The 11 Billion Dollar Bottle of Wine

The Possibilities of Interstellar Trade

This article originally appeared in Ares nr. 12 (Jan 1982), a science fiction/gaming magazine published by SPI. I was a contributing editor at the time. Despite its age, it holds up quite well, I believe.

Given what scientists say about the probability of intelligent life in the galaxy, it seems almost inevitable that, sooner or later, we will come into contact with another technological species. We can expect that the same kind of interrelationships which existed between primitive peoples on our planet will occur between the two species.

There are basically two ways which individuals or groups can interact--peacefully and violently. Peaceful interaction implies voluntary exchange between two groups which benefit both--that is, trade. Violent interaction implies the attempt by one group to coerce the other--that is, war. Much attention has been paid to the second possibility in the gaming field, but only recently has much been paid to the first.

The reason trade exists is that different groups are efficient at doing different things. For example, let us say there are two countries, A and B. A takes 15 man-hours to make a widget, but only 5 to make a thingummy. B takes 5 to make a widget and 15 to make a thingummy. Suppose each country produces as many thingummies as widgets, and each has 100 man-hours to allocate. Each will then produce 5 thingummies and 5 widgets ((5*15) + (5*5) = 75 + 25 = 100 man-hours). If A and B now open trade, each may concentrate on producing the item which it produces more efficiently; A will produce thingummies and B widgets. Since a thingummy costs A 5 man-hours, it can produce 20; similarly, B produces 20 widgets. They trade 10 thingummies for 10 widgets, since each wants as many thingummies as widgets. The final result is that each country has 10 thingummies and 10 widgets and each is twice as well off as before. (Indeed, trade is even in the best interest of both when one party has an efficiency advantage in both products, because trade will allow him to shift production into areas where his efficiency is greater.)

One problem not taken into account in the above analysis is the cost of transportation (and other barrier costs, such as import and export duties) which raise the cost of doing business with another group. Let us say that it takes 5 man-hours to transfer a unit of widgets or thingummies from country A to country B or vice versa. Each country will then have to allocate 10 man-hours to each unit of a good transported to the other country, and 5 to each unit consumed at home. It is still more efficient for A to concentrate on making widgets and B on making thingummies. However, the best A can do is to make 14 widgets (70 man-hours) and transport 6 to B (30 man-hours) while B does the reverse. Each country is still better off engaging in trade than not, but not as well off as they would be if transportation were costless.

This is, of course, an extremely important result for interstellar trade because the costs of transporting anything over interstellar distances is bound to be high, even given some kind of faster-than-light (FTL) drive.

In essence, in order to make trade in a good worthwhile, the cost of creating a good in one location and transporting it to another must be less than the cost of creating it in that distant location. To determine what interstellar trade (if any) is feasible, there are then two questions we must answer, at least in principle: 1.) what are the costs of interstellar transportation, and 2.) what are the costs of production in a highly advanced civilization capable of interstellar trade? Neither question can be easily answered, but we can, at least, make some conjectures.

Costs

In the simple analysis above, we assumed that the cost of production or transportation could be measured in "man-hours." For any more sophisticated investigation, this is inappropriate. An hour of a PhD's time is worth considerably more than an hour of an unskilled laborer's time. Furthermore, such things as the relative efficiency of production machinery (and other capital goods) and the cost of resources cannot easily be measured in man-hours. That is the primary reason why money exists--because it is an easy tool to measure relative costs.

Extrapolating costs into the future is difficult or impossible because technology constantly advances--changing both costs and relative costs--population trends are not entirely predictable, and the cost of resources may change dramatically as terrestrial resources become scarcer and extraterrestrial resources begin to be exploited. However, the cost of transportation is dependent on three primary factors: the cost of building and operating transport vessels, time, and energy required for transportation.

The first factor is very difficult to figure, but the second two are easily calculable, at least for sublight travel. Given a particular transportation system, it is possible to calculate the amount of energy needed to move something from point x to point y in a given amount of time. This will be discussed in more detail later.

Ignoring the cost of maintaining and building a transportation system, the amount of energy needed to transport a unit of mass is roughly proportional to the cost of transporting it. Thus, the less energy transportation requires, the more likely trade can occur and the more commodities it is profitable to trade.

Time is also an important factor, because the longer it takes to transport a good, the further in advance an investor must put up his capital before he will see a return. At sublight speeds, interstellar transportation will necessarily require between 10 and 10,000 years for a round trip. In America, there are few companies who are willing to wait even 10 years for an investment to provide a return. Government tends to think in even shorter terms; the insistence of Congress on space programs which produce short-term return and its reluctance to engage in projects that may prove immensely profitable over a period of decades, but costly in the short-term, is an example of this thinking.

