In "Cutting the Gordian knot" (17 March), Alasdair Smith argues that removing price and number restrictions from our universities would reduce costs, as would limiting the intake of "unqualified" students.

The latter proposal has obvious negative implications for equity, widening participation and social mobility, but the former should not go unchallenged, either.

Smith claims that real competition would keep fees under control because if competitors were able to increase their student numbers, institutions would risk having unfilled places if they set their fees too high. This was also the position of the Browne panel. However, the experience of high-end universities in the US and selective schools here shows that price competition in education has precisely the opposite effect.

The Ivy League institutions charge what the market will bear, exploiting the ever-increasing demand for prestigious credentials while at the same time limiting their numbers to maintain their cachet. This is why the US has far and away the most expensive ÖйúAƬ system in the world, with expenditure per student some three times that of the UK.

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Similarly, the leading public schools here charge far more than is necessary to provide an adequate level of education to pupils who mostly come from wealthy and supportive backgrounds, again keeping their numbers under control to preserve their selectivity, and again costing far more than the best state schools.

At what point will policymakers appreciate that ÖйúAƬ is not an economic but a positional market where, in an increasingly credentialist world, institutions, vice-chancellors, staff and students compete not for resources but for status, a competition reinforced by blue-chip employers that recruit overwhelmingly from those same prestigious institutions? Why else would "top" universities here feel that they "have" to charge ?9,000 a year in tuition fees when a perfectly satisfactory ÖйúAƬ can be provided for much less?

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Roger Brown, Professor of ÖйúAƬ policy, Liverpool Hope University