So.. if you levelled the socio-economic part, you'd start a positive cycle of generations improving, rather than the negative cycle of things getting worse.
Of course they are, but the confounding factor is genes shared between the parents and children. What do adoption studies say about those 2 variables?
Conversely if you have super intelligent biological parents... but are raised in a low-socio and low-education level family... your academic results are poor.
In summary: Genes have nothing to do with it.
If you are actually interested in good education policy you should read:
Students dramastically improved their grades in several schools once they were made into exercising with a heart rate monitor (higher heart rate - higher grade) every day:
http://www.amazon.com/Spark-Revolutionary-Science-Exercise-B...
That being said - it's a fun new word that's actually pretty accurate in this situation. The improvements were drastic, and how drastic they were shocked a lot of people (the drama).
Yes, there will still be an achievement gap - that the achievement gap currently reflects socioeconomic factors is unfair.
Money doesn't help nearly as much as time, until you have enough money to hire someone else (or not work).