This autumn, many English students will get some form of means-tested support through bursaries or fee reduction depending on their parents’ incomes. Each university has designed its own system to soften the rise in fees, which is up to £9,000 in most cases.

In the new system prospective students are supposed to compare what is on offer. But these offers differ in so many ways – such as whether you went to a state school, whether you were on free school meals, where you live, whether the university was your first choice, and whether you are a first-year student – that it is difficult to make any comparisons. Small differences in parents’ incomes – which applicants may not even know about – can make thousands of pounds’ difference in which offer is best.

In the most extreme case, Oxford University offers first-year students fee reductions and bursaries worth £13,050 (with government grants) if their parents earned up to £17,000 in 2010-11, but nothing if they had earned £44,000. But after allowing for differences in tax, tax credits and benefits, the family on £44,000 would only have been £13,250 better off in the first place. The £13,050 difference in student support cuts the gain from £27,000 of extra earnings to only £200. In effect they faced a 99% tax rate.

More generally, the problems show just how hard it can be to protect the poorest when any substantial universal benefits or services are withdrawn and the limits to what can be done through means-testing without painful side-effects.

Universities have tried to open access to poorer students by means-testing, but the cliff-edge grants will catch many out