I have posted few months ago some considerations on the relationship existing between the pro-capita wealth of a city and its dimension. On the average we can see a strong resemblance to the relation existing between the metabolic rate of an animal and its size (the Kleiber law). Whereas in the case of animals this relation is rooted in the way the heat generated by metabolic activity is dissipated by the animal, and in turns this is achieved through fractal dissipation, in the case of cities the wealth seems to be related to the city’s infrastructures and these again have a fractal topology deriving from the way we engineer them to optimize cost and performances (which is not very different from the way natural evolution has progressed, hence the similarities).
Another way of looking at the pro-capita wealth in a city vs its overall size is to use this relation as an indicator of the effectiveness of the city infrastructure.
Clearly, technology can improve and it has improved cities infrastructures but this has resulted in bigger cities, not really more pro-capita wealth (although we can see that cities with better infrastructures have a better pro-capita wealth (similarly to the fact that omeotherms have better metabolic rate than other animals).
An interesting question is if new technology (and new infrastructures) can radically change the relation between city size and pro-capita wealth (unlikely) or can increase the pro-capita wealth faster (more likely). My speculation that a change in the relation between pro-capita wealth and city size is unlikely stems from the fact that a city showing such an improved ratio will attract more people that in turn will decrease the ratio. On the other hand we can imagine that new infrastructures may allow a faster increase of pro-capita wealth (in natural evolution this would equate a species that can get bigger because of a more effective way of dissipate the increased metabolic rate).
My take is that this is becoming possible with a new sort of infrastructures, those based on bits, rather than on atoms. We have already seen a few examples fueled by the decreased transaction costs that characterize economic transactions based on bits.
Clearly, there is a broad variety of pro-capita wealth in different regions of the world and even within the same region. Furthermore, we see that the increase in overall wealth is not uniform and within a region some cities increase their wealth faster than others (and some might decrease its wealth whilst other are increasing it). This is mostly associated to some radical change in the economic landscape.
As an example, cities like Pittsburgh, Detroit were hard hit by the disappearance of steel factories and the decline of car automakers (and the automation of production lines). Others leveraged on new industry sectors, like Phoenix with the semiconductor industry, Bangalore and Chennai with software and so on.