How To Really Make Sense of Hotelling’s Law?

Have you ever seen restaurants or fast-food chains spaced very close to each other? In fact, this observation does not restrict itself to just restaurants and fast-food chains. Pharmacies, bakeries, coffee shops, and ice cream parlors are just a few among other business entities that follow a similar trend.

If you think about it logically, would it not make sense for these shops and businesses to spread themselves evenly throughout town? This way, customers who are distributed throughout the town would have better access. If this is indeed the case, what gives? Why do businesses end up so close to each other?

As it turns out, Hotelling’s law tries to explain this very phenomenon. In this essay, I will cover the fundamental framework behind Hotelling’s law using a simplified illustration. Following that, I will cover extensions and further applications of Hotelling’s law.

By the end of this essay, you should be able to form a generalised mental model for potential applications of this law. So, let’s get started.

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The Eponym of Hotelling’s Law — Harold Hotelling

Harold Hotelling was an influential American mathematician and statistician. He is well known in the field of economics for his scientific work — especially his generalization of the Student’s T-distribution. He was Associate Professor of Mathematics at Stanford University from 1927 until 1931, before serving as part of the faculty at Columbia University and Professor of Mathematical Statistics at North Carolina later on.

At one stage, legendary mathematician Abraham Wald worked under Hotelling. Another economic heavyweight, Kenneth Arrow, was a doctoral student of his. It is safe to say that Harold Hotelling was no ordinary mathematician.

Among an array of interesting topics that he worked on was the observation that businesses such as restaurants and shops tend to cluster close to each other. Hotelling began investigating this observation and tried to build a mathematical model that describes the behaviour. He published his work under the title, “Stability in Competition”, in the Economic Journal in 1929 (link in the reference section at the end of the essay).

Without going into detailed mathematics, one could grasp the gist of the matter using a simplified illustration.

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Hotelling’s Law — Illustrated Using Two Supermarkets on a Street

Let us say that you and I live at opposite ends of a street that features two supermarkets — A and B. As customers, we would ideally want the supermarkets to be spread evenly through the street so that both of us have reasonably convenient access to groceries from our respective ends.

This is indeed how the scenario starts. Supermarket A is placed at one-fourth the length of the street, and supermarket B is placed at three-fourths the length of the street. Neither of us has to travel a longer distance to access our respective supermarkets.

Rational customers from the first half of the street go to supermarket A (marked by the blue highlight on the street) and rational customers from the second half of the street go to supermarket B (marked by the green highlight on the street). So far, so good.

However, this situation changes when supermarket B figures out that it can move closer towards the centre of the street and capture more customers as compared to before. This increased customer base for supermarket B means that supermarket A is losing customers.

Consequently, supermarket A decides to move closer towards the centre of the street as well. This position jostling goes on until both supermarkets are placed right next to each other.

If either of them moves either way any further, the supermarket would risk losing customers. This situation represents a Nash equilibrium if game theory were to be applied to this situation. At this point, each of them gets one-half of the entire customer base on the street.

What is interesting to note here is that although this situation leads to an equilibrium between the two supermarkets, you and I as customers both have to travel longer distances compared to before. So, it is not the social optimum.

Now that we’ve seen a simplified illustration of Hotelling’s law, let us move on to its extensions and applications.

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Extensions and Advanced Applications of Hotelling’s Law

The illustration that we just covered was a one-dimensional case with just two players. Hotelling tried to consider more parameters in his complex economic model. Over the years, the model has been extended to higher dimensions and a higher number of players.

When such levels of abstractions are combined with ever increasing computational power, Hotelling’s law becomes easily applicable to more complex market dynamics that need not be restricted to physical distances. Multiple characteristics such as product size, colour, taste, texture, etc., could be taken into account.

As one of the more novel applications of this concept, models have been developed to predict the behaviour of political candidates — especially when there are just two dominant competing parties. In this political dynamic, in order to gather more votes, candidates from both parties would get as close as possible to the competing party’s stance whilst preserving their own identities.

This scenario could explain why sometimes there is a common complaint stating that both candidates are “practically the same” with respect to what they promise to do if they win.

Final Thoughts

While Hotelling’s law is derived from the observation of a lack of product differentiation, manufacturers use such analyses to design optimal product differentiation.

For instance, referring to the street metaphor once again, one of the supermarkets might choose to specialize in a niche market that is localized to one specific sector of the street.

Thereby, that supermarket would begin dominating that particular space without affecting the sales figures of the other supermarket.

Whenever there is variability in market prices, companies tend to modify their prices to compete for customers. In such cases, product and pricing differentiation is in the best interest of each company.

If there is one lesson that businesses take away from the applications of Hotelling’s law, it is the following:

“Competition is for losers. If you want to create and capture lasting value, look to build a monopoly!”

– Peter Thiel.

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Interesting comment from reader Allan Milne Lees post publishing:

“In the USA it’s also the case that cities have legal zones for certain types of business. Thus auto dealerships are clustered together because that’s the only zone they are permitted to operate in. Likewise, in many cities, hotels are similarly clustered.

Shopping malls are artificial clusters, though in general an attempt is made to house at most two of any particular sort of outlet, in order to maintain sufficient diversity to attract adequate footfall.

As for franchise restaurants, McDonalds spends huge sums modeling foot and auto traffic to determine the optimal location for its McSlop outlets; Wendy’s merely tries to locate itself as close as possible to a McDonalds and thus free-ride on their expensive research, which is another form of pareto optimization on the cheap.”

— Allan Milne Lees

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Reference: Harold Hotelling (scientific article).

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Further reading that might interest you: Do Startups Really Need Venture Capital? and Why Earning More Leads To Lesser Satisfaction?