The economics of interstellar travel

Dec 19 JDN 2459568

Since these are rather dark times—the Omicron strain means that COVID is still very much with us, after nearly two years—I thought we could all use something a bit more light-hearted and optimistic.

In 1978 Paul Krugman wrote a paper entitled “The Theory of Interstellar Trade”, which has what is surely one of the greatest abstracts of all time:

This paper extends interplanetary trade theory to an interstellar setting. It is chiefly concerned with the following question: how should interest charges on goods in transit be computed when the goods travel at close to the speed of light? This is a problem because the time taken in transit will appear less to an observer travelling with the goods than to a stationary observer. A solution is derived from economic theory, and two useless but true theorems are proved.

The rest of the paper is equally delightful, and well worth a read. Of particular note are these two sentences, which should give you a feel: “The rest of the paper is, will be, or has been, depending on the reader’s inertial frame, divided into three sections.” and “This extension is left as an exercise for interested readers because the author does not understand general relativity, and therefore cannot do it himself.”

As someone with training in both economics and relativistic physics, I can tell you that Krugman’s analysis is entirely valid, given its assumptions. (Really, this is unsurprising: He’s a Nobel Laureate. One could imagine he got his physics wrong, but he didn’t—and of course he didn’t get his economics wrong.) But, like much high-falutin economic theory, it relies upon assumptions that are unlikely to be true.

Set aside the assumptions of perfect competition and unlimited arbitrage that yield Krugman’s key result of equalized interest rates. These are indeed implausible, but they’re also so standard in economics as to be pedestrian.

No, what really concerns me is this: Why bother with interstellar trade at all?

Don’t get me wrong: I’m all in favor of interstellar travel and interstellar colonization. I want humanity to expand and explore the galaxy (or rather, I want that to be done by whatever humanity becomes, likely some kind of cybernetically and biogenetically enhanced transhumans in endless varieties we can scarcely imagine). But once we’ve gone through all the effort to spread ourselves to distant stars, it’s not clear to me that we’d ever have much reason to trade across interstellar distances.

If we ever manage to invent efficient, reliable, affordable faster-than-light (FTL) travel ala Star Trek, sure. In that case, there’s no fundamental difference between interstellar trade and any other kind of trade. But that’s not what Krugman’s paper is about, as its key theorems are actually about interest rates and prices in different inertial reference frames, which is only relevant if you’re limited to relativistic—that is, slower-than-light—velocities.

Moreover, as far as we can tell, that’s impossible. Yes, there are still some vague slivers of hope left with the Alcubierre Drive, wormholes, etc.; but by far the most likely scenario is that FTL travel is simply impossible and always will be.

FTL communication is much more plausible, as it merely requires the exploitation of nonlocal quantum entanglement outside quantum equilibrium; if the Bohm Interpretation is correct (as I strongly believe it is), then this is a technological problem rather than a theoretical one. At best this might one day lead to some form of nonlocal teleportation—but definitely not FTL starships. Since our souls are made of software, sending information can, in principle, send a person; but we almost surely won’t be sending mass faster than light.

So let’s assume, as Krugman did, that we will be limited to travel close to, but less than, the speed of light. (I recently picked up a term for this from Ursula K. Le Guin: “NAFAL”, “nearly-as-fast-as-light”.)

This means that any transfer of material from one star system to another will take, at minimum, years. It could even be decades or centuries, depending on how close to the speed of light we are able to get.

Assuming we have abundant antimatter or some similarly extremely energy-dense propulsion, it would reasonable to expect that we could build interstellar spacecraft that would be capable of accelerating at approximately Earth gravity (i.e. 1 g) for several years at a time. This would be quite comfortable for the crew of the ship—it would just feel like standing on Earth. And it turns out that this is sufficient to attain velocities quite close to the speed of light over the distances to nearby stars.

I will spare you the complicated derivation, but there are well-known equations which allow us to convert from proper acceleration (the acceleration felt on a spacecraft, i.e. 1 g in this case) to maximum velocity and total travel time, and they imply that a vessel which was constantly accelerating at 1 g (speeding up for the first half, then slowing down for the second half) could reach most nearby stars within about 50 to 100 years Earth time, or as little as 10 to 20 years ship time.

With higher levels of acceleration, you can shorten the trip; but that would require designing ships (or engineering crews?) in such a way as to sustain these high levels of acceleration for years at a time. Humans can sustain 3 g’s for hours, but not for years.

