Perhaps David Cameron and Nick Clegg might benefit from looking at Dartmouth in the US for some guidance on how to fund university education. Dartmouth College, named for William Legge, 2nd Earl of Dartmouth, was established in 1769 by the Rev Eleazar Wheelock in New Hampshire for "the education and instruction of Youth of the Indian Tribes in this Land . . . and also of English Youth and any others".

The US Supreme Court decision in the Dartmouth College Case of 1819, argued by Daniel Webster, paved the way for all American private institutions to conduct their affairs in accordance with their charters and without inter­ference from the state. Dartmouth is one of eight members of the Ivy League of elite private universities in the US - the others are Brown, Columbia, Cornell, Harvard, Penn, Princeton and Yale. Dartmouth's motto is Vox clamantis in deserto ("a voice crying out in the wilderness"). Believe me, it is miles from anywhere.

Admission is highly competitive, with a success rate of less than 13 per cent for the undergraduate class of 2013. But it costs a fortune to attend. Undergraduate tuition in 2010-2011 costs $39,978, plus room, board and mandatory fees of $12,297, making a grand total $52,275 (just over £36,000). For a four-year degree, that's a bucketload of money. Costs are similar at the other Ivies and many other US universities.

Strikingly, almost half of the students pay considerably less than that, because Dartmouth operates a highly egalitarian policy of "needs-blind" admissions. A family's financial situation is never considered when making a decision about admission, and financial aid is based solely on demonstrated need.

If the cap fits

About 50 per cent of Dartmouth undergraduates receive a scholarship. The average scholarship for the class of 2013 is $35,500, and the university awarded $63m in undergraduate scholarships in 2009. The school places special emphasis on those from less privileged backgrounds; roughly 14 per cent of scholarship students are the first generation in college and 33 per cent are from US minorities. Those whose family incomes are below $75,000 (£52,000) qualify for free tuition - 21 per cent of the present first-year class.

Unlike Brits, Americans are willing to pay for their higher education. They are also willing, as alumni, to donate money to allow people from less fortunate backgrounds to have the same privilege. Dartmouth has an endowment of roughly $3bn and owns 27,000 acres of rural northern New Hampshire, awarded to it by act of the state legislature in 1807.

Dartmouth is very different from the typical poorly funded UK university, which has just experienced significant cuts in revenue and faces more in the future. The one hope for universities in England is that Lord (John) Browne's review of higher education funding will recommend raising the cap on tuition fees. An increase in fees would be controversial, given that Liberal Democrat MPs were elected on a manifesto promising to abolish them. However, they need to rise, by a lot, and the Lib Dems should support that change even though the formal coalition agreement allows them to abstain in any parliamentary vote on the issue.

Cutting the number of university places to save money, as the Business Secretary, Vince Cable, suggested, does not seem wise. The data from the Ucas admissions service suggests there has been an increase of 105,000 (almost 23 per cent) in university applications this year. Yet the new coalition government immediately halved Labour's planned increase of 20,000 places. This will likely come back to haunt it. Youth unemployment stands at 20 per cent and will rise as large numbers of those who are rejected by universities can't find jobs during the recession. We should be aiming to send more young people to university, not fewer.

The most recent pay data from the Labour Force Survey, for the fourth quarter of 2009, indicates that a degree is worth roughly half a million pounds in higher earnings compared to someone with only A-levels or equivalent. Most of those benefits accrue to the individual, so it is hard to fathom why society should pay, rather than individuals, if their families can afford it. Why should the 70 per cent of young people who do not go to university subsidise the 30 per cent who do?

Research by the Good Schools Guide found that a number of leading boarding schools charge around £30,000 a year. They include Chelten­ham Ladies' College, Eton College, Harrow, Malvern St James, Sevenoaks School, Tonbridge School and Winchester College. It is not un­reasonable to expect those who can afford such sums for secondary school to pay the same for their children to go to university.

Help the hard-up

The lack of funding for universities has made it very difficult for them to hire and retain the highest-quality researchers. According to the Shanghai Ranking of World Universities, only five UK institutions rank in the top 50: Cambridge (at number four), Oxford (ten), University College London (21), Imperial (26) and Manchester (41). UK universities perform even worse in the Webometrics ranking, which is based on web presence: only three get into this top 50 (Cambridge is the highest-ranked non-US university at 27, Oxford is at 37 and Edinburgh only just makes it in at 50).

I agree with Andrew Oswald, professor of economics at Warwick University, who wrote in the Independent on 20 May that universities should be allowed to compete on price and quality and offer improved access to "young men and women from hard-up homes". The Dartmouth admissions policy helps here; a generous, needs-blind grants scheme should be established to ensure that improved access. It is time the UK moved to a more equitable system of university funding, with the rich subsidising the poor, rather than the other way round. If you want great universities that can compete with the US, you have to pay for them.

With the new government's cuts in public funding for universities, tuition fees will have to build up over the coming years to £30,000, and probably more at the elite universities. It's time for the equivalent of the Dartmouth College Case in Britain. Set the universities free. And as in the US, middle- and upper-class parents in the UK had better start saving for their children's education.

David Blanchflower is Bruce V Rauner Professor of Economics at Dartmouth College, New Hampshire.