Let's be a little cautious about the correlation between socio-economic status and innate smarts. There are powerful situational factors that can supress innate talent, and that persist from generation to generation.
Growing up poor, with no books in the home, parents who are gone all the time because they work two jobs each, belonging to a racial minority that is expected by teachers to underperform, and maybe even having been exposed to drugs in utero, not to mention the damaging effects of chronic stress on the brain, can all result in an adult who's brain isn't wired to perform as well as it could have under different developmental conditions. And guess what's going to happen to that person's children?
Yes, there is surely some effect of smarts on upward and downward mobility, but overall, mobility between SES levels is really pretty limited. (Equally true at the other end, by the way. Spectacularly stupid people who are born into upper class families don't tend to be downwardly mobile.)
