What sets city size? That is, what determines how many people all cluster together in an urban area? On the one hand, city size increases with feasible building height and with the gains to people and businesses from interacting closely with many others. On the other hand, city size decreases with how much space folks want, and with costs to transport people and goods within a city and from outlying regions. City size increases with more and cheaper nearby non-city economic activity.

Policy also matters; poor governance and positive externalities of density reduce city size, while being the center of government for a surrounding area increases city size. The size of big cities should be limited by the reluctance of nations to let their city activity be absorbed into big nearby foreign cities. And sunk costs and coordination failures can long delay the adaptation of city sizes and locations to changing circumstances.

In the farming era, cities held only a small fraction of the population, and so their size and locations were determined mainly by nearby farming activity. However, when most folks live in cities, then nearby non-city activity matters less, and decreasing transport costs make bigger cities more economical.

So how well have today’s city size and locations adapted to industry era tradeoffs? That is, how well do cities today trade the gains from more interaction in bigger cities for the added costs of transport and reduced personal space? While we expect optimal industry era cities to be more concentrated, i.e., fewer and larger, we also expect inertia, coordination failures, density externalities, and city mismanagement to slow the transition from an ideal farming era distribution of cities to an ideal industry era distribution. So cities today are probably too many and small. But how far off are they?

One clue – alas one that that is hard to interpret – is that today (log) city size follows a normal distribution, and (log) size changes follow a random walk. Another more informative clue is that in many large nations, a big (but not too big) fraction of the urban population is in the largest city. For example: South Korea 53%, Japan 44%, Egypt 43%, Argentina 37%, Bangladesh 34%, Philippines 28%, Mexico 24% (sources here, here). This weakly suggests that such cities might be running up against a political limit – the reluctance of neighboring nations to let these cities absorb their city activity.

How should we expect cities to change in a future em era, where trillions of human emulations live in virtual reality or in tiny android bodies? Since ems are easier to transport, require less space, and interact less with rural areas, optimal em cities should be even more concentrated than industry cities. Especially if ems learn to better subsidize density, to internalize today’s density externality. And since ems require quite different infrastructure from humans, and need large and rapid changes that most cities will initially be unwilling to allow, existing industry era cities may less constrain the size and location of em cities.

Together these suggest that em cities might be quite a bit more concentrated than our industry cities. Most ems might live within a half dozen or fewer really huge cities. Which would imply that only a half dozen nations would have substantial political power, allowing for easier global coordination.

If optimal em city concentration is really high, most ems might even live in just one biggest city. An analogy in the history of brains seems apt. Some of the first brains were spread out all over animal bodies, but then brains evolved to concentrate in one small region, to minimize signal delays within the brain.

Of course one big em city could be vulnerable to bad governance, so perhaps the biggest city would change as biggest cities became badly managed. Especially if ems had better ways (e.g. prediction markets) to coordinate their city switching activities. Creates an interesting picture of a competitive world government – at any one time most world economic activity might be under a single central city government, and yet cities might compete to offer the best world governance.