The theory of interstellar trade

by on March 11, 2008 at 5:50 pm in Economics | Permalink

By Paul Krugman, circa 1978.  He considers the arbitrage conditions for interstellar trade, given that not all traders will inhabit the same frame of temporal reference.  There is much humor in this piece. 

My own puzzling focuses on the determinants of real interest rates, given how time dilation changes the meaning of time preference.  As you approach the speed of light you move into the future relative to more stationary observers.  So can you not leave a penny in a savings account, take a very rapid spaceflight, and come back to earth "many years later" as a billionaire?  Hardly any time has passed for you.  In essence we are abolishing time preference, or at least allowing people to lower their time preference by spending money on fuel.  I believe that in such worlds the real interest rate cannot exceed the costs at which more fuel can "propel you into the future through time dilation."   

Whether the individual arbitrage conditions translate into economy-wide arbitrage conditions is a difficult puzzle.  What if everyone gets into a fast spaceship?  Do the savings accounts still bear positive interest?  How does the price of robots enter into this equation?

Is monetary policy neutral in such a world, with time travelers arbitraging against any attempt by the Fed to shift real interest rates?  Does the Fed have to subsidize the price of fuel to stimulate the economy?  Does everyone just end up in the future?

Mark March 11, 2008 at 6:37 pm

What happens to human capital during faster-than-light travel. Investing in specific skills training before travel would seem pointless. People would have to be trained in how to learn skills once reaching destination. How markets would value labour in an environment like this would be very interesting.

RobbL March 11, 2008 at 6:53 pm

Don’t you get roughly the same effect by freezing yourself or putting yourself into some form of suspended animation?

Bob Murphy March 11, 2008 at 7:05 pm

Whether the individual arbitrage conditions translate into economy-wide arbitrage conditions is a difficult puzzle. What if everyone gets into a fast spaceship? Do the savings accounts still bear positive interest?

I’m assuming that Cowen is thinking about this in a standard Fisherian way, where the subjective time preference schedules interact with objective real returns on capital to establish the market-clearing interest rate.

In that framework, yes, I think the possibility of everybody “skipping” 50 years would indeed allow them all to grow that much wealthier. As RobbL noted above, it’s basically a way for people to reduce the discomfort of waiting. Assuming we could keep some robots (or a few stragglers who get paid for being isolated their whole lives) to build up the capital stock etc., everybody could indeed be fantastically rich if they took a nap for a century. And so there would be nothing inconsistent with them all accumulating a fantastic bank balance, in terms of its purchasing power.

dWj March 11, 2008 at 7:21 pm

As long as it costs more than zero to travel, that will place limits on the ability to try to outrun everyone else. Even as travel costs drop, for reasons pointed out, productivity of capital would start to drop if large numbers of people started doing this, and so would demand for borrowing for consumption, so that interest rates should drop, but an equilibrium should exist before they necessarily get to zero.

Bernard Yomtov March 11, 2008 at 8:10 pm

There are also some practical considerations if you try to go a lot of years into the future. (What an odd sentence.) You will have to establish your identity when you return. Maybe the DNA bank will have been hit by an earthquake. The bank where you made your deposit might not exist. Indeed, the country where you made it might not exist, at least not in the same form as when you left.

What would have been the safest investment available, without hindsight, five hundred years ago? Suppose you could go back and make it. What would it be worth to you today?

Sam March 11, 2008 at 8:36 pm

What would be the point of coming back in a 1000 years and having everyone you’ve ever known be dead? Everyone except Robin Hanson perhaps…

Adam Hyland March 11, 2008 at 9:00 pm

http://www.amazon.com/gp/reader/0471135615/ref=sib_dp_pt#

Check Page 243: “The Economics of Interstellar Commerce”. While it certainly doesn’t predate Krugman, the notion has been explored before, at least superficially.

Adam Hyland March 11, 2008 at 9:17 pm

On a note, I recall reading that section of the book. It comes at the end of “island in the Sky”, a remarkably sober book about colonizing space (sober in light of crazier scifi/colonization books). For some reason I read it first and the pessimism of the article stuck with me, setting the tone for the whole book. That’s not bad–our views about space travel and the future need pessimism, but I felt that it was the overriding theme.

