Don't use GDP, use wealth statistics. This is quite a different number. For example in Germany the per capita GDP is 47k US$, median income is US$ 27k and median wealth - for a non-real estate-owning household of 2.04 people - is 14500 US$. Note that wealth does not equal money, it includes material goods as well.
Money, wealth, and consequently standard of living have wide gaps in any society, but of course what is "poor" in, say, Nigeria and "poor" in, say, Germany is very different. And yes, this includes the US and yes it includes your 316mio hypothetical colony. You simply cannot have wealthy people without having poor people, and in all societies you have people who - by whatever means, let's not discuss ideology please - will strive to concentrate power and wealth.
I honestly wouldn't try to work out the economy of the universe and then set starship prices, I would decide how common starships are supposed to be and then work backwards to set other prices.
In the setting I am working on I haven't gotten around to spaceship prices and economy yet, but I will work by analogy: Probably airplanes (though ocean-going ships might work just as well, or better, because you more easily live in one permanently and they are easier to maintain). Some people do own private airplanes, ultralgihts, Chessnas, learjets all the way to Airbusses. The major airlines represent your major interstellar corporations. A Chessna might be a good equivalent to a far trader in this scenario. Quick google search suggests that a chessna is about 1.5 mio US$, or 100x what a median household owns. Learjets are about ten times that, so it probably scales fairly nicely at least for what I have in mind.