Luis Bettencourt and Geoffrey West, Bigger Cities Make Do With Less (Scientific American, September 2011)

This new, more quantitative science of cities is becoming possible because of the increasing availability of information—official statistics as well as novel measures of human and social activity—on cities and metropolitan areas worldwide.

By sifting through this flood of data, covering thousands of cities around the world, we have unveiled several mathematical “laws” that explain how concentrating people in one place affects economic activity, return on infrastructure investment and social vitality. Despite the rich diversity of metropolitan regions across the U.S., China, Brazil and other nations, we found a remarkable universality in the way that socioeconomic characteristics increase with a city’s population. For example, if the population of a city is doubled, whether from 40,000 to 80,000 or from four million to eight million, we systematically see an average increase of around 15 percent in measures such as wages and patents produced per capita. If eight million people all live in one city, their economic output will typically be about 15 percent greater than if the same eight million people lived in two cities of half the size. We call this effect “superlinear scaling”: the socioeconomic properties of cities increase faster than a direct (or linear) relation to their population would predict.

The data also reveal that cities’ use of resources follows a similar, though inverted, law. When the size of a city doubles, its material infrastructure—anything from the number of gas stations to the total length of its pipes, roads or electrical wires—does not. Instead these quantities rise more slowly than population size: a city of eight million typically needs 15 percent less of the same infrastructure than do two cities of four million each. This pattern is referred to as sublinear scaling. On average, the bigger the city, the more efficient its use of infrastructure, leading to important savings in materials, energy and emissions.

Our findings also show that these patterns of increased productivity and decreased costs hold true across nations with very different levels of development, technology and wealth. Although we have much more information for cities in richer parts of the world, we are beginning to obtain good data from rapidly developing countries as well, and they seem to fit the same mold. The gross domestic product for cities in Brazil and China, for instance, closely follows the same superlinear curve that western European and North American cities exhibit, though starting from a lower baseline. We believe that the pattern holds true because the same basic social and economic processes are at work, whether in São Paulo’s favelas, under Beijing’s smog-filled skies or along Copenhagen’s tidy streets.

Although urban superlinear scaling, which represents the average, idealized behavior of a city of a given size, prevails around the globe, actual cities deviate to varying degrees from the roughly 15 percent enhancements that come with size. Detailed data covering 40 years show, for example, that San Francisco and Boston are richer than their size would indicate, whereas Phoenix or Riverside, Calif., are somewhat poorer. Curiously, these deviations persist for decades: cities tend to stay remarkably close to their overperforming or underper- forming histories. For example, cities that have attempted to improve their lot by creating conditions for the “next Silicon Valley” have often had disappointing results. Our research suggests that certain intangi- ble qualities of social dynamics—more than the development of material infrastructure—hold the key to generating virtuous cycles of innovation and creation of wealth. These processes, such as the de- velopment of a spirit of local entrepreneurship, a reputation for cutting-edge novelty, and a culture of excellence and competitiveness, are difficult to design through policy because they rely on the dynamics of a city’s social fabric across many dimensions. We expect the results of this exciting area of research will lead to better “recipes” for sustainable socioeconomic development.

What we can say with certainty, however, is that increased population promotes more intense and frequent social interactions, occurrences that correlate with higher rates of productivity and innovation, as well as economic pressures that weed out inefficiencies. In a city with high rents, only activities that add substantial value can be profitable. These economic pressures push urbanites to come up with new forms of organizations, products and services that carry more value added. In turn, higher profitability, excellence and choice tend to attract more talent to the city, pushing rents higher still, fueling the need to find yet more productive activities. This feedback mechanism, in a nutshell, is the principal reason cities accelerate innovation, while diversifying and intensifying social and economic activity.