### The Theory of Interstellar Trade

**The Theory of Interstellar Trade**^{[1]} is a paper written in 1978 by economist Paul Krugman. The paper was first published in March 2010 in the journal *Economic Inquiry*.^{[2]} He described the paper as something he wrote to cheer himself up when he was an "oppressed assistant professor," caught up in the academic rat race.
^{[3]}

Krugman analyzed the question of

how should interest rates 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 traveling with the goods than to a stationary observer.

Krugman emphasized that in spite of its farcical subject matter, the economic analysis in the paper is correctly done. In his own words,

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.

## Commentary

Responding to the paper, economist Tyler Cowen speculated on how time travel affects time preference discounting.^{[4]}

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."

Assume you have a spaceship that can approach lightspeed and thus you can make, say 1000 years, seem like 10 years. If you can gain the time value of money 100x faster, that effectively makes the interest rate 100x higher for you. Thus time preference is meaningless. This is a problem for economic theory. Krugman's solution is to force the interest rate to correspond to the cost of making the trip.

Here is the standard compound interest formula:

- FV = PV(1+i)
^{n}

Fuel costs for the above trip are $X. Let's say you have $1000 to invest and wonder whether it's worth taking a near-lightspeed voyage to increase your return 10 subjective years from now.

Stay on earth:

- A = $1000(1 + i)
^{10}

Take trip:

- B = ($1000(1 + i)
^{1000}) – $X

Krugman says that its necessarily true that A=B, for time preference theory to stay consistent; thus it will be driven by X. In the future, given a free market, spaceship fuel costs will be the primary determinant of interest rates. The less the fuel cost, the less the interest rate, and vice versa.

## Related theories and publications

In 2004, Espen Gaarder Haug published a theory he titled "SpaceTime-Finance" in *Wilmott Magazine* to show how a series of finance calculations had to be adjusted to avoid arbitrage when hypothetical traveling at very high velocities relative to other observers (traders). He illustrated how such necessary adjustments already could be measurable at the speed of the space shuttle, but also that such calculations and adjustments was of little or no practical relevance today since we all are moving at the nearly same speed relative to the enormous speed of light.

In 2008, John Hickman at Berry College, Georgia USA published in the *Journal of Astro Politics* an article related to the political and cultural obstacles that could be related to hypothetical interstellar trade.

## References

- [1]
- Espen Gaarder Haug. "SpaceTime Finance" in the book "Derivatives Models on Models" : John Wiley & Sons 2007
- John Hickman. "Problems of Interplanetary and Interstellar Trade."
*Astropolitics*. Vol.6, No. 1. (January 2008). pp. 95–104. - http://onlinelibrary.wiley.com/doi/10.1111/j.1465-7295.2009.00225.x/full