Yesterday’s post on population loss from rural areas generated some really interesting comments.

My main goal was to highlight some of the potential challenges facing rural areas, which I think is important. But as some people rightly pointed out: My home town of Waiuku is not exactly struggling to survive. Indeed, unlike much of rural New Zealand Waiuku’s population has been increasing and the general consensus is that it will continue to grow.

As I expect will the populations of many similar smaller rural towns in the Auckland region, such as Clevedon, Warkworth, and Helensville. And the growth is not just limited to the Auckland region; Kerikeri and Whakatane are two small rural towns that have been on my “superstar” list for a long time now.

But how, you might ask, can I be worried about population decline in rural areas while simultaneously observing that some small rural towns are growing gangbusters? General answers to that question is what this post is about, namely economic patterns in urban development. My main suggestion is that the rapid growth of a few of these small towns can be explained by their proximity to a larger urban area.

Economic patterns in urban development are important because they help you to understand the shape and structure of urban areas. Of course there’s other random things at play, most obviously geography, but there’s also underlying patterns that crop up with unerring regularity. I’m not an expert on all of these patterns, but I know enough to find them interesting.

The first, and probably most important, pattern to observe exists between what economists refer to as land rents and distance to the city centre. Below is a map of estimated land rents [$/sqm] in Auckland, which I made as part of my masters thesis. I say “estimated” because land rents are not often able to be observed independently from the physical improvements that they support, as such you have to “net out” the value of the improvements.

Land rents in auckland

What you see here is a pretty clear trend towards declining land values as one moves away from the city centre. Several plausible economic factors contribute to this decline, such as transport costs and agglomeration economies. There are also historic advantages that come from being the city centre, such as proximity to cultural amenities, which push up land values there. This pattern of declining land rents is usually referred to as the monocentric city pattern.

At this point you might be thinking “gotcha!” – what about sub-centres? Surely they prove the monocentric city theory wrong. Well, not really; the theory has over time been adapted, or more appropriately said extended, to deal with what is technically known as polycentric urban areas with multiple sub-centres.

Glaeser and Kahn developed an economic model of urban development that allows for the emergence of sub-centres at a certain distance from the city centre, in response households and business seeking to minimise their transport costs. This manifests as sub-centres located at a certain distance from the city centre, as illustrated in the slide below.


In the image land rents are on the vertical axis and distance to the city centre and on the horizontal.

This shows declining land rents around the city centre and an emerging sub-centre. The catalyst for the development of the sub-centre is when the economic benefits of doing so (i.e. the capitalised value of the transport cost savings attributable to the sub-centre, which is represented by the area of the small triangle) exceed the fixed costs of setting it up – usually the residual value of agricultural land and any infrastructure costs (represented by the horizontal p_agr line).

Voila! We now have a plausible economic explanation for Manukau, Albany, and Henderson. What’s important to note is that the emergence of sub-centres is above has been simplified to two (d,p) dimensions, whereas in reality cities grown in three dimensions (d,y,p). Not only does this hint at the presence of multiple sub-centres all located a specific distance from the city centre, but layers of sub-centres around sub-centres. Think of it as a Russian doll of sub-centres, if you like.

Which brings us to the interesting topic of “fractals”, which are a field of mathematics that considers self-repeating complex patterns. Wikipedia defines fractals as follows:

The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth.[2][4][5] Fractals are not limited to geometric patterns, but can also describe processes in time.[3][6][11] Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds[12] and found in nature,[13][14][15][16][17] technology,[18][19][20][21]art,[22][23][24] and law.[25]

Fractals are relevant to economic patterns in urban development because they seem to explain the patterns seen in sub-regional development, as seen below for Tokyo (source) from 1960 to 1995. Here you see a pattern of the central city with radial transport links connecting to peripheral sub-centres.


Over time the transport links are extended and the more sub-centres tend to develop, athough these new centres seem to be usually smaller and less dense than the ones closer to the city – exactly as we would expect from the simple two-dimensional model presented by Glaeser and Khan.

This is actually an example of an “adaptive nework”, which given a certain starting point (population and network) describes the process by which urban areas and their transport networks might expand. And perhaps even more interestingly, such networks are found in natural structures as well.

A group of Japanese researchers, for example, found that “brainless slime” was able to replicate the structure of the Tokyo subway. The reserachers duplicated“the layout of the area around Tokyo: They placed the slime mold in the position of the city, and dispersed bits of oat around the “map” in the locations of 36 surrounding towns.” This (somewhat over the top) article described the process as follows:

The mold explored slowly at first, but like any good transportation engineer it began to figure out traffic patterns. To continue growing and exploring, the slime mold transforms its Byzantine pattern of thin tendrils into a simpler, more-efficient network of tubes: Those carrying a high volume of nutrients gradually expand, while those that are little used slowly contract and eventually disappear [ScienceNOW Daily News]. When the mold got its system settled, researchers say, it looked rather similar to the actual Tokyo subway system, as you can see in the illustration.