In the end, there is no free lunch. While you could predict that interstellar travel would change time preference for some, there are a few caveats to make here:

1. Perhaps travel is so expensive that the change in time preference for some doesn’t impact the market as a whole. If you have a vanishingly small group of people pushing the discount rate down, does it affect the prevailing rate? You could argue that the income effect of the billionaires of the world might be analogous. While Bill Gates may have the latitude to spend more money on small purchases than they might be worth to him systematically, that does not do much to change the price I pay for those same products.

2. Travellers will face a STEEP opportunity cost. There isn’t any other way to describe it. They may (as the article in “islands in the sky” suggests) spend their wealth ENTIRELY on acclimating themselves to a radically different world or insulating themselves from that new world.

3. In the longer term, risk dominates. Inflation risk and default risk historically rise to 1.0 as time marches on. There are vanishingly view equity or debt instruments that are still valid from 200 years ago. they exist, most notably in the low countries and england, but they are few and far between. What happens in the event of hyperinflation, panics or fraud (although the last one could be accounted for given a persistent third party overseer)?

4. Adverse selection. This is a corrolary of the risk argument. What bank would be likely to write a contract to make an astronomical payment in the far future? A bank that is likely to be solvent that whole time (assuming the bank knows with certainty) might, but would be FAR less likely to do so than a bank who might default on the contract.

5. Explicit cost. While this might eventually become a non-issue, we have to be real about what is at stake. A long term space voyage is basically one way in the eyes of the company chartering the craft. Unlike a 767 from NY to London, when the space ship returns, it will be obsolete, or at least at the end of its viable life. Each trip presents a large fixed cost for the charter company. This may not translate directly as a large enough cost to a consumer if the flight manifest is big enough, but it isn’t trivial.

Just some thoughts.

Bob Murphy March 11, 2008 at 9:42 pm

I think several people have raised good objections to the original scenario. But what if we didn’t view it as people doing their enhanced waiting in one fell swoop? E.g. suppose there is a colony on Mars, and the flight crew who make the back-and-forth only age a three days for every work week. They don’t view humanity as slipping away from them, because they still get weekends off and live normally during them.

From their point of view, their ship is incredibly fast, and weeks consist of Sunday, Monday, Wednesday, Friday, and Saturday. Yet their monthly dividend payments are the same as before.

Bernard Yomtov March 11, 2008 at 10:07 pm

recep,

What has been the growth in the real value of gold since, say, 1508, and how much fluctuation has there been? Is it really the best alternative?

DK March 11, 2008 at 11:10 pm

the real problem is that if all the savers are off in space, the remaining earthbound voters will be sure to vote for inflationary monetary policy and confiscatory taxation. problem solved. and if you think you can fight it, you’d have to start paying lawyers and lobbyists with present dollars, before you’ve become superwealthy.

mm March 11, 2008 at 11:41 pm

In “The Forever War” I think the soldiers returning from combat were confronted with such high taxes and over-crowded world that the real interest gains were not especially significant. In addition upon returning the 2nd time everyone on Earth was gay and homogenous, and the 3rd time there was just one person’s genetic type replicated billions of times over.

In “Star Trek The Next Generation” a 20th century businessman with a previously uncurable disease is found, unfrozen, and cured. He thinks he should be magnificantly rich, but money doesen’t exist in the future like it did in the past since everyone’s needs are easily met.

So after taxes, chances of a new super flu which the future world is immune to but you are not, government revolutions (future world = socialist), human extinction scenarios, and changes in society which make life unendurable, the EV of such a trip could easily be negative.

Recep Peker March 12, 2008 at 12:09 am

Bernard,

I actually don’t know, but here is where I was coming from:
If you went to the mint today and bought a gold coin and just normal coins/notes of the same value (fresh out of the mint), I expect the gold coin to be the better investment over 500 years.

jb March 12, 2008 at 12:29 am

The best investment would be to start a religion. If you can prove you’re the religion’s founder, upon your return you get more or less everything owned by the believers.

