Well then, the costs at the non state schools must not be going up.
Wow, you really have no grasp of basic economics. All public colleges get $ from the State, so the "non-state" schools are private institutions who don't merely raise tuition when they must, but also when they can. Necessarily rising tuition at public institutions allow private ones to also raise their tuition without harming their size and quality of their applicant pool.
What a basic understanding of economics would predict is that private would react to the neccessary public tuition increase, by increasing their own tuition but not to a great an extent because they were already offering a highly priced luxury version of the product and they need to maintain high numbers of applicants in order to maintain high rejection rates that defines the "prestige" of going there.
That is exactly what has happened. Tuition at public institutions is 300% higher today than 30 years ago, but only about 200% higher at private institutions.
LOL @ "basic understanding of economics". There are 1000s of schools competing for students now. If price was how they were competing why would tuition be up 200%?
Why wouldn't East Bumfuck Tech offer a 1980s edcuation at 1980s prices and take all those kids paying $65,000 to go to Sarah Lawrence away?
For the same reason that every person doesn't own an economy car rather than a luxury car, and the same reason that countless varieties of a product exist at different price points. Yet, not a single rational person would claim, as you do, that price is not a factor in almost every decision, even when people choose the more expensive product.
Suppose a disease specifically kills of the apple crop, resulting in a doubling of apple juice prices. Your theory says that this will zero impact on the price charged for any other kind of juice. That is a perfect analogy for the illogic of your argument.
Unlike your infantile theory, consumer choices are not the product of considering a single factor, but rather of many factors, or which price is almost always one. But the other factors comprise the subjective value of each option. When choosing between options, people weight the estimated differential in subjective value against the differential in price.
People chose more expensive private schools because they feel the added subjective value is worth the added cost. There are people who could be and do get accepted to these private colleges but chose to attend public college due to the price differential.
If public tuition rises, then the added cost of private college (the price differential) is reduced. As accurately predicted by anyone who has taken intro economics, this will reduce demand from public college and increase demand for private colleges.
But since most of the more expensive private schools are already at capacity and their "prestige" depends on being exclusive, they don't want more students. This allows the private schools to increase their price, thus returning the relative price differential to what it was and without losing the quality and quantity of applicants and enrolled students.
Yet more brazen ignorance. Private schools are not competing directly with shitty schools that have no credibility and no historical prestige that is a massive advantage in the job market. They are a luxury item that enough people are willing to pay a premium for.