Gravity Core, Suppression Zone and Leapfrogging… the basics of spatial economics

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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.

In my opinion, the most interesting part of the model (in the urban context) is not in its final state but rather in its more common intermediate phase. The graph below was created by a mathematical model.  More about it – here.

I want to focus on the center of the graph above and highlight only the effects of the core.  I’m drawing only half of the above from the center to the left, and only the economic pressure created by the core.

Let’s look at some points and the areas between them. The line indicates the pressure to increase or decrease supply created by the center.

Gravity Core – Let us start from the area of ​​supply density, the city center if you will. In this region, there is continuing pressure to increase commercial activity and supply of goods or services. The area ends at a point called R0.

Suppression Zone – Beyond point R0 and up to point R1 extends the Suppression Zone. In this area there is constant pressure to reduce supply. Any economic activity established here will be suppressed because it will compete with the Gravity Core and will be overwhelmed by it’s huge surplus.

Leapfrogging Ring – Between point R1 and point R2 extends the “Leapfrogging Ring”. Encouragement for economic activity is created in this area because competitors can not reside in the Suppression Zone, while part of the available demand from it can be pulled by centers at the Leapfrogging Ring. With possible competition coming only from one side, there is positive pressure for additional economic activity in this ring.

Beyond R2 point there is no economic influence by the core (in fact there is but very negligible). Whatever happens at the Gravity Core can not affect this area … I’ll talk in future posts about cases where the Gravity Core effect spills out of R2.

If we want to ‘rephrase’ it on to a 2D map rather than a one-dimensional depiction, the graph above will of course look like circles. R0, R1, and R2 are radii that delineate the areas. In a more advanced model, I will present a better layout, but circles will suffice for now.

Before I’ll present some examples of ways in which even this abstract mathematical model is expressed in reality, let’s look at a number of features of the model:

  • The boundary of the Gravity Core – R0, is “sharp” and distinct.
    We see how in only a few meters we move from a place of growth and high economic activity to a deep suppression of any similar activity.
  • The radius of R1 depends on the distance that customers are willing to travel to get the product.
    This is the “Hassle-distance” I’ve talked about. The more they are willing to travel, the greater the radius will be. If the trip is expensive and annoying (high hassle-distance), the radius will be smaller and the Suppression Zone will shrink as well.
  • The Leapfrogging Ring is an excellent place to build a secondary Gravity core.
    According to the model, this is the place where secondary centers will be located in the city.

The differences between the theoretical model and reality are numerous. First, the model presents one average product and the city has many products to offer. Customers in real life are not evenly distributed nor is the surface flat and uniform. However, large averages work fairly well and observations from the real world that behave as the model predicts are abundant.

The boundary of the Gravity Core is “sharp” and distinct

LAS Vegas strip

Why are the hotels so packed? They have all this desert around them, there are roads everywhere, there is a great place on the other side of the airport, each hotel is a world in itself for its guests and yet … The hotels are crowded and we all know why.

We too would have been very hesitant about opening a new hotel outside of the Strip itself. The hotels in the Strip are exerting such economic suppression around them that any hotel that is not in the Strip will have to lower prices and probably will not succeed.

Note how you feel it in your gut. Even if I’ll tell you about residing in an imaginary hotel that is right at the edge of the strip, on the same road but 300 meters away from the currently most outward hotel there. “No”, you think “I want to be in”. You have just traveled 2000 miles for vacation in Vegas and you are hesitating about 300 meters. That’s the power of the Gravity Core in the city and the model describes it.

Broadway theaters in NY

The Suppression Zone is so strong that it actually has a brand for itself – Off Broadway. Why are all those musicals theaters crowded to a single location? After all, it’s not that tourists in New York won’t get to Central Park. Ostensibly, this makes no sense. The range of influence of these theaters is the whole world and yet they are crowded together. If I let you open a new theater and you have two locations … well, you understand.

Do you think the NY theaters would had the same effect if they were scattered all over New York? Got you, you hesitated. The model dictates they had to lump together. Over time they had no option. It is the economic Gravity pull that tightens them up.

DuPont and Main in the middle of nowhere

Don’t be fooled by the examples above. You can see the gravity core effect even in the smallest of towns.

If you are to open a new restaurant, why is it that you’ll rather place it in right between the existing ones, why not on the left or the right edge? even more, why stick so close to the competition?

It’s clear, it’s because people do not choose a restaurant based on it’s proximity to their home. Within a hassle-distance range, they don’t care. Being in the core pays of for you and for the other restaurants as well. No one is trying to minimize traveling distance and that can grow to be a market failure…

… so is the city ​​a market failure?

This article is getting too long as it is so let’s demonstrate the other points later. I’ll wrap it by placing a bomb on the discussion table. If you have followed the economic model and agreed with it, you have just agreed that the city ​​is a market failure, not a success, not an economic engine. The reason that the big city seems to be more “successful” than the surrounding suburbs is because of the economic suppression it exerted on them. Nice one, huh?


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