Even with only 1-g acceleration, the fuel costs for such a trip are staggering: Even with antimatter fuel you need dozens or hundreds of times as much mass in fuel as you have in payload—and with anything less than antimatter it’s basically just not possible. Yet there is nothing in the laws of physics saying you can’t do it, and I believe that someday we will.

Yet I sincerely doubt we would want to make such trips often. It’s one thing to send occasional waves of colonists, perhaps one each generation. It’s quite another to establish real two-way trade in goods.

Imagine placing an order for something—anything—and not receiving it for another 50 years. Even if, as I hope and believe, our descendants have attained far longer lifespans than we have, asymptotically approaching immortality, it seems unlikely that they’d be willing to wait decades for their shipments to arrive. In the same amount of time you could establish an entire industry in your own star system, built from the ground up, fully scaled to service entire planets.

In order to justify such a transit, you need to be carrying something truly impossible to produce locally. And there just won’t be very many such things.

People, yes. Definitely in the first wave of colonization, but likely in later waves as well, people will want to move themselves and their families across star systems, and will be willing to wait (especially since the time they experience on the ship won’t be nearly as daunting).

And there will be knowledge and experiences that are unique to particular star systems—but we’ll be sending that by radio signal and it will only take as many years as there are light-years between us; or we may even manage to figure out FTL ansibles and send it even faster than that.

It’s difficult for me to imagine what sort of goods could ever be so precious, so irreplaceable, that it would actually make sense to trade them across an interstellar distance. All habitable planets are likely to be made of essentially the same elements, in approximately the same proportions; whatever you may want, it’s almost certainly going to be easier to get it locally than it would be to buy it from another star system.

This is also why I think alien invasion is unlikely: There’s nothing they would particularly want from us that they couldn’t get more easily. Their most likely reason for invading would be specifically to conquer and rule us.

Certainly if you want gold or neodymium or deuterium, it’ll be thousands of times easier to get it at home. But even if you want something hard to make, like antimatter, or something organic and unique, like oregano, building up the industry to manufacture a product or the agriculture to grow a living organism is almost certainly going to be faster and easier than buying it from another solar system.

This is why I believe that for the first generation of interstellar colonists, imports will be textbooks, blueprints, and schematics to help build, and films, games, and songs to stay entertained and tied to home; exports will consist of of scientific data about the new planet as well as artistic depictions of life on an alien world. For later generations, it won’t be so lopsided: The colonies will have new ideas in science and engineering as well as new art forms to share. Billions of people on Earth and thousands or millions on each colony world will await each new transmission of knowledge and art with bated breath.

Long-distance trade historically was mainly conducted via precious metals such as gold; but if interstellar travel is feasible, gold is going to be dirt cheap. Any civilization capable of even sending a small intrepid crew of colonists to Epsilon Eridani is going to consider mining asteroids an utterly trivial task.

Will such transactions involve money? Will we sell these ideas, or simply give them away? Unlike my previous post where I focused on the local economy, here I find myself agreeing with Star Trek: Money isn’t going to make sense for interstellar travel. Unless we have very fast communication, the time lag between paying money out and then seeing it circulate back will be so long that the money returned to you will be basically worthless. And that’s assuming you figure out a way to make transactions clear that doesn’t require real-time authentication—because you won’t have it.

Consider Epsilon Eridani, a plausible choice for one of the first star systems we will colonize. That’s 10.5 light-years away, so a round-trip signal will take 21 years. If inflation is a steady 2%, that means that $100 today will need to come back as $151 to have the same value by the time you hear back from your transaction. If you had the option to invest in a 5% bond instead, you’d have $279 by then. And this is a nearby star.

It would be much easier to simply trade data for data, maybe just gigabyte for gigabyte or maybe by some more sophisticated notion of relative prices. You don’t need to worry about what your dollar will be worth 20 years from now; you know how much effort went into designing that blueprint for an antimatter processor and you know how much you’ll appreciate seeing that VR documentary on the rings of Aegir. You may even have in mind how much it cost you to pay people to design prototypes and how much you can sell the documentary for; but those monetary transactions will be conducted within your own star system, independently of whatever monetary system prevails on other stars.

Indeed, it’s likely that we wouldn’t even bother trying to negotiate how much to send—because that itself would have such overhead and face the same time-lags—and would instead simply make a habit of sending everything we possibly can. Such interchanges could be managed by governments at each end, supported by public endowments. “This year’s content from Epsilon Eridani, brought to you by the Smithsonian Institution.”

We probably won’t ever have—or need, or want—huge freighter ships carrying containers of goods from star to star. But with any luck, we will one day have art and ideas from across the galaxy shared by all of the endless variety of beings humanity has become.

