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Posted at 2:00 PM ET, 12/27/2010

The mathematics of cities

By Ezra Klein


Physicist Geoffrey West specializes in finding simple mathematical laws that unite large categories of seemingly unlike things. In the late 1990s, he published a seminal (and controversial) paper showing that "the metabolic rate of a creature is equal to its mass taken to the three-fourths power" -- that is to say, "larger species need less energy per pound of flesh than smaller ones. For instance, while an elephant is 10,000 times the size of a guinea pig, it needs only 1,000 times as much energy." Now he's focusing on cities.

There is something deeply strange about thinking of the metropolis in such abstract terms. We usually describe cities, after all, as local entities defined by geography and history. New Orleans isn’t a generic place of 336,644 people. It’s the bayou and Katrina and Cajun cuisine. New York isn’t just another city. It’s a former Dutch fur-trading settlement, the center of the finance industry and home to the Yankees. And yet, West insists, those facts are mere details, interesting anecdotes that don’t explain very much. The only way to really understand the city, West says, is to understand its deep structure, its defining patterns, which will show us whether a metropolis will flourish or fall apart. We can’t make our cities work better until we know how they work. And, West says, he knows how they work.

According to the data, whenever a city doubles in size, every measure of economic activity, from construction spending to the amount of bank deposits, increases by approximately 15 percent per capita. It doesn’t matter how big the city is; the law remains the same. “This remarkable equation is why people move to the big city,” West says. “Because you can take the same person, and if you just move them to a city that’s twice as big, then all of a sudden they’ll do 15 percent more of everything that we can measure.”

Photo credit: By Scott Olson

By Ezra Klein  | December 27, 2010; 2:00 PM ET
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Although it is interesting that a physicist is researching this topic, what the article in the link fails to make clear is what Dr. West is finding out that differs from what has already been found out by urban and regional economists. The concept of agglomeration economies -- economic efficiencies related either to the scale of the city, or the scale of an industry or cluster of industries in a city -- is central to urban and regional economics. There is a great deal of empirical information on this by economists such as Ed Glaeser at Harvard. There has been some theoretical modeling of this, including some work by Paul Krugman. What is Dr. West discovering that is new and different? There may well be something new here, but I can't tell what it is from the linked article.

Tim Bartik, Senior Economist, Upjohn Institute

Posted by: bartik | December 27, 2010 3:33 PM | Report abuse

What a messy 2nd paragraph.

Olson refers to a fact that doesn't lead to the argument (“This remarkable equation is why people move to the big city,”).

Hopefully Krugman is in the wing to write a take down of Olson's "discovery".

Posted by: laser83 | December 27, 2010 4:24 PM | Report abuse

To put it better, Olson found an abstract correlation which doesn't shed any light on why cities exist.

Posted by: laser83 | December 27, 2010 4:26 PM | Report abuse

Of course it should be common knowledge that many of our major cities are actually much smaller in terms of population than they were 50 or more years ago. How is this decline in population explained if there are such efficiencies in becoming ever larger? Just for example, Boston's population in 1950 was around 801,000, and today is around 645,000.

Posted by: AuthorEditor | December 27, 2010 7:45 PM | Report abuse

This is a garbled account of West's contribution to the understanding of the metabolic rate power law. The law was discovered empirically in the 1930s, and is named Kleiber's law in honor of Max Kleiber. Much more recently, West et al have offered an explanation for the law, based on a fractal model for resource networks.

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