Maybe we should learn from the ‘controlled’ experiment in the UK. There the new fees structure caps undergraduate tuition at £9k per year. Gov loans with very forgiving repayment terms are provided for students. The government expected only a few elite universities to charge the full £9k, with the rest charging between 6k and £8k. Their rationale was that universities would compete on price and try to deliver value for money. In reality, universities interacted with each other in entirely the opposite direction – they raced to the top. This is quite surprising, considering the huge variability between universities and courses: 3 years of tutorials in economics at Cambridge cost the same as staying at home and doing social work at the University of Huddersfield. LSE used to charge £8.5k (a symbolic gesture, more than anything), but bumped it up to £9k when it realised (1) their perceived value was derived from their price tag (the higher the better) and (2) that hyper-competition over league tables encourages aggressive spending programmes.
I think this tells us that universities will always charge as much as they can get away with, and that laissez faire economics does not work well in a market filled with institutions that are often shielded from free market effects (e.g. ‘lock-in’ to past choices, difficulties for new entrants into the market, no easy way to weigh-up costs/benefits of investment, etc.). Colleges in the US have a broad range of incentives to charge the highest acceptable market rate (which is usually between $55k and $85k for undergraduate tuition).