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:
- 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
- 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:
- Direct transport costs – i.e. what you pay in cash terms to move about.
- Congestion – i.e. the costs of additional travel time due to delays from things being busy.
- Economies of scale – i.e. efficiencies in the provision of public goods.
- Agglomeration economies – i.e. the economic benefits of density.
- Purchasing power – i.e. the value that you get for every dollar.
- 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?