Yes and no. Higher public tuition costs allow private entities to raise their tuition as well. While it depends on the college, I contend that most private colleges are not competing on cost. Schools like Harvard and Duke use price as a way to convey prestige, so they need to remain higher priced than their public counterparts. Schools like University of Phoenix compete on convenience, but if everyone else is charging higher tuition, then they can justify even higher tuition costs as well since everyone else is doing it and this new price is the de facto standard.

Now, I agree that the Feds need to cut back on loans in order to put pressure on the states to reduce their tuition costs. Essentially, the student loan system allows the states to receive free federal money by using students as the vessel of that transaction. I find that morally wrong. At the same time, there are a huge number of students who need some kind of loan to pay for college. I believe it to also be morally wrong to create a system where only those of means can enjoy public education. If the states adequately funded their universities, the universities held their tuition costs down, and either the state or the feds provided loans, then this wouldn't be an issue. However, this requires all of these institutions to agree on the principles of access to education and this isn't happening.

I don't know how to fix this. If the Feds eliminated their loan and grant programs, I personally believe that tuition costs would go down or stabilize because a large-section of the population would not be able to afford the current prices, so the universities would be forced to reduce tuition. This would benefit middle class families who have saved for education. I also believe this would prevent low income families from attending college and I'm not fine with this prospect.