Imagine that we one day invent an ansible, capable of near-instantaneous FTL communication, but we can not transport physical matter any faster than light.
Imagine also that we have gotten to the point where space travel is possible, but still massively expensive and obviously slow. We want to colonize other worlds despite this expense, but ultimately we must have some hope of these worlds leading to and expanding our economy to help justify such expenses; even if that economy takes a generation or more to build up after colonization starts.
However, a standard economy is nearly impossible: FTL travel is impossible. How is interstellar trade possible? With the high expense of space travel shipping goods from A to B is absurdly expensive relative to the cost of the goods, and the lag time between shipping and arrival, measured in years if not centuries, means that anything other than raw materials would be outdated by the time the arrived.
However, information has been bought and sold for generations, information is power and thus is fungible asset! Therefore I'm wondering if an economy could be developed which exploited FTL communication to make paying for resources possible across worlds. Can a world 'buy' a shipment from another world by producing value purely through FTL communications, which they, then, exchange with the other world. Can a colony eventually refund it's investors that helped fund it's deployment through some sort of value generated on their home planet and 'transported' to earth through ansible communication.
For the sake of this question lets assume enough colonies have been generated that scientists has gotten lots of feedback about interesting astronomical entities from lots of colonies, and thus we no longer consider the information that a newly formed colony can send back about it's home world/system to be able to provide any significant insights or advancement to our understanding of science or the universe.
edit: one extra small detail. Assume that colonies, at least for awhile, are significantly smaller than Earth, and as such tend to have less cultural or scientific development than Earth, simply by virtue of Earth having well over 100 times the number of people to generate these things.