C.R.E.A.M

Clusters Rule Everything Around Me

i have no idea why but this feels relevant to the post

Nobody goes there, it’s too crowded

Yogi Berra

A few weeks ago, I saw this (very interesting) tweet, asking why a single food chain had two stores in extreme vicinity to each other:

“paula” @paularambles

the placement of these two bröd & salts will forever puzzle me they are literally across the street from each other

So why do businesses pile up like that? Is it economically sound?

There’s three fields I think are relevant here: Industrial Organization (IO), economic geography, and urban economics. Let’s go in order.

Lines and circles

In economics, location is a tricky category to work with, since it can be considered both a quantity and a quality.

For example, buying a bottle of water at the airport is more expensive because there’s less supply and because the opportunity cost of going elsewhere is very high, but also because “a bottle of water at the airport” is, at its core, a different product than “a bottle of water at the drugstore” or “a bottle of water at a restaurant”. It’s both reduced supply (quantity) but also a different quality altogether, meaning that dumb canards about the Law of One Price simply don’t apply - the airport, the grocery store, and a restaurant are neither the same market nor selling the same product, simply because location is a thing.

Another way of seeing location is by imagining a city is a line. Imagine a beach with two ice cream vendors, who have the same marginal cost for their ice cream and have evenly spread out customers across the beach - and the customers don’t face any cost to walking from one end to the other. Where do they locate? Well, assuming they know all of that, start with each at one end. If one of them moves just a little bit, they can “steal” some customers from the other vendor. The other vendor, therefore, would move just a little bit too. This repeats itself until, counterproductively, both vendors end up at the exact same location - the middle!

Of course, it gets complicated fast. If the costs are not zero and not constant (i.e. going further costs more than proportionally to going closer), then they don’t actually go all the way to the middle, and instead end up at the 1/4ths and 3/4ths marks. And if one company has higher costs than the other, they don’t end up at equal distances - one has a higher market share simply because it can be worth it to more customers. With more than two firms, it’s hard to figure out exactly where they end up, even if all three are equal, because they’d constantly undercut each other, but it’s safe to say roughly equidistantly to each other.

You have to take the number of firms as a given, though. To figure that out, you need to assume their location - in this case, through a circle, where they all butt in and settle equidistant to each other. The most important thing is that the size of the market, transportation costs, and cost differences between firms determine how many firms are able to be accomodated: a larger market, with smaller costs, or with little to no cost differences is going to have a large number of firms; a smaller market, with high transportation costs, or wide efficiency gaps is going to have very few firms. This tells you that there are limits to how many businesses can locate in a given area, since getting there, being there, or selling there might not be equal for all.

And even if one firm is absolutely superior to another in all regards, the latter can still survive in a large enough market with large enough transportation costs if the former is subject to capacity constraints: a worse bakery that can bake 50 loaves can still be in business versus a better bakery that can bake 100 if the market for bread is more than 100 loaves.

So, by this model, the two identical firms from the original tweet should actually end up at the same location if transportation costs are constant and if demand is uniform. If they aren’t, IO can’t do much to help you.

I miss the old Krugman, no Nobel Prize Krugman

Why is the financial services industry concentrated in New York? Partly because the sheer size of New York makes it an attractive place to do business, and the concentration of the financial industry means that many clients and many ancillary services are located there. But a thick market for those with special skills, such as securities lawyers, and the general importance of being in the midst of the buzz are also important. Why doesn’t all financial business concentrate in New York? Partly because many clients are not there, partly because renting office space in New York is expensive, and partly because dealing with the city’s traffic, crime, and so on is such a nuisance.

Krugman (1998) “The Role of Geography in Development”

A key concept in economic geography is increasing returns to scale. Basically, in most areas of life, a process getting bigger either remains as efficient (constant returns), or starts getting less efficient (decreasing returns). For instance, working 5 hours on a project might be optimal, adding a sixth hour is as effective, but a seventh and eight hour are increasingly less productive.

How can returns be increasing, though? Seems counterproductive. The first is that, obviously, not all locations are equal - some places are more productive (for certain uses) than others. Secondly, some locations are more populated, which is important in terms of labor supply and demand: more firms can operate, which means higher wages and more spending, which means workers migrate, which means even more firms. Lastly, it’s just possible that firms can learn by competing with each other, or that there’s some other external property of having a bigger market. These are centrifugal forces, because they bring things together.

