The Theory of Interstellar Trade

This blog post is not about the movie Interstellar, which I haven’t watched yet, but about a rather wonkish paper (as its author would put it) that I stumbled upon very recently.

The American economist and Nobel laureate Paul Krugman wrote in 1978 the paper “The Theory of Interstellar Trade” [PDF, 516KB]. The paper is simply hilarious. One of the best pieces I have ever read. It has just 15 pages and in them the author sets out to search how interest charges should be computed in interstellar trade when goods travel at close to the speed of light. It mixes economy with very light special relativity and great doses of humour. The author himself remarked in the introduction:

It should be noted that, while the subject of this paper is silly, the analysis actually does make sense. This paper, then, is a serious analysis of a ridiculous subject, which is of course the opposite of what is usual in economics.

Well, given today’s ventures, it might not be so silly 😉

Let’s review some of the highlights and conclusions derived from the paper:

To start with, he sets some fundamental considerations:

There are two major features distinguishing interstellar trade from the interplanetary trade we are accustomed to. The first is that the time spent in transit will be very great, since travel must occur at less than the light speed; round trips of several hundred years appear likely. The second is that, if interstellar trade is to be at all practical, the spaceships which conduct it must move at speeds which are reasonable fractions of the speed of light.

Because interstellar trade will take so long, any decision to launch a cargo will necessarily be a very long-term investment project […]

The second feature of interstellar transactions cannot be so easily dealt with (physicists are not as tolerant as economists of the practice of assuming difficulties away). If trading space vessels move at high velocities, we can no longer have an unambiguous measure of the time taken in the transit. The time taken by the spacecraft to make a round trip will appear less to an observer on the craft than to one remaining on Earth. […]

To solve the problem he refers to the Minkowski space-time, and includes the following diagram with the note below:

"Readers who find the Figure II puzzling should recall that a diagram of an imaginary axis must, of course, itself be imaginary".

“Readers who find the Figure II puzzling should recall that a diagram of an imaginary axis must, of course, itself be imaginary”.

By comparing the returns from actual trade between planets with the return of bonds he arrives at the First Fundamental Theorem of Interstellar Trade:

When trade takes place between two planets in a common inertial frame, the interest costs on goods in transit should be calculated using time measured by clocks in the common frame, and not by clocks in the frames of trading spacecraft.

After proving the theorem take a look at this other passage:

theorem

 

The author then takes on investigating possible arbitrage in interstellar transactions, and arrives to the Second Fundamental Theorem of Interstellar Trade:

If sentient beings may hold assets on two planets in the same inertial frame, competition will equalize the interest rates on the two planets.

It goes without saying that I recommend the reading of this paper.

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