Interplanetary Economics! A response to Paul Krugman…

The exciting prospect of interplanetary economics is considered in Paul Krugman’s 1978 “The Theory of Interstellar Trade”, a paper in which he explores how interest rates should be calculated on goods in transit that travel at close-to-light speeds. At such high velocities, time varies between different inertial reference frames: the time taken by a spacecraft to make a round trip will appear less to someone travelling with the good as opposed to a stationary observer remaining on Earth.

However, Krugman does not account for how the wages of a worker travelling with the goods are calculated, nor does he consider their resulting effects. Due to the fact that time is relative, there must exist an agreed upon place to measure it against, making for a very interesting thought experiment. Hence, using Krugman’s economic model of the universe, let us ponder solutions to this problem.

To preface, first of all, fundamental considerations include that interplanetary trade will involve journey times in the realms of hundreds of year by cause of long travel distances. Consequently, decisions to launch a cargo will necessarily be a very long-term investment project and, as Krugman points out, will hardly be conceivable lest there are very extensive futures markets. Hence, we will assume that investors are able to make perfect forecasts of prices over indefinite periods.

Secondly, we will assume that the trading planets in consideration lie in the same inertial reference frame and that the spacecraft travel at uniform velocity. This simplification permits us to limit our analysis within the realms of special relativity. We can ignore things like gravitational time dilation as it would be negligible, at least within our galaxy. In this case, the planets Earth and Trantor — Krugman’s chosen destination — are assumed to lie in the same inertial reference frame.

For practicality, spaceships will have to be travelling at very high velocities. This is where time dilation becomes involved. If a trip from Earth to Trantor takes years to observers in the Earth-Trantor reference frame, it will appear to take n’ years to someone on board the spacecraft, following the Lorentz transformation where

n’ = n {1/(sqrt[1-(v^2/c^2)])} where is the velocity of the spacecraft and is the speed of light.

This means that the faster the spacecraft travels, the more the time will have elapsed back on Earth and the greater the divergence between the two values. Thus arises the problem of wages. Is an employer to pay a worker on board the spacecraft (perhaps in cryosleep) wages with respect to n, the time that they subjectively experience, or n’, the time that has passed back on Earth?

At first glance, it seems to make some sort of intuitive sense to award wages according to how long the worker subjectivity experienced, but if we consider the concept of opportunity cost associated with dilating your reference frame, it quickly becomes clear that the latter is the better option. If we suppose that n’ years have passed on Earth, during that period of time, the worker could have otherwise accumulated wealth by spending his/her time buying bonds (or other financial products) or working a job that would result in higher pay. Additionally, the market must consider the worker’s other expenses, such as the storage of their possessions during the trip.

Secondly, there is a non-monetary cost involved as well. The worker could have otherwise spent time with his/her family during the hundreds of years that are likely to have passed on Earth. Their wages must therefore recompense a rational worker to the point where they are fully incentivised to undertake the job.

On the other hand, I should also note that in the long run, the second consideration is likely to trend to zero: like many in the oil rigging industry, workers who are prepared for the job and do not have attachments will undercut the market at a lower wage, whilst people that value the outlined non-monetary variables will remain in the same inertial reference frame as their family and friends.

Therefore, wages for interstellar trade must be paid according to the reference frame where the most time has elapsed.

But here’s another interesting thought: do wages actually need to be based on time in the first place? A completely different solution would be to say that wages are not based on time at all, but rather that these interstellar trips have fixed payments for workers. In this case, the job would be assigned to the cheapest qualified individual. It then becomes a matter of who the lowest bidder is. For example, these could be people who:

  • Want to go to the destination planet anyway.
  • Do not care for their home planet/station.

Furthermore, I must highlight that the wages earned by a worker would raise issues if it is a fixed nominal value. After all, the real value of their earnings would decrease over time, and if the journeys take several hundreds of years, this is something that must be accounted for. The erosion of wealth and the decline of the real value of their earnings must be accounted for. Therefore, wages must accommodate to the rate of inflation and the rate of interest of current assets back on Earth (or any other ‘home’ planet).

It is fascinating, therefore, to consider the implication of this – if a worker’s wages are paid as a lump sum before the trip, it effectively becomes an investment, the end yield of which would depend on the asset management company’s performance and how they compete with the rate of inflation.iyVQG5Z

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