[This was originally posted in unfinished form this morning. It has since been rewritten.]
Is Auckland too big? Some people are asking that question.
For instance, in a Twitter exchange a while back Radio New Zealand producer Tim Watkin stated:
@pv_reynolds Patrick I thought you wanted people off the roads here! We all know Auckland's too darned big
— Tim Watkin (@Tim_Watkin) October 12, 2016
Others disagreed, observing that we didn’t have any obvious way to make Auckland smaller, meaning that people must have good reasons for wanting to be here:
— Stephen Davis (@nzsd) October 12, 2016
As it turns out, Auckland (1.6 million people) isn’t the only city where people are debating this question. The San Francisco Bay Area (7.6 million people) has the same challenges, as Kim-Mai Cutler has ably documented. So does Boulder, Colorado (300,000 people). Actual population size is not, it seems correlated with complaints about cities being “too big”.
BOULDER, Colo. — The small city of Boulder, home to the University of Colorado’s flagship campus, has a booming local economy and a pleasantly compact downtown with mountain views. Not surprisingly, a lot of people want to move here.
Something else is also not surprising: Many of the people who already live in Boulder would prefer that the newcomers settle somewhere else.
“The quality of the experience of being in Boulder, part of it has to do with being able to go to this meadow and it isn’t just littered with human beings,” said Steve Pomerance, a former city councilman who moved here from Connecticut in the 1960s.
All of Boulder’s charms are under threat, Mr. Pomerance said as he concluded an hourlong tour. Rush-hour traffic has become horrendous. Quaint, two-story storefronts are being dwarfed by glass and steel. Cars park along the road to the meadow.
These days, you can find a Steve Pomerance in cities across the country — people who moved somewhere before it exploded and now worry that growth is killing the place they love.
Economically, this is looking like an interesting question. Under what conditions can a city be “too big”, and are those conditions likely to hold true in practice?
There are some economic models setting out why and how cities might grow to be larger than their optimal size. (The same models also predict that cities can be smaller than optimal, but I will ignore this case for the moment.) Economist David Albouy and three co-authors investigate the theory of the issue in a November 2016 paper entitled “The optimal distribution of population across cities“.
Albouy et al develop a model of city size that includes two offsetting externalities associated with city size. On the positive side, agglomeration economies, or the economic and social benefits of scale and density. On the negative side, congestion and crowding, which are assumed to increase nonlinearly with city size. Putting it together, they get a picture that looks something like this:
This probably doesn’t make a lot of sense unless you’ve read the paper and sifted through the equations. But it’s pretty simple. If you’re seeking to maximise the net social benefits created by the city, you want it to be size ni (on the X axis). That’s the point at which the marginal costs imposed by the next city resident exceed the marginal benefits that they deliver.
But people will continue to move to the city even after it hits this size, as new residents receive the social average benefit from locating in the city, rather than the marginal benefit. Left uncorrected, the city will grow to a larger size (nm_large on the X axis).
This model shows how cities can grow to be larger than their optimal size, due to congestion costs that increase faster than agglomeration benefits beyond a certain size. However – importantly – it also make a very strong prediction that people will stop wanting to move to cities at a certain point. In other words, this model does not predict that cities will grow without limit: it predicts that they will reach a certain size and then stop growing.
In that sense, this model predicts that city size is analogous to road congestion. Although many roads are above the socially optimal level of congestion, congestion simply doesn’t increase without limit. At some point people decide not to drive any more, as illustrated empirically by Wallis and Lupton:
Within the model, there may be reasons why optimal size differs between cities. For instance, cities may:
- Have different types of agglomeration economies, resulting in a stronger or weaker case for increased size
- Have different transport systems leading to different relationships between growth and congestion
- Be located near more sensitive ecosystems, meaning that growth may be more damaging.
However, on the whole, the predictions made by the model are extremely difficult to reconcile with observed reality, which is that urban growth follows a ‘random walk’ process, with large cities more or less equally likely to grow as small cities. (This is often referred to as Ghibrat’s Law.)
In New Zealand, we can see this at work. Auckland has grown faster than most of the rest of the country over the last century (excluding smaller centres close to Auckland), and it’s expected to continue to do so. Canterbury, which contains one of NZ’s two next biggest cities, is also expected to grow rapidly. If models of optimal city size held true, we’d expect Auckland to be at a disadvantage for further growth:
As Fujita, Krugman and Venables observe in their great book on new economic geography, the idea that urban growth is more or less random is empirically plausible but tends to upend models like the one I’ve described above. Cities, it seems, are not like roads: They can always fit a few more people in without grinding to a halt. Although it is a common trope, there may be no such thing as a city that is “too big”.