In 1978 Dr Paul Krugman wrote a paper entitled *The Theory of Interstellar Trade*, supposedly to cheer himself up. Yet despite the self-described “silly” nature of the work, it contained serious analysis, and since being written has inspired several more works on the economic implications of interstellar travel.

The chief issue that economists have grappled with is that of time dilation. In short, Einstein’s theory of special relativity predicts that in an inertial frame of reference, an observer would notice that a clock moving relative to them would tick slower than one at rest in their own frame of reference. This means that if an astronaut stays on the ISS for six months, as a result of travelling relative to earth, they will age 0.005 seconds less than somebody on the ground.

Human spaceflight hasn’t yet developed to a point where time dilation will have significant effects. Yet for interstellar travel to be possible in the future, almost all proposals require travel at close to the speed of light. Once ships travel at more than 80% of the speed of light in the future, the time dilation becomes increasingly severe. In theory, with sufficient technology, a ship could reach the centre of the Milky Way, 30,000 light years away, while only 40 years would have passed for the crew. Yet for observers on earth, it would take at least 60,000 years for the ship to get there and back.

This creates some tricky issues for economist, of which one of the most significant has been suggested by Dr Tyler Cowen. He notes that if you left a small amount of money in a savings account, you could then take a spaceflight at a speed close to that of light and return a significant time later (earth time). For you, barely any time would appear to have passed, but many years on earth would have gone by. Therefore, the money in your savings account would have grown dramatically more than it would have if you’d stayed on earth for the same length of time experienced on the spaceflight.

This then renders the theory of time preference, which weighs up the trade-off in utility between present and future consumption, meaningless. In theory, interstellar travel could allow people to lower their time preference so much that it becomes essentially insignificant.

However, a solution has been formulated to this problem by Dr Krugman. He believes that in the future, interest rates will be forced to correspond to fuel costs. Imagine that you have a choice between staying on earth for ten years or spending ten years on a spaceship flying at close to the speed of light, which returns you back to earth one thousand years in the future. Using the formula for compound interest, you can derive the following two equations, using present value (PV) and the interest rate (i) to calculate future value (FV):

For time preference theory to stay consistent, the future value must be the same regardless of whether you take the spaceflight or not. Therefore, in the future the cost of fuel could determine interest rates. If fuel costs are high, then interest rates can be high, but if they are low, interest rates must also be low. This could have disturbing implications for the use of interest rates to fight recessions, limiting central banks’ monetary policy toolkit.

Interest rates are just one of many problems that will be affected by interstellar travel in the future. Economists have already noted that it will affect arbitrage, and that there will be debates over how interstellar workers should be paid; if one thousand years have passed on earth, should workers be paid for all of those, or only for the ten years that they experienced while travelling?

For now of course, these are just problems to amuse economists, but in the far future the implications of time dilation could be profound.

### See here for further reading:

*Krugman’s original paper: *http://www.princeton.edu/~pkrugman/interstellar.pdf

*Interstellar wages: *https://www.realclearscience.com/articles/2017/08/24/how_would_we_pay_interstellar_workers.html