Decision Theory for Planners #110 Why a City Scales like an Elephant

Geoffrey West the noted English physicist has studied scale for many years, moving from looking at physics, to biology to now cities and firms.

“I’ve always wanted to find the rules that govern everything,”

“It’s amazing that such rules exist. It’s even more amazing that we can find them.”

“We spend all this time thinking about cities in terms of their local details, their restaurants and museums and weather,”

“I had this hunch that there was something more, that every city was also shaped by a set of hidden laws.”

West took an idea from biology, Kleiber’s scaling law, and tried to explain it.  This looks at how the metabolism of a creature changes with size.  So for example while an elephant is 10,000 times the size of a guinea pig, it needs only 1,000 times as much energy. The metabolic rate of a creature is equal to its mass taken to the three-fourths power.  The number 4 seemed to pop up in all kinds of ways in similar laws of scale.

West sought to explain this by looking for laws which can be described as describing the infrastructure of space, the energy needed to take things around a network.  4 was no accident, it a network it describes the three degrees of freedom of space plus one which can be explained as the ‘fractal’ quality of networks, like the crinkliness of the UK coast which gets longer the closer you look at it.

This seemed to describe a certain increasing return to scale about physical phenomenon.

West looked at whether this applied to cities, gathering massive amounts of information with his co-worker Luis Bettencourt.  These ideas have been gathering increasing attention in recent months as they supply clues to describing a number of long understood but previously disparate phenomenon.

They found  massive economies of scale in settlements, just as in big animals.

They concluded that cities are a lot like elephants. In city after city, the indicators of urban “metabolism,” like the number of gas stations or the total surface area of roads, showed that when a city doubles in size, it requires an increase in resources of only 85 percent.

Economists had long studied the agglomeration economies of scale of cities.  Most famously Alfred Marshall

When an industry has chosen a locality for itself, it is likely to stay there for long; so great are the advantages which people following the same skilled trade get from near neighborhood to one another. The mysteries of the trade become no mysteries; but are as if were in the air, and children learn many of them unconsciously. Good work is appreciated; inventions and improvements in machinery, in processes and the general organization of the business have their merits promptly discussed; if one man starts a new idea, it is taken up by others and combined with suggestions of their own; and thus it becomes the source of new ideas.
Marshall, 1920

Marshall described three advantages 1) shared inputs, 2) labor market pooling and skill matches, and 3) knowledge spillovers, but all three of these are network effects explainable by the mathematics of West’s law, the ability of a good, member of a labour market or information to diffuse along a network.

Jane Jacobs argued that spillovers between industries in a diverse city was more important that spillover within a specialised industrial district, but in a more fundamental sense both effects have a deeper cause, how advantages scale.

In recent years Noble Prize Winner Paul Krugman and others in the ‘new economic geography’ have been grappling with a problem.  Without increasing returns to scale it is not possible to explain the growth and formation of cities at all, but acknowledging increasing returns undermines many of the assumptions of neo-classical economics.

But West found that not just the size of the economy increased by 15% per capita with city size, so did other things such as the number of crimes, traffic, even disease. It was the increased volume of such interactions in cities that Jane Jacobs promoted of course and West sees his ideas as offering a mathematical explanation of them. West describes the purpose of urban planning as finding a way to minimize our distress in cities while maximizing our interactions.

West and Bettencourt refer to this phenomenon as “superlinear scaling,” The slope leads to city growth from the positive feedback loop of urban life — a growing city makes everyone in that city more productive, which encourages growth which encourages more people to move to the city.

“When we started living in cities, we did something that had never happened before in the history of life…We broke away from the equations of biology, all of which are sublinear. Every other creature gets slower as it gets bigger [ because of the energy costs]. That’s why the elephant plods along. But in cities, the opposite happens. As cities get bigger, everything starts accelerating. There is no equivalent for this in nature. It would be like finding an elephant that’s proportionally faster than a mouse.”

So whilst large cities are more energy efficient per capita than smaller ones they lead to growth which consumes more energy overall. Man can break the constraints of biology by generating his own energy.

“The only thing that stops the superlinear equations is when we run out of something we need,…and so the growth slows down. If nothing else changes, the system will eventually start to collapse.”

For West only innovation can get us out of this resource bind

“It’s like we’re on the edge of a cliff, about to run out of something, and then we find a new way of creating wealth. That means we can start to climb again.”

This is an old idea in economics, the classical ‘steady state’ providing limits to growth of Ricardo, JS Mill and Marx, inspiring John Raes and Schumpeters concept of swarming innovations creating new opportunities for growth. Of Jevons concept that increasing cost from declining energy sources (in his day coal but today oil) will spur innovation in new energy technologies.

Bettencourt and West have also begun to look at the issue of the size of corporations, however the relationship is the opposite of cities, as the number of employees grows, the amount of profit per employee shrinks.

For West the the decline in profit per employee makes large companies increasingly vulnerable to market volatility. Since the company now has to support an expensive staff — overhead costs increase with size — even a small disturbance can lead to significant losses. As West puts it, “Companies are killed by their need to keep on getting bigger.” He may not realise it but that is pretty similar to Marx’s theory of the declining rate of profit. West so far does not explain the cause of the decline in profit per employee. Marx’s equations had the hidden assumption that capital intensity would increase at a faster rate than the profit generated/unit of labour, if it doesn’t you get an increasing rate of profit, and no capitalists rationally introduces a new technology that will reduce their profits to negative.

An explanation could be in the rigid way large firms are organised, limiting communication and innovation between staff that naturally occurs in small firms and between multiple individuals in cities. Large firms that promote such innovation tend to be the most successful. But combining the concept of increasing returns to scale of industrial processes with decreasing returns to scale at the level of the firm (the number of employees) seems to solve a number of puzzles in economics – such as why successful firms don’t expand infinitely (Sraffa 1926), and why small firms tend to create most new jobs.

It may also explain some puzzles in urban design. Andreas Duany is famous for his theory of scale invariance, that there are principles which apply at all scales of planning, from the region to the neighbourhood, such as access to open space.

West and Bettencourt’s ideas are new and sweeping.  At first site they appear to be anomalies.  For many large African cities there is no increasing efficiencies of scale, I would suggest though this is from a model of urbanisation which has seen investment in infrastructure fail to keep pace with city growth, leading to huge dis-economies.

A similar problem, which has led some urban researchers to be dismissive, is the decline of many large american cities and the growth and job creation rates of many suburban areas.  I believe though there are explanations for this.  American cities had grown beyond their bounds leading the centre taking on high city fixed costs and high tax earners living outside the city limits.  This can create a downwards fiscal spiral.  Also when industrial cities specialise in the same type of firm all growing together they can all decline together.  Finally when cities forget what they are about, creating economies of scale in labour and information, through encouraging loss of central urban jobs and low cost labour, cities can easily hollow out.  Where the disadvantages and costs of living in a settlement exceed the benefits people will settle elsewhere, spawning new cities or sprawl.  The problem though with sprawl is the increasing costs with scale and lack of increasing advantages.  Sprawl can drag an economy down in the same way an economy reliant on old industries can.

3 thoughts on “Decision Theory for Planners #110 Why a City Scales like an Elephant

  1. Pingback: Apple Campus 2 – The Size of a Town but Doesn’t Work as One « Decisions, Decisions, Decisions

  2. Pingback: Something about elephants… | browless

  3. Pingback: Hoyt, Minsky and the Asset Price/Credit Cycle « Decisions, Decisions, Decisions

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