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“It’s the economy stupid #3″ – Is there an optimal city size?

Previous posts here and here have discussed how the growth of cities can be attributed to some underlying economic advantages, namely shorter travel distances and economies of scale in the presence of fixed costs.

In this post I want to flesh out these economic factors in more detail. I’m particularly interested in whether cities will continue to grow, or whether they will reach an “optimal” size. To finish I outline the structure of a stylized model of the economic forces influencing city growth.

Before we get into too much detail I think it’s worth quoting J. K. Galbraith, who observed the “only function of economic forecasting is to make astrology look respectable.” Now while I’m a sceptic insofar as I accept models cannot replicate real-world complexity, I nonetheless think they are relatively useful “learning” tools.

They key question I want to know more about is whether there is an “optimal city size”. By “optimal” I mean a city size that maximises the economic welfare of its inhabitants. This question is important for obvious reasons. While cities overall are continuing to grow, which cities in particular can we expect to grow the fastest? And is city growth something we should encourage/discourage beyond a certain point?

I think it’s important to hypothesize in advance what I expect to find, if only to reveal my own hidden preferences and human tendency to “model what I am looking to find”. My perspective is that “yes” I do believe there is an optimal city size, at least from an economic perspective, beyond which further growth in city size becomes economically undesirable, at least from a social perspective.

Why do I think this? After all, the persistent growth of cities suggests the factors “pushing” us together are winning out over those that are “pulling” us apart. My reasoning is two-fold:

  1. While more people are living in cities, this is not the same as evidence to prove that individual cities themselves will continue to grow ad infinitum. Indeed, there is some speculation that it is medium sized cities that will drive the bulk of future growth; and
  2. More specifically, I believe the economic forces “pulling” us apart tend to increase as city size increases, whereas the economic forces that “push” us together tend to exhibit diminishing returns as a city grows larger. Put simply, there are benefits to increased size, but these benefits tend to level off.

Let’s expand on that second point a little. Transport costs are a useful example, because they are an economic factor that both makes cities more and less attractive as they grow. While people coming together in cities reduces travel distances, it also tends to create congestion. So if we were solely seeking to minimise transport costs then one would have to conclude that we probably would not allow cities to grow beyond a certain point.

Without further ado let’s outline some of the forces that would need to be in a model of the economic benefits of city size. In my mind the key economic forces such a model should consider are:

  1. Direct transport costs – i.e. what you pay in cash terms to move about.
  2. Congestion – i.e. the costs of additional travel time due to delays from things being busy.
  3. Economies of scale – i.e. efficiencies in the provision of public goods.
  4. Agglomeration economies – i.e. the economic benefits of density.
  5. Purchasing power – i.e. the value that you get for every dollar.
  6. Amenity – i.e. the impact of other people on your amenity.

Let me know if you think I have missed factors that you think are important.

In terms of how these forces vary with population, my gut feeling is that 1) direct transport costs more or less linearly as a city grows; 2) congestion increases non-linearly; 3) economies of scale increase, but at a reducing rate; 4) agglomeration economies increase, but also at a reducing rate; 5) purchasing power increases , but how I’m not so sure; and 6) amenity increases but then decreases (amenity itself is a bit vague).

In the next post I hope to outline some of the results of the model itself, but before I do I’d like to get some feedback on the forces that are in/out and how they might be modeled. How say you all-knowing blogosphere?

43 comments to “It’s the economy stupid #3″ – Is there an optimal city size?

  • I have been wondering about the optimal size city from an transport infrastructure perspective. There are probably some rough levels of population above which you need to start considering a substantially more expensive level of infrastructure but that will then be enough for quite a period of growth.

    e.g.
    -A city of 100k is not going to be able to justify needing much above say some decent arterials and a bit of bus infrastructure.
    -At 500k a city is probably starting to need some decent PT infrastructure (probably bus based) and perhaps a motorway which would represent quite a jump in spending but some expansion on that level is probably enough for another 50k-1m depending on the layout of the city.
    -In the range of 1-2m you are going to start needing to invest in some expensive dedicated PT infrastructure in a couple of core places but that will probably do until the population reaches say 3m
    -Above 3m you might be needing to looking at things like a complete motorway network and a dedicated metro type system.