The result is illustrated below (source). If one was being cheeky one might say that the mould developed a more efficient network than your average transportation engineer ;).

Not that I think we should read too much into the ability for mould to replicate a subway network (this seems vaguely reminiscent of a Simpons episode, or maybe it was SouthPark?)

But how does all of this relate to Waiuku?

Well, let’s be honest and accept that Waiuku, and most small towns in New Zealand, were probably established by people who weren’t thinking too much about these types of economic patterns.

Waiuku’s initial settlement was probably in response to its geographical advantages, and the original residents were probably just looking for a place to stick a spade in the ground and call home. From these humble beginnings Waiuku probably developed as a local town servicing surrounding agricultural hinterland, a small localised example of Krugman’s theories on new economic geography (i.e. regional/peripheral economic interactions).

Then came an external shock in the form of the Glenbrook Steel Mill – which had two major economic impacts. First, it greatly increased the supply of relatively well-paid manufacturing jobs in the area and hence in turn increased the residential population it could support. Second, it catalysed major improvements in transport infrastructure connecting Waiuku to the rest of the country. Indeed, it was only around the 1960s that the road from Waiuku to SH1 was first sealed.

Meanwhile, however, a more gradual external economic shock was looming on the horizon: Auckland continued to grow, especially to the south. This – in combination with the improved transport links – enabled residents to shop further afield, in places like Manukau. This in turn led to the gradual erosion of the intensity and diversity of commercial activity in Waiuku. The town was increasingly dependent on Auckland for employment and general retail activities.

And that’ trend has continued: Waiuku is a residential satellite town whose ability to support its population is almost entirely contingent on two things: 1) the Steel Mill and 2) metropolitan Auckland. Naturally, as the local residential population has grown the town’s ability to support more diverse commercial activities has also increased. But this growth is not attributable to Waiuku itself, but more the combination of its proximity to Auckland.

The key point is this: While the geographic, historical, and socio-economic factors influencing urban development are many and varied, some regular patterns/processes seem to emerge. In particular, small rural towns on the periphery of larger urban centres will become increasingly dependent on the latter for their well-being and growth. But this growth is not independent from the growth of the nearby city; it’s intrinsically linked to it.

It also suggests that places like Waiuku and Whakatane, which do have growing populations, may be the “rural” exception, rather than the rule.

PS. Those with a bit more time and interest in these things might enjoy reading this chapter on urban morphology, which is written by a lecturer in geography at the UoA, namely David O’Sullivan.

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  1. Waiuku began as a rural service centre so why there and not elsewhere? Because it was well placed for access by the dominant transport technology of the period: ships and boats; same as Warkworth, it’s a wharf town.

    1. Originally yes. And then an agricultural/manufacturing town. And now a dormitory suburb.

      Same goes for many other small rural towns, such as Kerikeri.

  2. Looking at your map Stu and particularly the green areas – seems like it would be smart to buy a property in either Tamaki/Glen Innes/Panmure region or in New Lynn/Waterview/Avondale area. I think it’s also interesting because it highlights how Auckland just doesn’t have urban ghettoes in the downtown (or if it does they’re really small), unlike some of the big USA cities.

    1. Yes, Tamaki Glen Innes is extremely under-valued given it’s relative proximity to the city centre. I also think that it still stands to benefit a lot from:
      1. Electrification
      2. Intensification of Sylvia Park, which will bring additional low-medium value jobs to the area, hence increasing employment; and
      3. The Tamaki Transformation project.

      So opportunities for land value uplift there. New Lynn also stands to gain a lot from similar initiatives over the next few years. So those would be my pick for suburban places where new home buyers should get into.

      Unless you’re OK with living in the city centre, because in all honesty it is still vastly under-valued. You won’t be able to afford so much land, but what do you get will likely see relatively spectacular capital gain, especially in the core central/eastern areas.

  3. would be interesting to look at different patterns of these subcenters at different stages of development. It seems that new areas have less centers that historically developed areas, and new areas have more single purpose centers (ie retail only, less non-retail employment).
    Ie on the North Shore there is Albany but smaller mixed-use centers are lacking, apart from the historical ones around Browns Bay.
    In East Auckland there are no large centres like Albany, but a bunch with retail only like Botany, Highland Park. Pakuranga is a bit better as is older, but not much.
    In these areas there is large amorphorous mass of mixed density jobs and retail across North Harbour and Rosedale, and Highbrook/East Tamaki.

