Socio-Economic Inequality Is Inevitable. Discuss.

David Neiwert has an interesting piece up commenting on, among other things, the perennial concern amongst those on the right about being outbred by immigrants. Which got me thinking about another, closely related idea that I've never really seen debunked: differential birthrates ensure that there will always be socio-economic stratification. Start with the assumption that fertility decreases as education levels rise. This would seem to indicate that over time you'll end up with fewer educated people relative to their less-educated peers. But this ignores the ability of people to increase their education. So let's make another assumption, that the final education level of your parents is positively correlated with your final education level. That doesn't seem terribly daring, but it would tend to indicate that increasing education levels among the least-educate aren't sufficient to counter the differences in birth rates. You still end up with 1/x type of distribution, with the number of people decreasing as education increases. A final assumption is that education level is positively correlated with income level. Umm... yeah, duh. This just in, fire hot, water wet. But if you put it all together it points to the seeming inevitability of there being a small class of haves and a larger class of have-nots. As the have nots become haves their birthrate decreases, concentrating increasing wealth in fewer people. So what, if anything, is wrong with this model? Assuming its correct, how would you go about reducing social stratification? You'd either have to decrease the spread in education or decrease the correlation between income and education. The latter doesn't seem likely, so it would have to be the former. But you can only reduce the gap so much; not everyone is going to get a PhD or and MBA (or even a BS for that matter). Which makes it look like the best you can do is narrow the gap. This narrowing might even be substantial, but its hard to imagine that it would be enough to eliminate the problems that come from unequal income distribution.