If population growth were the source of prosperity, Africa would be the richest place in the world and Switzerland the poorest. It's not the people, it's what they are doing - China and India are making the transition from predominantly agricultural to industrial, which gives you a massive boost because of all the cheap labour of displaced peasants. "Mature" economies can't repeat that trick because they've gone past the point of having a use for cheap labour, which is why unemployment is their big problem. What they need is trained and educated labour, which doesn't come cheap unless you steal it from less mature economies, either by hiring immigrants or outsourcing work; either is a short term saving that stores up trouble for later.Not if they've got the sense they've demonstrated so far.
And you can bet the Chinese are going to match dollar for dollar what the Americans are spending in military, eventually surpassing them.