    I have felt for a while that Auckland is at about that tipping point where we have pretty much exhausting the current projects for a city at a certain level which means everything from here on in gets more expensive but conversely the additional population means that the kind of expenditure is more easily justified.

    • Stu Donovan

      Ah thresholds and discontinuities – both very important and relatively difficult to model ;).

    • bbc

      Swiss cities are smaller than 500,000 and all have extremely large and well developed PT systems so I think your generalisations are way off Matt.

    • bbc

      As another example take Heidelberg, population of 150,000, well developed tram system, well developed bus system, heavy rail to neighbouring cities and towns…

    • Svartmetall

      Further example – Stockholm with 7 metro lines (if counted the German way like Munich does), 3 commuter rail lines, 3 light commuter lines, 4 long distance light rail lines, trams and buses plus regional rail, intercity and inter country rail. Population of the city is 1.6 million. Definitely well before the tipping point (though if you include the metropolitan area it is 2 million, but that isn’t really a fair comparison as a lot of these areas are self-contained towns). Very difficult to put sizes on things based on international examples. Oslo and Helsinki are even smaller yet have full metro systems (Oslo in particular with their T-bane have a very extensive system relative to their population and they’re very low density too compared to Stockholm and Helsinki which have far more apartments built around transport nodes than Oslo).

      As for smaller cities, Norrköping is a city of 87,000 with largely segregated trams with priority running and even a dedicated commuter rail system leaving every 20 minutes off-peak, not to mention standard long distance trains and a good bus system.

  • Matthew

    Wouldn’t the optimal city size be the smallest city that provides all the amenities you are interested in? For instance if you wanted to have a university in your city and it was too small for a university then the city isn’t big enough for you. If you were an opera buff, Ekethanua’s not really the place for you. The optimal size is probably based around job opportunities, and for many industries, that’s where agglomeration is important. For instance IT companies do like to be in bigger cities (which personally as a software engineer gives me the willies, as there is not much else I like about bigger cities)

    With the advent of the net the optimal size city for me is getting smaller. In ye olde days, i.e. before 1997, having a city with a bookshop and a music shop to cater for my eclectic tastes was important. Now that matters didly. I’m finally telecommuting at least a few days a week for work too. If I could break the bonds just that little bit more from my employer to not even need to come in during the week then I would sell up and move further into the boonies.

    Old people retire to the coast. They don’t retire to go and live in the middle suburbs.Or in other words fighting against the growth of the cities, is that a whole lot of people would rather not live in one, but only do so for work.

    • Peter M

      That’s quite an anti-urban approach though. Surely equally one could argue that the optimal city size is as big as possible before the disbenefits of a really huge city start to become unsolvable?

      Although Tokyo’s past 30 million and clearly still functions.

      • Matthew

        True. But I like cities when they are most like National Parks. Leafy trees and (dare I say it) fresh air. Cycle paths and walking tracks through parks and gardens. Away from the roar of traffic. In some of the smaller Scandinavian cities I have found those kind of moments. In Lulea, Sweden walking around a lake front. In Joensuu, Finland finding myself in a primordial forest in the middle of the town. One of my nicest memories of Auckland is walking the Coast to Coast track to Onehunga in the Domain, Mt Eden and One Tree Hill. Worst thing about Auckland are the crowds in Queen St.

        Cities I’ve liked to spend time in seem to be about the 50 to 80,000 people mark. Maybe Cairns at 120,000 people too, with lots of access to the mountains. Maybe I’m a bit unusual but of the NZ cities I tend to think Wanganui as the nicest of them. Napier and New Plymouth are just a tad dull. Dunedin is interesting geographically, but too cold and it’s polluted in winter. Ch’ch has always been bat shit boring and Auckland, whilst it has got some nice bits, taken as a whole, is less than the sum of its parts.

