Why do you imagine each woman would have 10 children?
One more point, about the cost. I can imagine that people 200 years from now will be so much wealthier than us that they can establish a Mars base just because it’s cool. And honestly, if economic growth doesn’t hit some sort of limit, we’ll have that Mars base and Moon base, just because there will be plenty of people who think it would be cool to have a Mars base, and they’ll have the disposable income to make it happen.
Which means the current carping about how NASA should do this, or not do that, is completely misguided. Establishing a permanent Moon base with 2007 technology with a 2007 global economy is impossible, just like establishing a permanent base at the South Pole was impossible with 1807 technology and an 1807 global economy. Even though our Antarctic bases cost millions of dollars the cost is pretty trivial compared to the size of the global economy.
So there’s no sense in complaining that we need to be establishing Moon bases NOW, before the Chinese do. The Chinese aren’t going to establish a Moon base, no one is going to establish a Moon base, until our economy grows to the point where it’s not out of the question for a rich guy willing to piss away his fortune on something cool.
Space will be done because it’s fun, interesting, exciting and cool, not because it makes economic sense. Sure, some people will make money from space, just like people make money running tours to Antarctica, or taking climbers up Mt Everest. But space travel will be a net sink for money, not a net generator. If the global economy in 2207 is 100 times larger than it is in 2007 we’ll be able to afford all kinds of whacky adventures and stunts and we’ll just laugh at the cost and impracticality. Otherwise, forget it.