Back in 1978, when post-tax real interest rates were negative in many parts of the world, Paul Krugman wrote a paper about the impact of 'time dilation' in near-speed-of-light interstellar trade. But this would be equivalent to cryogenic freezing. The effect is the same. The 'elapsed time' for the agent is different from that of Society as a whole. People who love their families & who want to age at the same pace as them will prefer to avoid both. Those who have few friends or other affectionate ties may want to take advantage of the 'magic of compound interest' to make an investment now & 'speed up time' so they get a big reward after very little time has elapsed from their own perspective.
The net present value of a project differs for different people if they have different opportunity cost/cost of funds & if the 'turnaround time' is different for them.
I am stupid & lazy. It would take me 10 years to turn a one K investment into 2 K. But it is the best I can hope for and so I do it. You are smart and industrious. You could turn 1K into 2K, in just one year, doing exactly the same thing. But there's an alternative investment opportunity available to you, but not me, which nets you 3K. So you pass on the project.
What would happen in an economy where time-trave or cryogenic freezing were cheap & ubiquitous? The answer is that there would be downward pressure on the real interest rate. if it positive, because 'time preference' is eroded at the margin. The reverse happens if it is negative because people would borrow, invest & go to sleep or fly away. Suppose nobody has 'affectionate ties' & thus is prepared to get frozen or shot into space for a near light speed round trip. Then real interest rates would tend to zero. . If some people have 'affectionate ties' but others don't, then, overall, there will still be some 'time preference' & non-zero real interest rate & hence non-zero discounting.
Krugman's paper begins thus-
The total interest payable (or the discount rate applied to a self funded project) is compounded on the length of the project or its 'turnaround'. Thus, if I buy cotton in Surat & send it to Manchester where it is auctioned then, if the average transit time is 5 months, and it takes one month for the money amount to be remitted to Surat, then the applicable 'base' interest rate is half of the annual rate because the 'turnaround was' 6 months.
If the cotton is sent to Alpha Centauri & the voyage takes 50 years then, assuming, the transaction can be notified to Earth in 5 years (since Alpha Centauri is about 4.5 light years away & information (but not goods) can be transmitted at light speed), then the total turnaround time is 55 years.
Krugman was a mathematical economist- i.e. he didn't know how business is done. The fact is, Lombard Merchants in the 13th Century knew the right answer to the question he posed. It is simply a fact that the interest 'clock' stops ticking when the loan is repaid. Obviously, if you are using your own funds, then you stop 'discounting' when you get the lumpsum on sale. You don't have to worry about wiring it back to the loan originator because you are he.
Consider the first theorem of Krugman's
This would make no difference if interest rates go to zero. But they won't if there is preference diversity (e.g. some have affectionate ties which cause them to prefer 'natural' ageing). It may be that 'affectionate ties' is a function of 'synergy'. People who are more productive within a particular group, have stronger bonds & thus greater reluctance to 'fast forward'. If total factor productivity is rising more rapidly on one planet than another, interest rates are likely to be higher in the former. This means that the merchant who arrives in the higher productivity planet will settle- or at least invest- there.
Krugman's argument relies on the notion that opportunity cost (discount rate) depends on the interest rate on the home planet. Such is not the case. Assuming information can be transmitted at the speed of light, there will be some long enough maturity bond on a different planet which would represent the opportunity cost.
Obviously, if interest rates everywhere go to zero (which makes sense if 'time-preference' is literally preferring at which future time you want to spend any particular period of your life) then Krugman's theorem is harmless. Otherwise, it is simply wrong. Voyage time plus information transmission time has always been crucial to robust trading networks. The real interest rate (on riskless assets) may be zero or positive or negative. But logistic & arbitrage networks are relatively independent of it.
This is Krugman's
Only if they are both zero for endogenous reasons. Otherwise, we could see both transport of goods from low growth (stagnant productivity) planets & capital flight from them. They may have negative real interest rates & depopulation while the high growth (rising productivity) planet has positive real interest rates & demographic growth. The reverse is also possible. A backward planet may get some money from aliens to invest in sweated labour or extractive projects. Its elite maintain higher real interest rates so as to permit capital inflow.
Krugman says interest rates will equalize even though simulaneous arbitrage is impossible because
Interest costs depend on voyage length. Only if voyage length is zero could they be neglected. But, that means, either we live in an Occassionalist Universe where God is the only efficient cause, or every point in Space-Time is immediately contiguous to every other. We are in a one period economy of a kshanikavada Buddhist type.
Krugman ends his jeu d'esprit by invoking the Star Trek slogan 'may the Force be with you'. That force was stupidity. It is with him still.
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