Also, I suspect that yes, the benefits of having these people graduate high school is a wash. Currently, a high school degree is a signal that you are not dealing with the utter dregs of society and that the student can do what they are told for 12 years. If we spend $16k/year graduating everyone, a high school degree will be a signal that if an employer is willing to devote $16k/year to supervising the employee, they might be able to get some useful low skill labor out of them.
As for your theory of poor kids dropping out and then going bad/getting arrested, it just doesn't fit my experience. At the school I dropped out of, the kids were carrying metal long before they dropped out, and there was nothing that Dangerous Minds could do for them.
Look, I haven't worked out all the numbers. I've just a feel for the orders of magnitude. If you want to "spend 3x more", we will spend more on education than we spend on SS, Medicare and the military combined. I don't see any remotely reasonable way that the benefits would exceed this cost. But feel free to post your own numbers.
[Edit: just noticed I used a slang term. "Dangerous Minds" is a mocking term for nice liberal white girls trying to save their students. http://www.imdb.com/title/tt0112792/ (Also usable as a verb.)]
However, we may need to triple what we're spending to teach kids in Englewood, or Harlem, or Oakland.
If we could add 100-200bn to education spending to triple the resources allocated to the bottom 10% of school systems, that might very well be worth it: those students are disproportionately likely to benefit from that spending, earn hundreds of thousands of dollars more throughout their life, secure jobs that include health insurance, avoid expensive prison terms, and draw less on welfare.
This also assumes that the educational buckets are "drop out, high school, college, and advanced degree". What do you think happens if we substitute "college" with "trade school"? What percentage of students will learn a formal trade if they complete high school that wouldn't if they had to get a GED first?
You also ignore the externalities of high school drop-outs; for instance, what percentage of high school drop-outs end up in prison? Note also that juvenile prisons are spectacularly more expensive than adult prisons. Are you hoping to stipulate that the burden to society of supporting drop-outs is wash against the competitive advantages given to people who complete school?