I teach part-time in a private for-profit college in Germany (in which German-citizen students get up to half their tuition paid by the government) & tuition is comparable to the least expensive public state universities in the US.

I don't know how the numbers work out but I suspect you could run a private college in the US for less than the mid to high 5-figure $ per student per year they seem to charge.

But then the school would be ranked as a low cost institution, and carry a stigma that many parents and students would want to avoid. There's a reason USC is raising tuition right now. Signaling that it's worth it...

My daughter is going to school in the fall, and I ran into this pricing strategy immediately. Her choice of college started tuition at over $50k/year, but offers "scholarships." These aren't Pell Grant etc, but scholarships that apply only to this institution. You get a scholarship for touring the campus. You get another scholarship for being a state resident. Eventually, you're effective tuition rate is cut in half.

This strategy is brilliant because it works on 3 axis; first, the parents feel like they're getting a good deal (since the effect of anchoring the tuition at $50k is hard to resist). Second, the school can appear elite since it charges a high tuition. Third, the student (and parents) feel good because their kid "earned" scholarships.