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Power laws, population, and prosperity

Anthony Butler
4 min read

This week, I was discussing the plans announced by the Saudi government last year to double the population of Riyadh by 2030.  I mentioned, much to the apparent surprise of some of the audience, that doubling the population of the city could help make the city a much greener and sustainable city; and could lead to a very material improvement in the quality of life of all the residents -- if the population could be doubled or more.  

If this sounds counter-intuitive, it may be because we typically view urban development through a naive qualitiative lens which equates growth with, for example, traffic, pollution, and other negative externalities.  These narratives are not informed by a quantitative understanding of urban growth which continues to be an interesting area of research.  

For a quantitative approach to urban development, one of the most interesting and useful can be found in the work of Professor Geoffrey West and his team of researchers at the Santa Fe Institute in the United States.  West, an English-born theoretical physicist, moved from studying phyiscals to researching how animals scale; building on something called Kleiber's Law to discover that, for the vast majority of living organisms, the metabolic rate scales to 3/4 to an animals mass.  In other words, as an organism gets bigger, it's metabolism slows but it lives longer: indicating that each living thing has a finite number of heartbeats and smaller animals – with faster metabolisms – consume them faster.

Professor West's extended this research in a remarkable way; observing that cities also scale in much the same way.  Just as a larger animal consumes energy more efficiently, he found that, if a city size is doubled, the city will intuitively require more infrastructure, such as petrols stations, roads, or sewerage pipes, in absolute numbers; however, just as the larger animal can use its energy more efficiently, doubling the size of the city requires less than double the growth in infrastructure.  This is known as a sublinear increase.  For example, the number of petrol stations per person, for example, will fall by approximately 15 percent.  The more people, the less of any resource you need per person.  

This is also something universal and not specific to a particular city: the same phenemona is observed in Europe, Asia, and North America.  Tokyo, New York, Melbourne or Riyadh follow the same pattern.

This has important implications for sustainability: if the efficient use of infrastructure and resources is an important feature of a sustainable city, then increasing the population of cities is a one effective mechanism of achieving this.  

This is not the only remarkable discovery to emerge from Professor West's work.  The most interesting – and most relevent in the context of Riyadh – is that, if a city population doubles, socioeconomic quantities, such as average wages, number of patents, or gross domestic product (GDP) will also scale superlinearly with an exponent of 1.15 (i.e. 15% improvement).  The more people, the more of a socioeconomic output per person.  

For example, the below diagram, taken from West's paper, demonstrates how wages increase when population increases and, as can be seen, in the case of this particularly city there's approximately a 12% gain.

Similarily, the below diagram depicts the number of "supercreatives" which one can think of as entrepreneurs, innovators, artists, and similar.  By doubling the city population, one can also expect a 15% gain.

As an aside, as cities grow in size, people also walk faster.  If time is money then perhaps, as wages and costs increase, the value of people's time increases hence they become more hurried.  

By doubling the size of Riyadh, the GDP contribution of Riyadh to the overall country will also experience a similar superlinear growth; there will be an equivalent increase in average wage per person; and, with the increase in "supercreatives" and patents, the entrepreneurial and intellectual contribution of the city to the national and global economy will experience a commensurate superlinear increase.  Meanwhile, as the city pursues its objectives around sustainability, the increase in population will also lead to more efficient – sublinear – consumption of infrastructure.  

Going back to West's research into the lifespan of animals, a further interesting observation about cities is that whilst they become 15% more innovative socio-economically and become 15% more efficient in energy, materials, and infrastructure consumption, they also live forever.  The reason is that, unlike animals, they are able to innovate fast enough to address the entropy that this growth creates, such as crime or pollution.  For this reason, it's very rare that we hear of a city disappearing and dying; and it is also where, historically, some of the periods of most intense innovation have been driven by city-states.  

As an aside, companies, on the other hand, do not share the same ability to innovate their way out of the negative consequences of growth.  West also studied some 22,000 companies and found they have similar characteristics to animals.  As they increase in size, they slow down; and their sales, profit, and assets grow sublinearly.  Only by reinvention can they sustain further growth before eventually dying like animals – and most are unable to innovate fast enough.  Hence, the average lifespan of a company (unlike a city) seems to be about ten years.  

Whilst Professor West has many lectures online of varying complexity, the below interview with Professor West is one of my favourites and is a highly accessible explanation of these universal laws as they apply to animals, cities, and companies.

Anthony Butler Twitter

Anthony is a Senior Advisor to a G20 Central Bank on emerging technologies and applied research. He was previously Chief Technology Officer for IBM, Middle East and Africa. Lives in Saudi Arabia.

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