people. In fact, the largest city in the EU should have a population of 58 million people, the second 29 million, and the third about 19 million. The fifth largest city would be roughly the size of today’s Paris or London, with more than 11 million people. The GDP of the largest city would be 6.5 times larger than that of Paris or London today, which corresponds to an increase of 30% per capita in these cities.

To the best of my knowledge, the authors have not been hired to promote further EU integration or as part of anti-Brexit campaign. All this, you know, is a pure mathematical exercise!

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(1) Bettencourt, L., & Lobo, J. (2016). Urban scaling in Europe Journal of The Royal Society Interface, 13 (116) DOI: 10.1098/rsif.2016.0005