Quite apart from this psychological reluctance to think too far ahead is the very real economic cost of delayed return on investment. When determining whether an endeavor will be profitable, an investor must keep "opportunity costs" in mind. If an investor has a choice of two investments, both profitable, and chooses the one which is less profitable, he has, in real terms, lost money; he could have made more by taking the more profitable investment. If one can earn 17% of one's money in a money market fund, and investing in a small game company is likely to produce a profit of 10%, there is no reason to invest in the company.

If, say, an investor can earn 10% of his money per year by investing in his own planet, over a period of ten years he can increase his wealth by 160%. To be profitable, an interstellar trading voyage would have to generate more profit than this. So the high time required for interstellar voyages result in high opportunity costs. (In 100 years, at 10% an investor would have increased his wealth by more than 15,000 times.) High opportunity costs combined with high transportation costs make interstellar trade extremely (though not necessarily prohibitively) expensive.

Energy Costs of Sub-Light Travel

Many different interstellar propulsion systems have been proposed, and the energy required for each is different. Since we want to encourage interstellar trade, it behooves us to make relatively optimistic assumptions. In Ares nr. 1, John Boardman investigated the times and costs in energy entailed in using an anti-matter drive capable of 100 percent conversion of energy into gamma rays, accelerating off reaction from such conversion. It is possible to conceive of even less costly drives--such as a ramscoop which gathers its reaction mass en route--but Boardman's drive is at least theoretically feasible while the ramscoop concept has some real technical problems. The Boardman anti-matter drive can then be taken as the most optimistic drive for sublight transportation.

Boardman derived a formula to determine the mass ratio needed between the initial mass of a ship and the mass of the final payload (see table below) assuming the ship accelerated to a given speed, coasted at that speed, and decelerated to rest at its target. He also derived a figure (5704 megawatt-years) for the amount of energy required to produce a kilogram of anti-matter. Combining these two, we can determine the amount of energy needed to accelerate a ship to a given speed and then decelerate to rest. Evidently, the higher the "coasting" speed, the greater the initial investment and the faster the ship will get to its target.

Historically, the US economy has grown at an average annual rate of 3% (corrected for inflation) over the past 150 years. If we assume that net human growth will continue at the rate of 3% in the future, we can calculate the opportunity cost of tying capital up in an interstellar voyage by assuming an average 3% rate of return were the capital invested at home. Obviously, the longer the voyage, the higher the opportunity cost. Compound interest mounts up very rapidly.

The important point is that the opportunity cost goes down if the maximum velocity of the ship goes up (because the ship gets to its destination and back sooner, so the interest is compounded for fewer years). The initial investment goes up, however as the maximum velocity of the ship goes up (because more energy is required to accelerate it to a higher velocity). Evidently, there is, for a voyage of a given length, a maximum velocity at which the minimum net cost is achieved. Table 1 shows the minimum costs for voyages of several lengths between 5 and 100 light-years.

Table 1: Minimum Cost Journeys Using Anti-Matter Drive
Distance	Velocity	Time	Invest (MW-yrs)	Invest 1981$	OM	Cost (MW-yrs)	Cost 1981$
5	.23c	43.9	6,820	2.99	3.66	25,000	10.9
10	.38c	53.4	14,000	6.13	4.85	67,900	29.7
25	.59c	86.0	32,800	14.40	12.70	417,000	183.0
50	.74c	136.9	64,900	28.40	57.20	3,710,000	1,630.0
100	.84c	240.2	120,000	52.60	1,120.00	145,000,000	63,600.0

Key:

Distance: distance in light-years from earth to star.
Velocity: maximum velocity of ship as percentage of speed of light.
Time: time for a round trip in years.
Invest (MY-yrs): initial investment in megawatt-years per kilogram.
Invest (1981$): initial investment in billions of 1981 US dollars per kilogram.
OM: opportunity multiple.
Cost (MY-yrs): total cost in megawatt-years per kilogram.
Cost (1981$): total cost in billions of 1981 US dollars per kilogram.

Assumptions: The figures in this table are drawn using the following assumptions: Boardman anti-matter drive; refueling at destination; vehicle mass neglected; 100% efficiency drive; acceleration = 9.8 m/sec²; rate of return on investments at home is 3% annually; $.05 in 1981 dollars per kilowatt-hour ($438,000 per megawatt-year).

The cost of the energy needed to move a kilogram of matter at the minimum cost velocity of .23 times light-speed to a point 5 light-years away and back is 6,820 megawatt-years, which at average American prices of 5 cents per kilowatt hour works out to about $3 billion in 1981 dollars. When including opportunity costs, the total cost rises to about 25,000 megawatt-years, or about $11 billion. Costs increase rather more than linearly; the total cost of a 100 light-year trip is about $64 trillion dollars (about 20 times the US Gross National Product in 1981).

