This is a question about educational economics.
There is a phenomenon when studying countries like the USA and Chile (that have implemented voucher systems) that reducing the friction in a "marketplace" in education (e.g. choosing a school) results in a reduction in equality. It results in stratification of students into schools that match with social class.
It seems fairly obvious to me that this is a phenomenon that I'm sure has been studied or talked about in economics in a general way - I just don't even know where to look.
I'm looking for research into the idea that where there is some kind of inelastic good (e.g. health, housing, education) then reducing friction in a market will always have an effect of reducing equality.
Has anybody studied this? Any pointers to literature? Or if I'm just wrong in my observation of this being "fairly obvious" then I'd love to hear it.