Quoting myself from a much earlier comment:
It's been a while since I chewed through the Gates foundation stuff but this one seems up-to-date about early programs:
https://docs.gatesfoundation.org/documents/Lessons%20from%20....
Page 16-17 talks about known effective programs and their costs. Note that the more expensive programs (almost all exceeding $15K per student--sometimes dramatically) are almost always more effective. Under $10K is almost uniformly not helpful and the further you get from 10K the less helpful they get. You can have effective programs for $10K, but it's really hard. Money really does make things easier.
From Page 21: "At the highest level, this “doing many things well” requirement results in a high degree of difficulty and is a key reason why high-quality early learning that sticks is so infrequently seen."
From Page 22: "ESSENTIAL ELEMENTS OF HIGH-QUALITY PRE-K THAT STICKS"
"3. Teachers delivering high-quality instruction is a key differentiator between early learning that sticks and early learning that, more than likely, will not stick. ...
4. All exemplar programs have two adults in the classroom—one lead teacher and one paraprofessional/aide— at all times. ...
5. All exemplar programs have maximum class size of 22 children or fewer and adult-to-child ratios ranging from 2:15 to 2:22. Adult-to-child ratios at the lower end of the range are particularly advantageous for classrooms where a significant number of English language learners (ELLs) are present and/or where a significant number of children with special needs are present.
6. Lead teachers with a B.A. plus suitable early learning credential, paid at same level as K-3 teachers. ...
7. Dosage. Three of the four exemplars offer pre-K that runs 6-6.5 hours/day, for 180-205 days/year. The other (Maryland) offers full-day (6.5 hours/day, 180 days/year) and part-day (3 hours/day, 180 days/year) options. It is clear from the exemplars and consistent with research findings that within high-quality pre-K programs the dosage required is related to the size of the achievement gap that must be closed for each low-income child. For low-income children who enter pre-K already on a trajectory to be kindergarten-ready, a high-quality part- day option may be sufficient. For most low-income children, at least one year in full-day, high-quality pre-K is needed to be kindergarten-ready. For low-income children for whom English is not spoken at home, children with special needs, and children who are significantly below age-level competency in one or more domains, it is likely that two years of high- quality, full-day pre-K is ideal and, in fact, may be necessary for most of these children to be kindergarten- ready on time. "
It goes on to other things as well.
And these exemplars are at the $10K-$12K per student mark, roughly. And even successful ones still can't get funding--"New Jersey was poised to expand the Abbott Pre-K Program in 2013, but budget pressures have delayed that expansion.".
And the Gates foundation is VERY gently suggesting that all the mediocre, non-useful programs should be shut down in preference to spending ALL that money on the most underperforming students. While this is likely the best use of resource, it is going to be a politically unviable one.
The upshot is that teaching properly is expensive, and money really DOES have an impact. And the effectiveness "breakpoint" is somewhere around $12K with some adjustmemts for cost of living. And your primary expense is the teacher vs class size--see page 17. The cost per student with a teacher at BA I qualification ranges from $10K with a 15 student class size to $8K with a 20 student class size. Of course, teaching effectiveness is inversely related to class size--pick your optimization point.
I don't always like the Gates foundation because I think they sometimes helicopter in, muck things up, leave, and then other people have to clean up the mess. However, they have been quite forthright with publishing their information and do acknowledge when they have NOT succeeded even when it goes against their agenda. That I applaud.