        • Luke C

          Wellington actually succeeds in this regard very well. Can take a train heading towards Kapiti or Johnsnville and in 10mins from CBD passing through scenery that could be the middle of nowhere. Also from most suburbs in city can take a 20min walk up a hill and easily find nature, and stunning views.
          As for cities the size of Wanganui they have severe difficulty retaining young people, people who go to University rarely come back, or maybe not for a decade or so. Wanganui especially lacks any sort of social life, clubs etc, many people migrate to Palmerston North at least or Wellington for a better scene.
          One interesting thought I have had about Auckland is the very poor view those outside of it have. Many young people from the regions look at either moving to Wellington, then thoughts skip straight to the big 5 Australian cities or London. A common site on facebook is regular posts about how great Melbourne trams are, the shopping, the nightlife etc. These are all aspects influenced by the urban environment and thus quality public transport. If Auckland has a big improvement in these areas will capture more young people from around the country, and thus improve economic performance.

    • JohnP

      I would count rock concerts as among the amenities I’m interested in, and fortunately Auckland’s big enough that we get a fair number of these (thanks especially to Vector Arena). However, another million people would probably give us a much better shot at getting Soundwave or something like the Big Day Out again. Fingers crossed!

  • Peter H

    What I remember, its the cost of water that limits the size of a city.
    Will need to reread. Culture of Cities: Lewis Mumford.

  • Malcolm M

    Some of these 6 factors would be more related to distance, and some to population. A car-dependent low-density city such as Auckland would have a different relationship to a high-density city such as Tokyo, Hong Kong or Singapore. A high-density city has fewer dis-economies of scale, because the physical distance to facilities (eg a shopping centre of a scale that requires 100,000 people) is shorter and more of the trips are undertaken on PT.

    Constrained geography would affect the relationship. The sprawl promoters happen to laud cities built on level plains of low agricultural value, such as Houston Texas. The West Coast North American cities of Vancouver, Portland and Seattle have geographical constraints that limit the direction of sprawl (like Wellington). Los Angeles could sprawl until it reached the mountains, after which the size relationship suddenly changed.

    Water supply may have affected cities in the past, but pipeline costs have shrunk and desalination plants can form an alternative supply, but at additional cost.

  • @Peter H,
    I don’t any modern city has reached a limit due to water cost
    Cities such as Tokyo have grown to over 30 million (if you include the conurbation) and show no signs of having water problems,

  • Luke C

    I think there needs to be some measure of how the city attracts skilled/creative/innovative people. This is about providing for a very wide range of niche interests, access to good food, range of potential partners and also outdoor recreational activities. If a city is too large it gets too difficult to easily escape the city for a weekend as such a vast area of the surrounding area becomes commuter belt and anywhere within an easy day trip becomes over developed and crowded. At this point good recreational opportunities diminish, and people want to leave after a while for a smaller place that has most of a cities amenities but not too crowded. Economically successful cities need these people to drive real growth, ie not just based on consumption and immigration but actually increasing wealth.
    There is also alot of crossover with my first point and immigration. Many immigrants like to live somewhere where they can retain their culture and hence religion, festivals, traditional foods. Cities provide much better economies of scale for this to occur. There is probably no optimal size for this though, as long as city keeps attracting new cultures, each culture will want to build up an economy of scale in this regard. With say 10,000 inhabitants one culture may have reached this optimal point, however there are still another 200 nations, let alone cultures.
    So trying to summarise, adding measures of education (esp tertiary), immigration and ethnic diversity will help determime optimal city size.

    • Stu Donovan

      Hmmm interesting. Very Richard Florida-esque.

      • Luke C

        Just googling him now, haven’t actually heard of him before, but must of come across some writing that he has influenced.
        I don’t think I intended it to be as ‘snobby’ as he comes across. More wanted to convey that I think Aucklands narrow economic focus (too much focus on distribution etc, not enough exports etc) is partly due to emigration of many young people to Sydney, Melbourne, London in search of more vibrant urban places. And therefore think these issues should be included in the measure of economic success and city size. Guess my hypotheses would be that Auckland is not big enough, but Sydney and Melbourne at about 4 million are better sized.