    Of course no idea how to actually rank these centers with available statistics. Foot traffic maps would certainly show the older ones up, but not much foot traffic around Botany or Albany! Also the roading pattern plays a huge role is showing how these centres develop. If centres are at corners of major aerials foot traffic is miserable, however for example Howick is much better as not on major arterials like Botany is.

    1. Exactly right. And that’s precisely what you would expect – if you look at that sub-centre diagram in the above post, the impact of higher transport costs (which applies to older areas) would be to “steepen” the slope of the decay in land values as one moved away from the city centre and/or sub-centre.

      That in turn would tend to bring the sub-centre spacing relatively closer together, because their relative area of suburban “reach” would also decline. As real transport costs reduce, as we experienced from circa 1950 to 2000, then you would expect the sub-centre spacing to increase along with their overall scale. Hence instances where mega-malls would replace the local shops.

      Thus, economic patterns in land use are intrinsically related to transport costs, as one would expect.

  4. Wow, a great post Stu, easily the best I’ve read since I’ve been lurking on this site (which is about a year). And the standard is set pretty high. I first got involved with AM/FM/GIS back in the mid-80s when it was in its infancy and horrendously expensive, eg early MicroStation seats cost $100k+ each. The initial distinction between AM/FM and GIS has long since disappeared, while seats are just a few thousand each and run on bog standard PCs.

    Your land rents map is fascinating – without being too specific, I live in the in the red zone (no, not the Christchurch red zone) so did a quick calc and got $1772/m2 for land value. Just as well it’s a small site. We moved here as our businesses cover the greater Auckland area, and sussed out that we would be approx. 20km from each of the Albany, Henderson, Manukau & Botany sub-centres. Your sub-sub-centre argument (ie organic growth) makes a lot of sense too.

    As an aside, it still puzzles me that some advocates of intensification claim that this reduces land costs, which simply ain’t so as your map clearly shows. The only way I can rationalise this is to assume they are comparing tiny city footprints (eg multi-storey apartment blocks) with suburban sections. But having said that, the apartments in my area are $1m+ so it still doesn’t stack up, and compared with my townhouse the values are higher on a square metre basis (of the building). I’m not arguing against appropriate levels of intensification per se, just that the cost argument seems flawed.

    1. I think the point is that with intensification you can get more units per square metre and therefore land cost is a much lower percentage of what you have to pay. I mean there’s a reason why the Upper East Side in Manhattan is apartment buildings and not single houses.

      1. Yes I get that, but why would you pay $1m for a 100m2 apartment on a one-tenth share of 100m2 of land when a nearby 250m2 townhouse on its own land is only $1.2m-$1.5m? You’re paying almost as much for 10m2 of effective land (plus some common area and maybe parking area) vs say 300m2 of private land plus 2.5 times the floor area. The only reason I can think of is convenience, which is a good enough reason of course. Interestingly, I think all my apartment-dwelling friends own beach houses as well. When I’ve asked why, the short answer is that they would go stir crazy if they didn’t.

        And last time I looked the Upper East Side wasn’t exactly cheap.

      1. AM/FM stood for Automated Mapping/Facilities Management and was generally used by utilities, whereas GIS was used by territorial authorities and considered at that time a poor relation. The essential difference was that AM/FM linked to databases (typically Oracle) including connectivity etc as well as financials, whereas GIS was really just a map with some descriptors and financials attached. Of course that distinction is irrelevant now as they have merged.

        The early AM/FM software I was involved with was Intergraph, built on a Bentley MicroStation CAD software platform. MicroStation’s competitor was/is AutoCAD, a bit like the Betamax/VHS fight that VHS won with better marketing even though Beta was generally considered technically superior. Interestingly, MicroStation V8i reads dwg formatted files, but AutoCAD can’t read dgn formatted files. I believe there was some attempt at establishing compatibility a few years ago, but it doesn’t seem to have eventuated. Another advantage of the dwg format is that there are AutoCAD clones around such as ProgeCAD Pro (which I use) at a fraction of the price.

        But I digress. I’m pretty sure that Smallworld now dominates the market, at least in Australasia – a NZ development incidentally. Both Intergaph and Smallworld GIS files can be downloaded as dwg files which is very useful for incorporating in design drawings. Smallworld links to SAP and probably other enterprise systems, so it all becomes quite seamless. I’m not familiar with other GIS systems although I have played with ESRI.

        I hope this is helpful and not just tl;dr!

    2. Thanks Jonno, and I’m glad to know that my land value estimate was correct for your house :).

      With respect to land values: The obvious response to high land values is to provide less land per house. Whether the ultimate price are higher or lower depends on a number of other factors, especially the capital intensity of the development.

