$200k over twelve years, or ballpark of $16k/yr. Quick Google research says that this is on the higher end of public school expenditure levels, but not unheard of.
Critically, there's an big economies of scale advantage in schools relative to homeschooling. Resource specialization has advantages. Just spitballing, I'd imagine the curve would show it's at least 2-3x cheaper to provide an equivalent education to a student at a mid-sized school relative to a student in a 5-student homeschool environment, and probably 5x+ for single student - obviously depends on the parent's earning capacity and skill as a teacher. The argument for homeschooling is almost never about cost though, due in part to this enormous disadvantage.
Usually not. School funding is not allocated at the "neighborhood" level but instead the county level. There is almost no difference between per student funding between the richest and poorest counties: http://hechingerreport.org/the-gap-between-rich-and-poor-sch... ("I keep specifying 'state' and 'local' funding because the picture gets more complicated when you factor in federal funding. Once you do, almost all of the funding gaps disappear.").
You can argue that poorer students should get more funding than richer ones to help equalize other gaps. I'm not sure I agree with that. Most of that money would go to middle class teachers and administrators. I bet those kids would be better off if you just wrote them a check (or put the money in a trust fund that would then pay them an extra couple of hundred dollars every month for the rest of their lives).
There are also differences at the neighborhood level. We see that in California quite a bit.
> A yawning gulf separates even school districts serving students from similar demographic backgrounds. For example, in 2009-10, the latest data available, per-pupil revenue was $14,076 in Palo Alto versus $7,679 in Milpitas, both unified districts serving K-12 students. But clearly, affluence counts: In San Mateo County, the Woodside elementary district took in $18,894 per student, while Millbrae elementary got $7,362 per student. [1]
The latter example is a 2.5x difference in funding, within the same county. This is in part due to some local support in Woodside [2] but its more than just that. The gaps are huge.
I disagree about not equalizing gaps, because there's one scarce resource here that isn't even discussed: quality teachers. By default, quality teachers are more likely to want to work in nicer communities, and we don't need to compound that by offering to pay them less (sometimes far less) to work in underprivileged schools.
Meanwhile, giving undereducated kids money instead of education is a great way to fulfill the old adage 'a fool and their money are soon parted'.
[1] http://www.mercurynews.com/2012/02/26/some-california-school...
[2] http://www.almanacnews.com/news/2015/12/01/woodside-elementa...
Similar where I live now in Maryland: https://conduitstreet.mdcounties.org/2016/04/26/chart-shows-.... Baltimore City, among the poorest, spends the second most. Surrounding Baltimore County, which is much wealthier, spends substantially less. Montgomery County, the richest in the state and a suburb of D.C., spends about the same as Prince Georges County, a much lower income county next door.