Actually, $11 billion is not bad when one considers that the Apollo program cost around $10 billion. To look at the energy figures, the initial investment of 6,820 megawatt-years is about 3% of the installed electrical generating capacity of the US as of 1975 -- it would take 6 fairly large nuclear plants operating full-blast for a year to produce the antimatter needed for the trip. That is a lot of energy, but it is by no means beyond our capabilities. (Of course, the technology does not exist at the moment, and is likely never to exist at least in the idealized form postulated by Boardman.) This limitation implies that sending miniaturized, robot probes to the nearer stars is well within the realm of feasibility and will, barring nuclear war or some other catastrophic end to human civilization, probably occur sooner or later.

However, the cost is per kilogram, which means that human beings are unlikely ever to go to the stars, given the mass entailed in the life support system necessary to keep a human alive for several decades.

Standards of Living

Eleven billion dollars is a lot of money -- or is it? We have postulated that the economy will continue to grow, world-wide (or perhaps I should say solar-system-wide), at a rate of 3% per annum. Many countries have growth-rates higher than this (and quite a few less), so it seems a reasonable presumption -- assuming 1.) technology continues to advance, 2.) we begin to exploit the vast resources available in the solar system off earth, and 3.) economic growth does not get choked off by the continued growth of parasitic government at the expense of the productive sector of the economy (the last is the most questionable assumption).

As an example, let us say that the average individual on the earth commands about $1,000 per year (the figure is probably somewhat, but not much, lower, averaged over the earth's population). Figure 1 shows how much money individuals will, on the average, be able to command in the future. Talking of "money" in this context may be confusing; we are talking, actually, about the resources, energy, and goods which an individual commands. The average individual will be able to command $1 billion in about 500 years -- which means he will be able to afford the equivalent of a Cray computer and a fleet of space shuttles. He will not be able to hire huge numbers of domestic servants -- because the average servant will, after all, make somewhere around $1 billion himself.

Real economic growth comes from technological advances that permit increased productivity. Mechanization, division of labor, computerization, robots, etc., mean that fewer and fewer man-hours are needed to produce a given good, and thus that individuals can be paid more (in terms of goods and services) than they could be paid under less productive arrangements. There may be a limit to this process, but we are nowhere near it; indeed, mechanization of services (as opposed to industries) has only begun to occur with the computer revolution. Economic growth means a greater ability to command goods and services; it does not mean a greater ability to command others.

Some things, however, are not susceptible to growth of this kind. There are only so many Rembrandts; the soil of Burgundy can only support so many grand cru vineyards. If a Rembrandt sells for $1 million today, when the average income is $1000, it will sell for $1 trillion when the average income is $1 billion. (All things being equal.)

Historically, per capita energy consumption has been very closely linked to economic growth. Both have increased in the US at an average rate of around 3%. Consequently, as standards of living increase, the amount of energy which an individual can command increases -- and his ability to contribute to what now seems an incredibly expensive sublight trading mission increases. If an average income of $1 billion does not make everyone able to own a Rembrandt, it does make it much more possible to engage in interstellar trade. If a Rembrandt sells for $1 trillion, spending $11 billion to import the equivalent of a Rembrandt from Alpha Centauri does not sound so bad.

How reasonable is it to expect that per capita incomes will increase a millionfold over the next 500 years or so? Assume that the population increases at a rate of 2% per annum (roughly the current global average). Total energy use will increase at a rate of 5% (3% per capita plus 2% increase in population). Current total world consumption of energy is around 8 x 10⁹ MW-years per year. The sun puts out about 1.28 x 10²⁰ MW; in 500 years at a growth rate of 5%, humanity would consume a little bit more than twice the energy produced by the sun (and the human population would be about 8 x 10¹³, eighty-thousand billion people). It seems unlikely that we could produce enough energy to provide the equivalent of a second sun for humanity. However, if we assume that the population would level off at 100 billion people, humanity would consume about 5 x 10¹⁷ MW, about 1/2% of the sun's output. Thus, if we solve the population problem sometime in the 22nd Century, all will be well and our children will be billionaires.

Assume that this picture is over-optimistic. Assume that the $11 billion/kg is off by a factor of ten, and that a better figure is $100 billion/kg. Even today, such a cost, though huge, could be paid. And barring the collapse of civilization, growth will continue. The relative cost of interstellar trade should decline. Doubtless, it will never be as common as trans-Atlantic traffic is today; nonetheless, it seems feasible.

Commodities

We said that in order to determine the feasibility of trade in a given good we would have to know 1.) the cost of transportation and 2.) something about the cost of production of the good. The first question we have answered, and the second we can talk about. If the standard of living has increased a millionfold, what this really means is that the cost of goods has decreased a millionfold. If per capita income increases from $1,000 to $1 billion, an individual can command a million times as much energy or resources. Effectively, we are holding the dollar cost of goods constant while increasing the number of dollars available to individuals.

