Economics and the Final Frontier

"This paper, then, is a serious analysis of a ridiculous subject, which is of course the opposite of what is usual in economics" read the last lines of the introduction and immediately you know that you are in for a treat.  The above line is from Paul Krugman’s Theory of Interstellar trade. This paper, as he claims, was written when he was ‘an oppressed assistant professor caught up in the academic rat race’ to amuse himself.

Nonetheless, the paper is interesting and amusing at the same time, thanks to Dr Krugman’s intentional puns,star trek and star wars references throughout the paper. The paper explores an as yet non-existent type of commerce: interstellar trade. He quips that inter planetary trade at speeds much lower than the speed of light within the Solar System would be essentially the same as international trade or regional trade as there is no observable time dilation in transit. But, if interstellar trade between our planet and another planet outside our solar system is to be viable, the speed of the transporting vehicles must be very high, so high that is a reasonable fraction of the speed of light. Now, travelling at the speed of light comes with a few side effects, which can be explained and quantified using Einstein’s theories of special and general relativity. But, as he explains in his paper, he uses only special relativity as he does not understand general relativity. He starts out by assuming two planets, Earth and Trantor. And prices of goods: PE  ,PT   - price of Terran (Manufactured on the Earth), Trantorian goods on earth PE*, PT* - price of Earth-made goods, Trantorian goods on Trantor. And also for simplicity’s sake, he assumes both the planets are in the same inertial frame (frame in which there is no relative acceleration between two reference frames). Now, he postulates that since interstellar distances are ginormous, the trade will not be a short term commitment but a long term investment that will be well though through. Also, due to travel at near light speed, time will essential run slowly for those on board the space craft, leading to a difference in perceived duration between transit time as observed by those on board and those on the two planets. Since both the planets are assumed to be on the same inertial frame, time duration on the two planets is the same. The dilation in time is given by Einstein’s equation Where n is time and v is speed of the space craft and c is speed of light. Also, it is assumed the interest rates are assumed to be same on both planets to simplify things further. Now, assume an alien merchant on Trantor decides to buy Trantorian goods and sell it on earth to get and the transportation cost of theses goods is c. Then total cost = c + PT* QT* Assuming that on reaching earth, the Trantorian goods are sold to earn PT* QT* and this money is used to buy Earth-made goods then PE x QE = PT* QT*QE= PT* QT*/ PE. And then the ship returns to Trantor and the Earth-made goods are sold back yielding revenue =PE*x QE=PT* PE*QT*/ PE. Now, to see if this set of transactions is economically profitable, it is compared with its opportunity cost of capital, which is the worth of an investment made in bonds on Trantor at a cost of c + PT* QT* compounded over 2N years (N years each way). But this logic has a flaw, that is, if the merchant travelled on the space ship, he would have taken less than 2N years to go to and fro and would therefore have earned a higher economic profit i.e. Assuming cost of transportation of goods is negligible Economic profit = Revenue – Opportunity cost Opportunity cost of capital = Initial investment compounded at an interest rate of r over N years = (c + PT* QT*) (1+r)2N Economic profit in time frame of the Trantor= PT* PE*QT*/ PE - (c + PT* QT*) (1+r)2N (1) Economic profit in time frame of the Trantor = PT* PE*QT*/ PE - (c + PT* QT*) (1+r)2N’(2)   Since (c + PT* QT*)(1+r)2N > (c + PT* QT*)(1+r)2N’ Where 2N’ = 2N implies N’ < N(2) > (1) implying there are a few conditions when the trade is profitable in the frame of the space ship but not on the planet. So which one is to be accepted? Dr Krugman says that the opportunity cost of the trade, is buying a bond on Trantor, which is completely independent of time elapsed during interstellar travel and therefore, that must be the measure of opportunity cost. From this, he states the first fundamental theorem of interstellar trade which is: The interest cost of goods in transit between two planets in the same inertial frame is always calculated using time on clocks in the common frame (either of the two planets). Next, if in the long run the interstellar shipping industry becomes extremely competitive then, profits are driven to zero and cost of shipping is negligible, PT* PE*QT*/ PE - (c + PT* QT*) (1+r)2N =0PT* PE*QT*/ PE  = (c + PT* QT*) (1+r)2N Substituting c = 0PT* PE*QT*/ PE  = PT* QT*(1+r)2N Cancelling QT*and rearranging PE*/PT*= PE (1+r)2N/PT Which implies prices of goods will never be equalised and will be a permanent difference in prices. Now, using the above result, we can deduce that due to competition, investing in a bond on Trantor for a duration it takes to sell Trantorian goods on earth, buying Earth-made goods and selling them on Trantor and the trade itself should have the same return on investment and on applying the formula we get observe that it happens only when the interest rates on both the planets are the same. Now that is an interesting result as the same theorem that says prices will never get equalized, states that the opportunity cost of capital will be equal. This is one of the eccentricities of interstellar trade. This paper opens up the fascinating possibilities of how forward exchange will be affected, how goods in transit will be insured as their weights change and many more. Although Dr Krugman’s paper does not explain the other vast possibilities, it definitely is a stepping stone for the space faring economist, who I believe is not very far into the future, if people like Elon Musk can help it. Here is a link to the original paper, which by the way contains a lot more puns than mentioned (psst! It’s only 14 pages long). Meanwhile, here’s an awesome picture of Dr Paul Krugman (It’s so not edited, I swear).

(Fun fact: Keynesian economics suggest any activity that creates work is useful, including torching cars and breaking windows) Dr Krugman is an American Keynesian Nobel winning economist who currently is a Distinguished Professor of Economics at the Graduate Centre of the City University of New York and a New York Times Op-ed columnist. He won the Nobel Memorial prize in 2008 for his contributions to New trade theory and economic geography.

- Sai Kumar