When you look at a map of national borders, straight lines measure some sort of indifference, either that of two countries signing a treaty that divided up land neither of them cared that much about in the first place or because colonial administrations found it convenient. And if you see squiggles, you're generally looking at some national border that makes it inconvenient to kill people on the other side. These natural borders also make it harder to share a language with, do business with, or marry someone on the other side, but borders are much older than the concept of getting everyone to speak the same language. For example, The Discovery of France notes that modern French was a minority language until quite recently, and that the first time more than half the population spoke it was around 1900, a few decades after France established universal public schooling and insisted that it be taught in French.

A purchase is a bit more civilized, at least in comparison. And it used to be reasonably common: Denmark sold some of its colonies in what is now Ghana to the UK, and sold America the place now known as the U.S. Virgin Islands. The US was actually a pretty active buyer, having purchased about 58% of total American land area, though that includes the Treaty of Guadalupe Hidalgo, in which the US made a payment for territory as part of a peace treaty. So, this was technically a territorial purchase, but was driven by something other than the US determining that the present value of future tax revenue under American rule would justify the upfront cost. But that turns out to be a common feature of these purchases: if the seller hasn't lost a war with the buyer, they're likely worried about losing one with someone else, as when Napoleon decided that Louisiana was not an especially valuable colony if the world's largest navy was between it and the homeland. There are even some purchases that were the aftermath of wars; the Netherlands annexed a few villages from Germany after the Second World War, but sold them back (though they kept one hill). In other cases, historical contingencies helped: Bavaria became part of the German Empire in a negotiated settlement that preserved some of Bavaria's independence and involved substantial bribes to King Ludwig II, who was more interested in Wagner and architectural projects than in running a country.

The nation-building that led to coherent nation-states—with a common language, minimal internal trade barriers, internally-consistent laws, etc.—also made it much more expensive for territory to change hands. Most of the wealth in a country comes from the complementary outputs of different people across firms, the government, and other institutions, and this wealth tends to vanish in military conflicts. And if those people aren't excited about being under a new sovereign, they also won't produce as much (and if they are more excited about being ruled by one country than another, the popular country presumably doesn't have to pay; West Germany had a provision in its constitution that let other parts of Germany join automatically if they chose to.

So wars over territory tend to be more trouble than they're worth, economically speaking, and purchases of territory also tend to diminish the value of whatever they buy, so the market doesn't clear. In fact, it's been more common for older purchases to get unwound—the Panama and Suez canals, and Hong Kong all reverted to more local control.

But all of this assumes that the economic upside is driven by human capital. Greenland is just not the kind of location that's going to attract global immigration and nurture the agglomeration effects a services sector is built on. But they do have natural resources, and the US has both a bigger and more experienced extraction sector as well as capital markets that are unusually willing to finance expensive ventures like mines.¹ Even ignoring the strategic implications, the US buying Greenland would probably pay for itself from the taxes US companies will pay to dig up rare earths (less whatever deadweight loss you want to assume as a result of the US subsidizing American rare earths extraction rather than imports).

But that raises the question: what's the point? McDonald's was able to open a location in Paris even though America hadn't annexed France, and American mining companies are multinational by default; US-listed mining companies get the overwhelming majority of their revenue from mines outside the US. There might be some tiny reduction in frictional costs from having a consistent legal system, but there won't be much from language, since schools in Greenland already teach English.

There's going to be deadweight loss of one kind or another in the market of trading cash for territory. In one sense, applying one country's laws to another country's people can yield obvious upside, but there isn't a good mechanism to turn Singapore into a franchise operation or to otherwise shuffle territory around. The productive places are hard to dislodge from their home country, and for the unproductive ones, any payment that plausibly compensates for the forgone upside is embarrassing to accept.

A country can try to form closer ties with another country. The two can facilitate trade, and cross-border investments. This is a normal way for countries to relate to one another. It's not as seamless as being in the same nation-state. On the other hand, if there's some manufacturing or resource extraction facility that can be built anywhere in the world, there's a long list of countries ahead of California in the list of jurisdictions where it's easiest to build. Annexing more territory is an investment with a very uncertain payoff. And most countries, faced with similar uncertainty, have prudently decided that their current borders are roughly what they're stuck with.

The Diff mostly focuses on technology and business, not geopolitics, but sometimes these intersect.

• We’ve examined how big tech companies and governments have converging incentives.

• We looked at how commodity price moves in response to an anticipated war made that war more likely ($).

• In a worst-case scenario, there’s one not-quite-obvious trade to make.

• We reviewed Tony Judt’s Postwar, which talks early on about how modern borders were made.

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1  Though the US has not yet annexed Vancouver, where the real experts on financing bold new mining ventures reside.