An economy needs people and stuff. Productive people take a long time to make. We can make stuff in factories really quickly, but most stuff quickly hits diminishing returns. For example, a worker with two laptops won't be twice as productive as a worker with one laptop. Right now, developed economies mostly grow through innovation. We make better stuff. But if there are substitutes for people that can be mass produced in factories, then you can grow the economy very quickly without increasing the number of people.

Average wealth per person would skyrocket in such a scenario, though of course individuals will vary greatly in how much wealth they accumulate in this sort of takeoff. But if the economy doubles every year, even a small investment (of one year's wages) would be enough to live off of indefinitely. Likewise, governments will vary greatly in how much they tax & redistribute the wealth of their citizens.

After a decade of such doublings, it's hard to say what the world would look like. A 1024x increase in wealth would be more than the difference between us and hunter-gatherer tribes. And all of this assumes that AI will be benevolent.