This being so, it is obvious that common resources and products are not going to be worth trading over interstellar distances. Spending 25,000 MY-years to import a kilogram of lead makes no sense. What might be worth importing?

First, perhaps there are extremely valuable resources which cannot easily be produced in our solar system: monopoles, or superheavy metals, perhaps (if such things exist at all). If, however, there are monopoles on Alpha Centauri because the Centaurians can manufacture them, it is likely that it will be more efficient to purchase the techniques from them rather than to import monopoles.

Which brings up the point that manufactured goods of any kind are probably not worth trading, because given the high costs of transportation, selling the manufacturing technology makes more sense than trading in the goods themselves. What does this leave?

This leaves goods the value of which is not transmittable, which cannot be described and reconstructed, but have somehow intrinsic value. A Rembrandt can certainly be described and the Centaurians could certainly print copies of Rembrandt paintings from information we send them, but those copies would not be the originals. Lithographs sell for prices about 5 orders of magnitude less than originals. Originals have intrinsic value; any copy, no matter how perfect, is but a copy.

So one possible category of trade objects is luxury items, not only objets d'art, but such things as exotic wines and liqueurs and the like. (I refuse to believe that any reproduction technology, no matter how sophisticated, can reproduce the bouquet of wine to the complete satisfaction of a wine snob. The future may see the trillion dollar wine.)

The last category of goods it might make sense to trade is genetic information, or something similar. Given sophisticated genetic manipulation techniques, getting the raw material -- the genetic codes -- of alien species might prove extremely beneficial, especially if the species is very alien in biology. By manipulating such beasties, we might be able to engineer new genetic products that could not be created with the genetic material available on earth. On the other hand, the genetic code is a code; and one day we may be able to read the precise order of amino acids on a strand of DNA, and thus be able to precisely describe a gene to an interested party. There is, naturally, a hell of a lot of information encoded in even the simplest bacterium, and transmitting this much information might be difficult. On the other hand, radio data transmission rates have increased by several orders of magnitude over the last few decades, and it may be that we will be able to transmit instructions for building genes in the future, thus obviating the need for trade in genes.

In summary then, though human civilization is likely to be engaged in interstellar trade, there probably will not be much worth trading, since any society capable of doing so on a major scale can probably produce almost anything it needs at home. Trade in esoteric and extremely rare resources like superheavy metals might be possible; genetic material is another possibility. The most likely trade good would seem to be the relatively frivolous trade in luxuries.

Trade via Radio

There are immense gains to be made from trade with other stars through exchange of information. A space-going civilization is almost certain to have developed technologies which we have not, and vice versa. Exchange of scientific information would also be worthwhile, and surely both our cultures would be enriched by exchange of the artistic masterpieces of our two heritages. Such trade would not require physical transportation of objects, however; a more likely possibility is telecommunication. Getting into radio contact with another civilization would be extremely profitable to both of us, and the cost to operate a large radio transmitter would be immensely less than the cost of operating an interstellar trading vessel.

This kind of trade, however, cannot be built on a direct, bargained exchange. If it takes, say, ten years to send a message and get a response, making a deal would be an effort requiring a lifetime. If making a profitable exchange necessarily requires first coming to an agreement on the terms of that exchange, information will be exchanged at a very slow rate. Instead, it seems likely that both of us will transmit whatever information we think the other might find useful or interesting, transmitting other information as requested. In essence, as Asimov suggests in one of his stories, we will both be talking at once. Whether this kind of exchange can even be termed "trade" in the classical sense is debatable, since there is no agreed exchange of items of value; but it is certainly a voluntary arrangement benefitting both parties. It is also evidently the most cost-effective and simplest way to deal with alien friends.

Trade Faster than the Speed of Light

In this article, I have talked about the possibilities of sublight trade at some length. Trade in FTL vessels may be a more interesting topic, despite the fact that FTL will probably never exist.

The problem is that any FTL drive will necessarily depend on physical principles of which we have not the slightest glimmer at the present time. Consequently, we can not make any assumptions and have no real way of speculating about the costs of such trade or the forms which it will entail. The basic principles, however, remain the same. The lower the cost of transportation of goods, the more trade will go on. One expects that any mechanism for traversing distances measured in light-years is going to be very expensive, even if it involves (or perhaps especially if it involves) somehow transcending Einsteinian mechanics. Consequently, interstellar trade is always likely to be limited. The fact that travel can occur at trans-light speeds means that opportunity costs are much reduced, of course; the cost of building and operating an FTL-drive ship, however, cannot even be guessed at. In the accompanying module, we investigate the costs of travel using the Traveller system, and how that system reflects (or fails to reflect) reality.

Calculations	Traveller

Calculations goes into the math behind the assumptions in this article.
Traveller explores the cost of trade in Marc Miller's science fiction roleplaying game of the same name.

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