  • SteveC

    I think that tightening up on definitions could help this post, the first question that came to me was size of what aspect of the city? population? physical area? gross contribution to the nation’s economy?

    Malcolm M makes a good point and I think that urban form plays an important role in a city’s economic efficiency, distributed employment/productive centres enable a pattern of shorter trips for people and goods compared to a centralised “fried egg” city with a residential and industrial periphery

    building on these centres allows growth of size of population and economic growth without pushing the physical size overmuch

    • I agree, this is all too abstract for me. Cities are all specific. Wouldn’t it get a little more interesting to ask: What is an ideal size for Auckland? Or is that what you are building up to Stu?

      • Stu Donovan

        well yes and no. Abstract is useful because it helps highlight generalities (and there are some).

      • Stu Donovan

        But yes, I’m building towards that – I think you start with modelling the generalities and then model the specifics. Horse before cart my friend.

        Also trying to get a feel for whether the concept of an “optimal” city size that is neither too small nor too large resonates with other people, or whether I’m up the creek without a paddle.

  • Josh

    What about the dynamics and contour of the land in said city?
    How can you judge a city built on flat land to one of hills and estuaries?

    The case for auckland stands Between the manukau and waitemata harbour. There maybe no optimal size for a city built on a culture of 1/4 acre sections and fishing rods. As far as I can see there are many great suburbs in Auckland that incorporate the beauty of being a kiwi. And theregoes what I’ll call the dynamic.

    • What culture of 1/4 acre sections. The city was originally built on quite dense residential development in the inner suburbs and larger sections didn’t come along till perhaps the 40′s however if you look at the section sizes for much of the city they are in many cases considerably less than 1/4 acre.

      • The 1/4 acre section is a myth, like No8 wire. It’s a little lie we tell ourselves about ourselves: Generally on the way back to our apartments to hire a professional to fix something. Oh of course there are examples, but it is in no way the general size of people’s sections, if they have a section at all. Most people with over 1000 m2 with a single dwelling on it are in the countryside proper and it’s a lot bigger than this.

        • SteveC

          a lot of the 50′s development on the Shore was 1/4 acre lots, many of these now have been sub-divided or cross leased to provide infil housing which is unfortunate as it has entrenched a relatively low density and fragmented land ownership so that it is now more difficult to aggregate sufficient land to build a cluster of suburban two to three story townhouse/apartment developments with good amenity

          we enjoy the luxury of a 1/4 acre that probably meets the five minute pint test, is 15 minutes walk to a busway station, 30 minute walk to Takapuna and a 10 minute drive to the CBD out of peak, but the zoning prohibits subdivision

      • Peter M

        Most development these days is on around 350-400 square metres for standalone housing, whereas a quarter acre is over 1000 square metres.

  • Frizzy

    The optimal city size is 2.4 million at 2041 no?

  • Josh

    The culture that is buying up places in Albany Through to whangaporoa. The sprawl that occurred over the last two decades which you believe shouldnt have proceeded.. I’m sorry but 1940s has no place in 2012. Demand for coastal areas is astronomically high and your largely bias opinion of intensification shows a lack of understanding towards what kiwis want. Let’s enjoy what Auckland has to offer, not what you think it should be offering.

    • Harry McDonald

      It’s hard to know where to start with such a comment. It’s full of grammatical errors which does not inspire confidence in Josh’s intelligence. He fails on simple reading comprehension, completely failing to understand the “1940s” comment. It is the 1940s where Josh wants us to go.
      He apparently knows what kiwis(sic) want but accuses MattL of holding a “largely bias (sic) opinion”; whereas his has no bias at all?
      “What Auckland has to offer” is what generations of Citrats have decided upon. Demand for central city areas would exceed demand for coastal areas at present going by offerings on Trademe.

  • Peter H

    In Hamilton the cost of water – waste water infrastructure has set the direction of growth to the north east. There is plenty of land to the South west, but the cost of upgrading waste water infrastructure to northern sewage plant limits growth to the south.

