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For my question I'm assuming that we're talking about colonies on the very biggest bodies that are 100s of kms in size. I'm assuming that by this point humans have become cyborgified/roboticized enough to run off electricity and not require a closed atmosphere or really care that there's low surface gravity and they can fly about. Nonetheless they need all forms of industry and production that we need today. These are colonies that don't really rely on trade from Earth or the planets very much. Do they need each other?

For example, if there were separate colonies on the minor planet/biggest asteroid Ceres, and others on Vesta, Pallas, and Hygiea, would it ever be worthwhile for these asteroids to trade with each other?

They have their own local resources and they could mine smaller uninhabited asteroids, but is there anything each of the major group could specialize in composition wise, or are they just too homogenous? Is it perhaps that everyone else would need Ceres but Ceres wouldn't need them?

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    $\begingroup$ The reason for Trade is often specialization, not raw materials. For example Germany has very little raw materials that can not be found elsewhere, yet it is among the top exporting countries. $\endgroup$ – Daniel Oct 16 '20 at 8:04
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    $\begingroup$ @Daniel: Not to mention Japan, which doesn't even have any significant amount of mineral resources (other thank rocks, of which they have more than enough). $\endgroup$ – AlexP Oct 16 '20 at 11:51
  • $\begingroup$ Not sure how your cyborgs procreate, but if there is enough biology left, then genetic diversity might be a good reason to maintain relations with each other. $\endgroup$ – Eike Pierstorff Oct 16 '20 at 17:36
  • $\begingroup$ @AlexP "Rocks" are "mineral resources". What Japan lacks are the right kind of rocks. $\endgroup$ – J... Oct 16 '20 at 19:49
  • $\begingroup$ (16) Psyche is most likely very different from other asteriods in terms of ressources. $\endgroup$ – Karl Oct 17 '20 at 10:28
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Let's ignore all trading - what is the relationship between settlements?

Let's assume that the asteroids are perfectly heterogeneous and there is zero material reason for them to trade with each other, what does the ship traffic look like?

It is highly unlikely that a single asteroid colony would be self sufficient, even over long term. You need replacement parts and things not manufactured on each individual asteroid. These things would come from Earth (Or Mars or someone other massive settlement of humans).

If there are 10 settlements, does Earth send 10 rocket ships with each settlements order? or does it send one to a central hub, which then on forwards the other 9 orders. For the same reason container ships don't stop at every minor town, supply rockets will have a similar hub and spoke arrangement.

Combine with this the transit time and cost of getting replacement parts from Earth, and your settlements will be exchanging rockets with parts and tools simply because it's faster and cheaper than relying on Earth if your neighbours have spares.

This means you have rocket ships between the settlements already, before you even factor in differing resources around the belt.

Now lets look at resources:

From Wikipedia's asteroid page:

The physical composition of asteroids is varied and in most cases poorly understood. Ceres appears to be composed of a rocky core covered by an icy mantle, where Vesta is thought to have a nickel-iron core, olivine mantle, and basaltic crust.[72] 10 Hygiea, however, which appears to have a uniformly primitive composition of carbonaceous chondrite, is thought to be the largest undifferentiated asteroid. Most of the smaller asteroids are thought to be piles of rubble held together loosely by gravity, though the largest are probably solid.

So in short we don't know for sure, but it looks like composition is pretty varied. Your asteroid settlements will be probably trading raw materials.

However, look at more complex manufacturing. Does each colony need its own circuit board printing factory? Does each colony need its own IC manufacturing plant? Should each colony have its own chocolate factory? Trading allows for these specialist production facilities to be dispersed around settlements near each other in delta v costs, this is more efficient, and baring external factors like a war, is going to result in profitable trading for everyone.

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  • $\begingroup$ Self-sufficient over the long-term? Depends on how long they lasted. True, trade allows people to prosper by leveraging comparative advantage, but complications arise. Manufacturing in the United States got a BIG push from the Napoleonic Wars, where the British embargo ensured that their choice was doing without, or making their own. $\endgroup$ – Mary Oct 16 '20 at 12:35
  • $\begingroup$ Only one chocolate factory is needed, provided it has the standard-issue glass elevator for distribution. $\endgroup$ – Darrel Hoffman Oct 16 '20 at 17:33
  • $\begingroup$ I disagree with the idea of a central hub. The cost of sending a rocket of mass M would be the cost of getting it outside the Earth's gravity well + the delta v to reach the asteroids. It could be very well more economical to send 10 M rockets to the 10 settlements, than sending a 10M rocket (or even a 9M one) to a central settlement, specially since then you need additional shipments to places that can be as far away from each other as they are from Earth. The economies of transport in Earth may not be appliable in space, specially if rockets are automated. $\endgroup$ – SJuan76 Oct 16 '20 at 20:14
  • $\begingroup$ Cheaper to go asteroid-to-asteroid, yes, but probably not faster: a Hohmann transfer from Earth gets a launch window to any asteroid about once a year, with a flight time of about a year and a half. Transfers within the Belt have flight times of several years. $\endgroup$ – Mark Oct 16 '20 at 20:30
  • $\begingroup$ Chocolate should be made locally, but the less important items like pcbs and electronics could be made elsewhere. $\endgroup$ – NomadMaker Oct 18 '20 at 23:10
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Efficiency and resources

Here on Earth it is commonplace that a lot of resources aren't close to each other. It can very easily take hundreds of kilometers to find the right kind. Your asteroids are less likely to have many kinds of resources. The heavier the elements, the more rare they are, the less likely they are on your asteroid or an asteroid in your vicinity. Trading is then a logical way to solve this. Some asteroids have more than they need from one resource, while lacking another.

The second is industry. Steel for example isn't a singular product. There are many kinds, fulfilling niches of usefulness. Having all kinds of production is difficult with both limited space and resources, and with some resources is short supply it makes more sense to trade them refined already instead of trading raw resources and producing them yourselves.

You might think to automate a lot of processes and mining also remote asteroids. This is of course possible, but only if there are enough asteroids and space between you and the next cyborg civilization this can be done without conflict.

So in all likelihood they would trade with each other to both benefit. Even if they both can supply themselves with everything that's needed, trading can be beneficial due to lower costs for a certain resource.

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There's 2 major sources for trade.

Staples and luxury items.

Luxury items will always be in demand because they're status identifiers.

Staples would probably be metals or machinery, these can be used to pay for the luxury items when possible or traded as necessities where they are not. But there will always be trade even in war time.

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