The type of economy where your mining operation takes years just to start yielding marketable product, let alone generate revenue, because the speed of light makes the economic feasibility of interstellar voyages to obtain otherwise valuable resources significantly more complicated.
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$\begingroup$ The question is unanswerable without some idea of interstellar transport costs for the setting. The real-world answer to that is that they're so high that no kind of interstellar trade or resource extraction is economically feasible. $\endgroup$– John DallmanCommented Jul 30, 2016 at 1:01
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$\begingroup$ Cost-efficient antimatter production is possible but it relies on room temperature superconductors to stabilize the electromagnetic containment fields. It can be synthesized for a high price, but it's much more profitable to mine it when the odd, extremely rare deposits of this naturally occuring material are discovered. Essentially getting there and the energy required to do so is not an issue. The relative timescale such an investment would rely on might be though, which is what I'm asking. $\endgroup$– Z.SchroederCommented Jul 30, 2016 at 1:43
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1$\begingroup$ Charles Stross' science fiction novel NEPTUNE'S BROOD (2013) deals with interstellar economics and relativistic transportation. Charlie's a smart cookie. He will have figured many of the implications. Start there, then onwards and upwards. $\endgroup$– a4androidCommented Jul 30, 2016 at 7:29
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1$\begingroup$ Charlie Stross wrote a crib sheet to give background to NEPTUNE'S BROOD. Familiarity with its predecessor, SATURN'S CHILDREN, will help. At antipope.org/charlie/blog-static/2014/09/… The Wikipedia entry on NEPTUNE'S BROOD helps with more detail. $\endgroup$– a4androidCommented Aug 1, 2016 at 10:28
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1$\begingroup$ IDK by might be so that you wish to read this Q first, and answers to it worldbuilding.stackexchange.com/q/45472/20315 $\endgroup$– MolbOrgCommented Aug 2, 2016 at 12:30
2 Answers
If you want a respectable answer for this question I highly recomend: "The Theory of Interstellar Trade" by Paul Krugman, it seems for me that he answered your question: https://www.princeton.edu/~pkrugman/interstellar.pdf
It's not clear that an interstellar economy can develop under these conditions. Even with economic antimatter production to provide slower-than-light interstellar travel at a cost that isn't utterly ridiculous, there's still a major problem with travel times and human lifespans.
It takes at least a couple of decades for an exploration vessel to go to a different star, survey the solar system, and report back by laser. You need crews that are willing to be away from humanity for at least that long, not for the glamour of being the first to travel to the stars, but for money. You need businesses that are prepared to put up very substantial investments that may well not pay off at all, and cannot do so while the current management are in charge of the company (although they can achieve failure, as a ship breaks down or blows up (antimatter, remember) half-way to its target star).
You need a society with an entirely different timescale to do this. The most obvious way of doing this is for human lives to become much longer, of the order of a thousand years. Once that society has adjusted to that change, it will be utterly different, and might be willing to stage routine commercial projects on these timescales.
Colonisation of other star systems might be another way to create an interstellar economy, but that's a lot more challenging than people assume. We have romantic ideas about "settling the frontier", and some very, very, misleading ideas from films and TV about how easy it would be.
There are basically two reasons for colonising somewhere: to make money by taking over and exploiting a populated place (the model of the European colonial empires, which won't apply), or moving a community that doesn't want to carry on living where it is and is prepared to take big risks to escape (the model of the first colonies in the USA). It seems very unlikely that there will be lots of planets out there that have atmospheres we can breathe, animals and plants we can eat and so on. Terraforming a planet at the far end of a slower-than-light interstellar supply line looks really expensive. We could build space habitats there, but unless there's some resource that makes it easy, we might as well do that in our own solar system, which will be much easier.
If we can make antimatter economically, we can make other elements too. In fact, it will be cheaper than making antimatter. So there aren't any resources that are more valuable.
These problems are why faster-than-light travel is often an accepted impossibility in SF. It makes many kinds of story possible.