I am sure I heard on Radio 4, late one night, that, throughout its entire history, British Leyland made a loss on every Mini car it sold. When the Mini first came to market, the management decided that it should cost no more than the cheapest car then available, the Ford Prefect, and this set the baseline for pricing ever after. But British Leyland never knew about the loss: economic historians did the calculations after the company's demise. The company didn't have to bother. The taxpayer would bail it out, come what may.

The universities used to be a bit like that. They received a government grant, they paid the wage bill, they bought books and lab equipment, and those students who could be bothered graduated with a degree of some kind. No one knew what anything cost and probably no one cared. It would have been unseemly to ask. But Margaret Thatcher ushered in a new age of accounting and internal markets. Each department would be given an income and expenditure account, and the instruction to balance its books.

At first it was assumed that the calculations would reveal that science departments were bringing in the cash to subsidise loss-making arts departments. In anticipation, a number of departments in my own subject, philosophy, were closed down. It was, for a few months in the 1980s, a national news story.

But once universities stopped guessing and actually did the sums, it didn't turn out quite like that. Arts departments are cheap to run, and philosophy apparently the cheapest of the lot. You don't need labs, and, as for new books, well, Plato and Descartes haven't written very much lately. In many universities, more profit could be made out of philosophy students than any other, and this fuelled an impressive expansion of the subject from the mid-80s to the mid-90s.

This was all done on marginal cost calculation, encouraged by a government wanting to expand higher education on the cheap, constantly rejigging the financial incentives. The universities responded with enthusiasm. The cost of an extra arts student is trivial, just £100-£200 a year for some extra hours of tutorials and a bit more examining, but the extra benefit is £1,000 or more in fees. So come on in!

It all came to a juddering halt with changes in the funding formula, together with a belated realisation that marginal cost calculations can't go on for ever. Extra students require larger lecture theatres, more halls of residence and additional staff. Once these are factored in, the bursar begins to feel rather queasy. Although different universities use different accounting systems, current figures suggest that, if you do the sums properly, in many universities every department in the arts faculty makes a loss on every home undergraduate it takes. When account is taken of each student's share of the cost of the library, the registry, computing facilities and the student union, there is almost nothing left to pay for their teaching. But taught students must be. What is more depressing is that the figures suggest that there will still be a loss for many departments after the introduction of top-up fees.

The reaction has set in. You can't unbuild the lecture theatre or the halls of residence, although you can let them rot. You can't very easily shed tenured staff, but you can plan for a "phased reduction" in numbers, using voluntary redundancy combined with abolishing the posts of those who retire. It is hard to see how this can fail to lead to increasing class sizes and a higher workload for those who remain, unless teaching is to be done by an expanded and exploited class of casual labour. Most likely we will see a good old British hodgepodge of measures.

If you are expecting me now to come up with the solution, you'll have to excuse me while I ask for extra time to think. Somehow we have managed to devise a system where everyone is going to feel that they are getting a raw deal. Students and their parents will think that they are paying too much for too little. The universities will still be losing money. Academics will find it ever more difficult to keep up with their workloads - or even to get a proper job in the first place. The government will be upset and resentful that no one is thanking them for the extra resources they have generated. This needs sorting out - assuming, that is, that we don't want our university system to go the way of our car industry.

· Jonathan Wolff is head of the philosophy department at University College London. His column appears monthly