Adam Hyland March 12, 2008 at 2:41 am

Recep,

Thanks. I don’t mean to impugn you by making general comments about gold, investment and intrinsic value. I do agree that without the prospect of at least minimal management, a physical commodity is probably a better choice than a corporate investment.

I vote for Hafnium. :)

Adam

8 March 12, 2008 at 7:17 am

A more likely scenario is that a con-artist would convince people of the wealth they could earn by traveling light years into space. Or a government deals with overpopulation by sending citizens on a journey with promises of wealth.

If I killed everyone you know, how much would I have to pay you? I think the interest rate of a normal “time traveler” would be much higher than the rate we see today. Maybe the only willing travelers, who would accept a low rate, would be extreme narcissists or very naive people who fail to calculate the risks.

Bernard Yomtov March 12, 2008 at 9:15 am

Recep,

I asked two questions. Let’s say gold was safe. What return would you realize? (Though I don’t know why gold would be safe. Maybe it would be found and stolen. Maybe the place you hid it would become inaccessible for some reason. Or maybe someone will build a huge structure like a stadium right on top of your hiding place, so retrieval costs are enormous.)

bob March 12, 2008 at 10:05 am

Heh heh! “. . . this is a serious analysis of a ridiculous subject, which is of course the opposite of what is usual in economics.”

brian March 12, 2008 at 1:11 pm

Krugman’s paper has some gems. I’ve only read the first couple pages, but here are two so far:

From the abstract…. “A solution is dervied from economic theory, and two useless but true theorems are proved.”

“Interplanetary trade…raises no major theoretical problems, since it can be treated in the same framework as interregional and international trade. Among the authors who have not pointed this out are Ohlin (1933) and Samuelson (1947).”

Anyway, I saw the title and thought it was going to be a reference to trade in the world of Eve Online, a game where some people make their virtual living conducting interstellar arbitrage.

Person March 12, 2008 at 2:52 pm

If everyone skipped into the future, no one would be putting their capital to work in the meantime.

I think that’s under the assumption they could have fully automated production processes. An incredibly big assumption, when you consider all of the natural corrosion that will occur, not just on materials, but the expansion of biological life. Is the system robust vs. meteor strikes?

Then there’s the possibility of having a skeleton crew. But, as others have suggested in various ways, they could enact confiscatory redistribution on your gains in the meantime: you arrive, only to find out, “Hey, your gains are taxed at 100%, and we enacted a ‘help the folks that actually did the work’ program, that gives it all to them! Tough break. You can sue, but we’re the judges too.”

Person March 12, 2008 at 4:59 pm

Yancey_Ward: You forgot the hedonic adjustments. Drinking the beer would be like a taste of pure heaven, something people on earth before your voyage could only dream about ;-)

And then you’d leave and go to a lower-grade automated bar that gives the exact same beer for $1000 but without all the branding :-P

David Friedman March 12, 2008 at 10:46 pm

I think a number of complications raised here depend on people making productive use of capital while moving at a velocity near that of light. Krugman, if I understand him correctly, is assuming that all the production happens planetside–spaceships are merely transport.

There is, however, a much more serious problem with the piece, which suggests that Krugman is better at economics than at physics. For details, see my blog:

http://daviddfriedman.blogspot.com/

Patrick March 13, 2008 at 2:32 am

Tyler, interesting post. Would you be interested in syndicating your content on the home page of my site? It’s an online community of finance professionals ( http://www.wallstreetoasis.com ). I could add an RSS feed that will allow me to promote your blog posts to my home page (when i think it will lead to a good discussion and/or is appropriate), but I wanted to make sure you were comfortable syndicating first. The syndicated post would have a link back to your original post. Thanks, Patrick (you can reach me at wallstreetoasis@wallstreetoasis.com if you have any questions).

jean September 21, 2009 at 10:30 am

Time traveller arbitragers may appear but they would not be able to nullify the interest rate.
The cost of the trip grows exponentially with the time you save (at least if you use a rocket. It may be different if you use an interstellar motorway), so this would impose a positive lower limit to the preference for the present.

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