(Roughly) Daily

… so why is it that there’s so much emulation, so much sameness in the marketplace? Byrne Hobart explains Hotelling’s Law…

The economist Harold Hotelling has already inspired one Diff piece, on the optimal extraction rate for finite resources ($), but Hotelling has another rule that explains political non-polarization, fast-followers in tech, and the ubiquity of fried chicken sandwiches. Companies, parties, subcultures tend to converge over time, and a simple model can illustrate how.

Consider a stretch of beach 100 feet long, running east to west. Beachgoers are positioned randomly on the beach. There are two hot dog vendors who are both selling to beachgoers. Where should they position their hot dog stands?

One option is for one vendor to be a quarter of the way from one side, and the other to be a quarter of the way from the other side. This means that everyone is, at most, 25 feet away from a snack. That’s socially optimal. But let’s suppose the vendor on the eastern side moves a bit to the west. Everyone east of them will still patronize them, because they’re still closer, if not the closest. But some customers in the middle will switch! So the other hot dog seller responds by moving east, and the same result ensues. Eventually, you end up with two vendors in the middle of the beach, and now the median distance customers travel, 25 feet, is the former maximum distance anyone used to travel.

You can substitute any other cost or one-dimensional positioning feature for this. If there are two snack food manufacturers, the socially-optimal setup might be for one of them to sell something sweet and the other to offer something salty, but the same convergent force will eventually lead both of them to sell a salty-sweet combo; customers with specific preferences will be worse-off, but they’ll still have a favorite, while any convergence captures some of the customers who were close to indifferent before.

Making the model more reflective of the real world illustrates some of the assumptions it depends on. For example, we were always assuming exactly two competitors, but now let’s add in new entrants and departures. The model gets simpler if one of the initial two hot dog vendors quits—ironically, in this case the monopolist’s profit-maximizing position is also the social welfare-maximizing position (though they’ll probably respond to their new monopoly power with higher prices). In snack foods, if the formerly diverse market is now just a choice between salty-sweet and sweet-and-salty, a new entrant might introduce some product for the flavor purists and capture the market that way.

The model does describe cases where there are limits to new entrants. For example:

• In a voting system that tends to disproportionately reward winners, you’ll expect some convergence between parties. They want enough differentiation for voters to feel like they’re making a choice, but beyond that it makes sense for both sides to compete on similarity rather than difference.¹
• Businesses that are dependent on continuously delivering products with low value density will tend to have a few national brands and lots of regional ones, as with Coke and Pepsi. Both beverages are pretty similar, and retain just enough differentiation for customers to feel like they’re making a choice. The amount is small, but nonzero: in the 1980s, when Coke was losing to the sweeter Pepsi in blind taste tests, they introduced a new, sweeter formula, a decision they reversed after a consumer backlash.
• Software products with high switching costs tend to get more complex over time, as standalone products get subsumed as features of a larger suite. As long as the pace of increased complexity is controlled, this doesn’t hurt user experience too much. It does eventually lead to a sprawling mess, but by then a new kind of switching cost kicks in—the sunk cost of learning to use the system is so high that it feels wasteful to switch.
• This model also describes regulated industries that lack extraordinary returns on capital. It’s hard for a bank to become a monopoly because it takes so much capital to grow, and while even the largest banks have some regional skew to their branch networks, they tend to settle on a similar model. They also diversify in similar ways: issuing credit cards, getting into investment banking, having a capital markets business of some sort, etc…

Hotelling’s simplified model describes an iron law: under the right set of assumptions, sellers end up homogenizing their products, and niche interests end up under-served. In the real world, there are countervailing forces, and in practice the dimensions on which companies compete are messy enough that “adjacent” doesn’t really work. But Hotelling’s Law also illustrates why there’s relentless pressure for homogeneity: if some people like product A and some people prefer product B, something halfway between the two will capture part of that audience. And the producer of A or B is probably in a better position to make this new compromise product C…

One can observe that this dynamic often leads, beyond sameness, to steadily declining value/quality as well. So, one might wonder why, if all it takes is an innovative new entrant to stir up a market, that’s not going on all the time. The answer is, of course, complicated (and varies from sector to sector). But if there is a root cause, your correspondent would suggest, it’s the concentration of power and control in a market that yields oligopolies that can effectively preempt new competitors. (See, e.g., here, here, and here.)

The economics of every burger chain launching a chicken sandwich: “Hotelling’s Law,” from @ByrneHobart.

* Karl Albrecht

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As we noodle on normalization, we might spare a thought for a man who innovated, then (for a time) enjoyed the benefits of an oligopolist, Thomas Crapper; he died on this date in 1910.  Crapper popularized the one-piece pedestal flushing toilet that still bears his name in many parts of the English-speaking world.

The flushing toilet was invented by John Harrington in 1596; Joseph Bramah patented the first practical water closet in England in 1778; then in 1852, George Jennings received a patent for the flush-out toilet.  Crapper’s  contribution was promotional (though he did develop some important related inventions, such as the ballcock): in a time when bathroom fixtures were barely mentionable, Crapper, who was trained as a plumber, set himself up as a “sanitary engineer”; he heavily promoted “sanitary” plumbing and pioneered the concept of the bathroom fittings showroom.  His efforts were hugely successful; he scored a series of Royal Warrants (providing lavatories for Prince, then King Edward, and for George V) and enjoyed huge commercial success. To this day, manhole covers with Crapper’s company’s name on them in Westminster Abbey are among London’s minor tourist attractions.

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