Wednesday, October 13, 2010

"'The Economics of Interstellar Trade' a critique"

Click the link. It is not decorative. Nor is this one. Or this one. (which take you to the original article so don't click them twice -- we wouldn't want any time wasted here would we ?).

I find the analysis in "A Theory of Intersteller Trade" unconvincing. You assume that the Trantorian merchant can costlessly accompany it's cargo, however you neglect to consider the economics of interstellar tourism. Imports and exports of goods are easily managed as you demonstrate, but invisible exports are not.

WLOG (with loss of generality) I assume that agents are risk neutral make marginal utility 1) and also, as is standard, assume that they are depraved selfish swinish creatures who care only about consumption.

With these assumptions, the interest rate r must be related to the subjective rate of time preference (symbold font) r, hence r (are you sure you understand the notation).

Consider the advantages of a round trip to Trantor. One can leave invested wealth K behind. After a delay, measured in Earth's inertial frame* of T the wealth will have increased to Ke^(rT)
but the subjective delay will only be T/A where A= (square root of (1 - v'v/c^2))... how did you make actual equations without equation editor, LaTex or (shudder) Tex ? This means that the Value of K will be increased by this operation from the value in the absense of interstellar travel -- K to
K^(r(T(A-1)/A)). This operation can be performed infinitely many times so uh well seems like V is infinite.

Note the infinite benefits of interstellar travel must exist for any interest rate. If r < rho then people can be infinitely happly by borrowing infinity, consuming it then paying it back with interest by consuming - infinity at some future date).

Arbitrage implies that the K in this example is total wealth on planet, as the agent can consume - (total wealth minus its wealth to accumulate such K before leaving). Thus arbitrage proves that travel at speeds approaching the speed of light must cost the greater of the value of Trantor and the value of the Earth. Here simple economics has provided us with the answer to what appears to be a difficult problem in physics and engineering.

I have made extensive use of the simplifying approximation of risk neutrality (so did two of the guys who just won the Nobel prize by the way). Of course I also used the entirely standard assumption that economic agents are perfectly indifferent to the prospect of everyone they have ever known dying before they meet again.

(by the way, you claim not to know general relativity but assert correctly that the Earth has an approximately fixed inertial frame provided it is approximately in free fall -- of course that only holds at the center of mass of the Earth where we find ourselves to withing an interstellar scale approximation)


Anonymous said...


snjmom said...

"LaTex or (shudder) Tex"

Argg, the curly brackets!