      The value of land attached to my central city apartment ($60k) is less than that associated with most single detached dwellings, although of course it’s smaller. The high prices you quote for apartments thus seem to be associated more with the nature of the developments that have occurred and the types of people who want to live there (high income) rather than inherently high costs associated with more intensive development.

      I do think intensification will lead to more affordable housing once additional transport, energy, and infrastructure costs are considered. But those benefits may not fall to the landowner, but instead be dispersed throughout society. Ultimately I guess they are probably either capitalised into land values or are captured by central government taxes.

      1. It would be interesting to know what land area (footprint/vertical no. of units plus share of common areas) your $60k represents, in comparison with mine. My land value is approx. 60% of the CV, a figure similar to that which has been quoted on this blog to demonstrate the crazy land values in Auckland. And yes, I was referring to relatively large apartments, but my main point was that they aren’t very good value for money. My house is in the same general area so proximity to PT, motorways, shopping precincts, schools etc is identical. I understand that more people can live in an apartment block than in standalone houses built on a comparable area of land, so that meets the intensification criterion, but shouldn’t it make apartments relatively cheaper?

        1. My apartment is 50 sqm; not sure exactly how much land I own but I could find out. It’s worth $60k of ~$280k apartment, so about 30%.

  5. What I find interesting about the metropolitian centres identified in the Auckland plan is how much they fall into a couple of travel time bands from the central city via PT and connect to places further out. At roughly 20 minutes from the centre we have New Lynn, Takapuna and Sylvia Park. At roughly 30 minutes we have Albany, Westgate, Henderson, Manukau and Botany while at just over 40 minutes out we have Papakura. Many of those connect through each other so you go through New Lynn to get to Henderson, through Takapuna (well close to it) to get to Albany, Through Sylvia Park to get to Manukau etc.

    1. What’s also interesting is how the older centres seem to be located a bit more “organically” than the newer ones (i.e. along rail corridors, relatively evenly spaced, near the centre of something). Albany has always struck me as the weirdest of centres because it’s not actually in the “centre”, it’s on the very edge of Auckland.

  6. Are we talking Land Rents or Land Values ? The graph is labelled Value but you talk of Rents. Is there a major difference in the spread anyway ?

    Not really questioning the thrust of your argument but it’s hard to see how land rents in the southern slopes of Herne Bay can be put in a similar category as Panmure ?

    Based on council valuations Herne Bay would be ~$1500 / sqm, Panmure ~$500 / sqm, Or am I missing something here ?

    1. Good question and I should have been more precise – in this context they’re the same.

      Now, the more interesting thing you raise is the issue of average versus marginal prices. My analysis relates to the latter, i.e. the marginal price of land in these locations. You can think of that as the price someone is prepared to pay for a section that is 1 sqm larger than another. The average price of land, in contrast, is calculated as the total land value divided by the area, as you have done.

      Now what’s the difference? Well, the average price tells you exactly that – but what it does not tell you how much people would really value an extra sqm. Generally marginal land prices tell you much more than average prices, because they contain a lot of additional information on how the supply of land (or more specifically lot sizes) in a particular location matches demand.

      And you can have situations where you have high average land prices but relatively low marginal land prices (the value at the margin is typically lower than the average). That might arise in situations where the suburb has a number of large lots (e.g. Herne Bay) but the people who want to live there value small lots. And vice versa, where you have a suburb with a lot of small lots (e.g. Panmure) but the people who want to live there want larger lots.

      Is that clear as mud?

      1. A good explanation Stu. A couple more scenarios: in Herne Bay or Epsom the large lot might be a few square metres short of being subdivisible, so its excess over the minimum size has no true monetary value (although it has some amenity value). But if say 10m2 could be bought from a neighbour to create a second lot then the marginal value of that 10m2 is phenominal. OTOH, a rural lifestyle block may have a small building platform plus hectares of bushclad land that cannot be built on or readily accessed. The latter portion again has no true monetary value, even if technically subdivisible, but its amenity value to the owner may be significant.

  7. Thanks for the plug Stu! Like all self-respecting lecturers I’ve been at the beach for the last couple of weeks so missed this one. Of course the real oracle on all this stuff is my academic mentor Mike Batty. He’s actually made his book Fractal Cities freely available to the world: Meanwhile, a bit less public spirited, but I’m still finding my way in the world, here’s the website of my own forthcoming book: While this isn’t about cities as such, many of the sorts of processes that are discussed in the book are the types that those mad Japanese folks used to demonstrate that slime mould and cities are (in a certain limited sense!) quite similar.

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