It would depend on the details. Let's say public universities educate X students at a cost of $Y. If the government says "We can't pay $Y, we'll pay $Z", then

It would depend on the details. Let's say public universities educate X students at a cost of $Y. If the government says "We can't pay $Y, we'll pay $Z", then the universities will almost certainly say "We can't educate X people for $Z, we can at most only educate $Z * X/$Y people for $Z". Then the remaining slots are for sale to the highest bidder, who will on average be able to pay more than the average of all X could, because they're the highest bidders. More generally, those who have to pay for themselves are in general more price-sensitive than those who have someone else to pay for them. That's true of the students who have the government to pay for them, and it's also true of the government who has the taxpayers to pay for them.