Are unions collusion?

Oct 31 JDN 2459519

The standard argument from center-right economists against labor unions is that they are a form of collusion: Producers are coordinating and intentionally holding back from what would be in their individual self-interest in order to gain a collective advantage. And this is basically true: In the broadest sense of the term, labor unions are are form of collusion. Since collusion is generally regarded as bad, therefore (this argument goes), unions are bad.

What this argument misses out on is why collusion is generally regarded as bad. The typical case for collusion is between large corporations, each of which already controls a large share of the market—collusion then allows them to act as if they control an even larger share, potentially even acting as a monopoly.

Labor unions are not like this. Literally no individual laborer controls a large segment of the market. (Some very specialized laborers, like professional athletes, or, say, economists, might control a not completely trivial segment of their particular job market—but we’re still talking something like 1% at most. Even Tiger Woods or Paul Krugman is not literally irreplaceable.) Moreover, even the largest unions can rarely achieve anything like a monopoly over a particular labor market.

Thus whereas typical collusion involves going from a large market share to an even larger—often even dominant—market share, labor unions involve going from a tiny market share to a moderate—and usually not dominant—market share.

But that, by itself, wouldn’t be enough to justify unions. While small family businesses banding together in collusion is surely less harmful than large corporations doing the same, it would probably still be a bad thing, insofar as it would raise prices and reduce the quantity or quality of products sold. It would just be less bad.

Yet unions differ from even this milder collusion in another important respect: They do not exist to increase bargaining power versus consumers. They exist to increase bargaining power versus corporations.

And corporations, it turns out, already have a great deal of bargaining power. While a labor union acts as something like a monopoly (or at least oligopoly), corporations act like the opposite: oligopsony or even monopsony.

While monopoly or monopsony on its own is highly unfair and inefficient, the combination of the two—bilateral monopolyis actually relatively fair and efficient. Bilateral monopoly is probably not as good as a truly competitive market, but it is definitely better than either a monopoly or monopsony alone. Whereas a monopoly has too much bargaining power for the seller (resulting in prices that are too high), and a monopsony has too much bargaining power for the buyer (resulting in prices that are too low), a bilateral monopoly has relatively balanced bargaining power, and thus gets an outcome that’s not too much different from fair competition in a free market.

Thus, unions really exist as a correction mechanism for the excessive bargaining power of corporations. Most unions are between workers in large industries who work for a relatively small number of employers, such as miners, truckers, and factory workers. (Teachers are also an interesting example, because they work for the government, which effectively has a monopsony on public education services.) In isolation they may seem inefficient; but in context they really exist to compensate for other, worse inefficiencies.


We could imagine a world where this was not so: Say there is a market with many independent buyers who are unwilling or unable to reliably collude, and they are served by a small number of powerful unions that use their bargaining power to raise prices and reduce output.


We have some markets that already look a bit like that: Consider the licensing systems for doctors and lawyers. These are basically guilds, which are collusive in the same way as labor unions.

Note that unlike, say, miners, truckers, or factory workers, doctors and lawyers are not a large segment of the population; they are bargaining against consumers just as much as corporations; and they are extremely well-paid and very likely undersupplied. (Doctors are definitely undersupplied; with lawyers it’s a bit more complicated, but given how often corporations get away with terrible things and don’t get sued for it, I think it’s fair to say that in the current system, lawyers are undersupplied.) So I think it is fair to be concerned that the guild systems for doctors and lawyers are too powerful. We want some system for certifying the quality of doctors and lawyers, but the existing standards are so demanding that they result in a shortage of much-needed labor.

One way to tell that unions aren’t inefficient is to look at how unionization relates to unemployment. If unions were acting as a harmful monopoly on labor, unemployment should be higher in places with greater unionization rates. The empirical data suggests that if there is any such effect, it’s a small one. There are far more important determinants of unemployment than unionization. (Wages, on the other hand, show a strong positive link with unionization.) Much like the standard prediction that raising minimum wage would reduce employment, the prediction that unions raise unemployment has largely not been borne out by the data. And for much the same reason: We had ignored the bargaining power of employers, which minimum wage and unions both reduce.

Thus, the justifiability of unions isn’t something that we could infer a priori without looking at the actual structure of the labor market. Unions aren’t always or inherently good—but they are usually good in the system as it stands. (Actually there’s one particular class of unions that do not seem to be good, and that’s police unions: But this is a topic for another time.)

My ultimate conclusion? Yes, unions are a form of collusion. But to infer from that they must be bad is to commit a Noncentral Fallacy. Unions are the good kind of collusion.