If you’ve been following my posts and the theoretical model I’ve presented, you too have come to the rather disturbing conclusion – That this model fits any free market. Whether it is a city, a manufacturing plant, or a service company, it seems that every free market seeks to achieve agglomeration, a state where there is only one supplier and zero competition.
What determines a city’s size and the area of its economic impact? What is the connection between ‘Hassle-distance’ and the theoretical gravity model I’ve demonstrated earlier? I want to elaborate more on the Suppression Zone of the city and I’ll tie it all together here.
“The city is an economic engine”. This built-in assumption is now rooted in so many studies that it had become taken for granted. To the point where no one pauses to ask whether or not it’s true anymore. If you are as fascinated with cities as I am, it is clear to you that this claim is pivotal, so why are its supporting arguments so vague and easy to refute?
Quite a few studies demonstrate that large cities are associated with high levels of productivity. This statistical correlation is the basis for the assumption that the city is an economic engine. This is the claim that I intend to dismantle. I am not arguing with the facts, only with the conclusions made by the various researchers.
Let’s continue with urban mathematics shall we? If you are fascinated with cities as I am it’s a path worth taking. This is the ‘WHY’. The deeper understanding of why the city behaves the way it does.
Let’s see what the model I have developed is actually teaching us. As a reminder, the model progresses up to “Nash equilibrium” for one product, with equal distribution of suppliers and customers. The model illustrates how a market failure was created, similarly to the model of the ice-cream vendors. In this article, I would like to show examples of the phenomena that the model produces.
OK, here it is, the most complicated part of the book. I’ll try to explain this urban mathematics thing as clearly as I can, but I guess I’ll need to re-write it few times. This article would probably be tricky to follow but fortunately, there are pictures.
So, deep breath…
My goal here is to find the mathematical equivalent of (don’t panic) Nash equilibrium on a large scale with many players. Just as in the example of the ice cream vendors, I am looking for the easiest way to explain why businesses are clustered in the city, using the simplest possible algorithm.
Hmm, sounds reasonable so far. Are you with me? let’s go.