At the same time, there are forces separating people: these are the centripetal forces. Firstly, transportation costs can be non-zero and even non-linear (i.e. increase more than proportionally with distance), which puts a “maximum size” on a location. Secondly, if you’re including location you have to include land, which is not free - and if there is a maximum size to an economic center, there is also a scarcity of land to build it on. Lastly, large areas can become congested, which results in general unpleasantness for the inhabitants - too much traffic, too few amenities, too much competition, etc. Of course, labor is also not perfectly mobile (not many people move very far away), which also limits the size of a market.

This concept is so important because small differences have small impacts under constant and decreasing returns; but can have enormous effects under increasing returns. If demand is slightly bigger somewhere, ceteris paribus, it will accumulate more and more and more economic activity simply because the returns to that location get higher and higher, and therefore more and more demand adds up. This is why some countries have such marked population imbalances: certain areas were either slightly more populated, slightly more productive, or slightly more accesible hundreds of years ago. The pull and push of the centrifugal and centripetal forces is what leads to the patterns of settlement and location we now see, usually in extremely chaotic ways where seemingly trivial factors affect development for eons.

One of the more interesting extensions of these models is that economic activity simply occurs randomly in some location, usually by a mix of optimal qualities and historical accident, and then simply starts spreading around the same region due to the interplay of forces for expansion and for limitation of economic activity. It even applies to development and trade, where some countries simply become wealthy randomly, and then their neighbors follow suit. Fascinating!

This approach, pioneered by Paul Krugman (which, alongside his work on trade, got him a Nobel Prize) has held up surprisingly well, and has shockingly high predictive power for its simplicity. Even with very mild assymetries within or between areas, the centrifugal and centripetal forces of agglomeration mean that economic activity will take interesting patterns of concentration. But how and where?

Economics talking jive

What We Imagine We Can Design

I’ve written about agglomeration twice before, mainly because it’s so important to understand cities specifically. Agglomeration simply refers to the tendency of economic activity to concentrate somewhere, and agglomerations usually occur very randomly - the reason why certain cities or neighborhoods concentrate a lot of very niche activities is that, as seen above, there is a labor market for them, there is a demand for them, or there are advantageous natural or productive qualities to them, all usually because of very obscure and seemingly inconsequential events.

Economic activity is largely concentrated between cities, and normally cities have certain areas dedicated to specific (even very specific) activities. The key principle to take into account here is that cities are not just big buildingd because cities, due to the centripetal forces that limit their absolute size, are closed systems: if you individually show up to work 10 minutes earlier, you’d get a parking space; if everyone did, the lot would just fill up faster. As a complicated whole, cities act as a market for two main factors: land and labor.

The urban market for labor is interesting, but straightforward giving the preceding ideas. Because some cities have some specialized trait or industry, people move to them, which means other people move there as well to work in non-tradable services that those people will demand: even if LA is specialized in entertainment, New York in finance, and San Francisco in tech, all three are going to have a lot of restaurants, stores, and lawyers, simply because actors, bankers, and coders all need food, clothes, and divorces as much as anyone else. And when these services move in, the city grows too, because suddenly the market for the same services got bigger - lawyers need lawyers and therapists need therapy. The economic advantage of cities comes from agglomeration, so that the bigger the labor market is, the more opportunities to just sell regular services become, and the bigger the benefits for all industries.

The market for urban land is different, because urban land is not homogenous and not infinite. Soviet urban planners built hundreds of identical apartments in identical buildings, but they have different prices because the land they sit in is different - some areas are cooler, some are more convenient, some are safer, some are less noisy. And a five bedroom house that sits next to a ten story building is more expensive than five one-bedroom apartments because it sits on more land of equal value than all five of them together. So land is a huge constraint on urban development, because people will not live too far away from certain things, and therefore the size of a city has a limit - meaning that the value of land is actually binding for location and density.

Conclusion

All put together, this tells a compelling story: within geographically bound cities, a lot of specific activities will concentrate somewhere to compete for customers and labor, subject to limited demand and non-zero land costs. However, these clusters are limited by the non-infinite willingness of customers to travel and to wait. And in the real world, this is exactly what occurs!

maia @maiamindel

this is true for a variety of sectors and a variety of cities - for example, this is kampala (uganda), where 40% of *all* businesses are in the same area - because customers are more likely to go to one spot due to information and transportation costs!

“paula” @paularambles

the placement of these two bröd & salts will forever puzzle me they are literally across the street from each other https://t.co/1B1hXt2lom