The Theory of Interstellar Trade - Commentary

Commentary

Responding to the paper, economist Tyler Cowen speculated on how time travel affects time preference discounting.

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.