    I thinking Human scale set the ultimate size of a city, It is not hard to become part of a village (place with local shop), not much harder to be member of town community (school, shops, clubs), A city is made up of a number of Towns, the town that does the most trading and Banking will get naming right of the city. It is this city centre that needs to provide a place for peoples social needs, if it does not another town will provide these needs, e.g. business moving from Wellington to Auckland or Competition between the East Coast cities in Australia.

  • Stephen H

    If an optimal size for a city exists, it will also be dependent/determined on the function of the city within local, regional and global networks. For example a global city such as London or New York will have different needs, and ability to support itself than a city such as Auckland, or even Hamilton. The relative importance/definition of the 6 factors will also change depending on the function of the city.

    Detroit could be used to illustrate this – up until the early 70s it probably functioned as a second tier global city, and had an income stream, facilities and a population base that reflected/supported that. However, as car manufacturing moved away, and it became closer to a regional city, it has been unable to support itself – ie it is too large for its function, and has experienced huge problems, and population decline as a result. Whether this decline can be stablised, and it can achieve a size/function that is sustainable and appropriate to its function will have be seen.

    It will be interesting to see, as global economic power shifts to Asia over the next 50 years, whether something similar will occur in large western financial centres. Will London be able to, or need to afford its amazing tube system if it is no longer a global finance hub?

    To sum up- space and place matter!

  • Josh

    Harry, if intelligence was measured by comprehension i’m sure you’d win hands down. Good on you mate. And clearly I miss read the 1940s comment by matt in the haste of blogging, nice spotting Harry.. All I can say is we’ll know soon enough what aucklanders want.

  • David O

    Having spent a chunk of this year in Tokyo, our species’ largest settlement, I’m not convinced that we’ve yet found the ‘optimal’ size for a city – or at any rate, I find it hard to know on what basis one could declare a single optimal size. Tokyo works pretty well. Could it be better? Probably. Would it be better if it were bigger or smaller? It’s not clear that size is the issue. London is not quite so big – lived there for many years, and for many purposes it’s a pretty damn good place. Lived in Glasgow, ditto. Lived in State College, Pennsylvania for a while. While I wouldn’t want to be there still, it’s located in ‘Happy Valley’ and many of its residents consider it ‘optimal’ (even as it rapidly changes before their very eyes!). Auckland’s not so bad either. Like a poster above, I think density is its problem (if anything) rather than size.

    Anyway, you get my point.

    Your list of forces is a good start, and as you and others have said they scale in various ways which suggest that for any particular city in any particular place there may be better and worse sizes to be, depending on a wide range of contextual factors. I’m just a bit concerned that a ‘one-size’ fits all ‘solution’ is beginning to look a bit like these guys:

    http://www.nytimes.com/2010/12/19/magazine/19Urban_West-t.html?src=tptw&_r=1&

    And while they may or may not be good physicists, I’m not sure they know much about cities.

    PS I’m being deliberately provocative – I love the ambition of this idea – hasn’t anyone told you this is just a blog?

  • Matthias

    I think Auckland is at a particularly awkward size. Big enough to have lots of problems, nowhere near big enough to get economies of scale. I suspect the housing and transport problems in the city are going to limit Auckland’s ultimate population to a level well below what the planners are expecting….
    Personally I think Auckland’s optimal population was at 1-1.2 million.
    Give me the old Auckland of 1998 any day!!!!

    • I disagree, I look forward to the Auckland of 2-2.5 million where those economies of scale really zing and good non-car transport and urban environments are a necessity, not a ;luxury’.

      • Matthias

        I don’t disagree that a city of 2-2.5 million would have its benefits, rather the current population is problematic, and the current problessm in the city, that will be very hard to resolve – high housing and cost of living, traffic issues, and a weakish economy with poor-ish prospects – will make it difficult to actually get anywhere near 2 million without some really radical reform
        I see a fair bit of migration out of Auckland by both young and old in coming years

  • Lloyd

    Its the density, not the size that matters. Check out Newman and Kenworthy.
    Increase density, increase efficiency, decrease energy consumption. Simple.

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