Now, here's a cultural success story of truly epic proportions. The Edinburgh Festival Fringe alone has sold 1.7m tickets this year - that's more than twice the number sold by the Manchester Commonwealth Games. It does this every year.

And the official Edinburgh International Festival hasn't even finished yet, so its figures are still to come. The Edinburgh Book Festival has attracted 200,000 to its Charlotte Square tent city, which means that the Edinburgh culture-fest's final score will be well over 2 million. The Adelaide arts festival, Edinburgh's nearest rival, shifts only 250,000.

This is an astonishing achievement and gives the lie to those who claim that people aren't interested in drama, literature, music and physical theatre anymore. And it isn't all comedy, by any means. Less than a quarter of the Fringe shows are standups, and the quality of the theatre is higher than it has any right to be. There are lemons of course, among the 2,050 separate productions across 250 venues, but plays like Truth in Translation, The Container, Damascus, Long Time Dead, Ravenhill for Breakfast, Art of Laughter, even Tony! The Blair Musical stand comparison with anything you are likely to see anywhere else this year.

And the point of it is that these "cultural Olympics" as the first minister, Alex Salmond, calls them, happen largely spontaneously and with very little public funding. There is no overall curator of the Edinburgh Festival Fringe and its subsidy from Edinburgh council is worth less than the Lord Provost's car. There are large venues, of course, like the Assembly Rooms, Underbelly and Gilded Balloon, but these are under no overall artistic or financial direction.

The Edinburgh festival is demand-led; it is the public themselves who decide what is good and what is bad by voting with their tickets. Milton Friedman would have been proud of them, because on the whole they tend to get it right. With a few exceptions - like the over-hyped Spanish outfit Fuerzabruta who have reinvented Pink Floyd stadium events; or the Lady Boys of Bangkok, who are becoming as much a part of festival tapestry as the Tattoo. But these are essentially sideshows.

So, hurrah for the free market. Except, as we know, the market never works in a vacuum - it requires political and economic infrastructure if it is not to collapse under the weight of its own dynamism. Edinburgh's population doubles in August as every corner of habitable space is rented-out at inflated rates. It is becoming more and more expensive to "do" Edinburgh with ticket prices rising. It is also getting older.

Younger people simply can't afford the cost of coming to Edinburgh, where you can get through a thousand pounds in a matter of days. And this is serious. No one wants the festival to become a kind of Saga vision of Glastonbury. One solution might be to integrate Edinburgh into the UK music festival circuit by allocating free space in the city for camping, and by selling flat-rate omnibus tickets at a discount.

There are other hardware issues. Venues are often appalling, with poor seating, restricted views, bad ventilation ... this may have a certain underground appeal for guerrilla theatre but a grown-up festival needs grown up facilities. Someone needs to sort out the marketing of the festivals and dress the city properly so that people realise that they are participating in the greatest cultural event on the planet. And publicists have a job to do reminding the rest of the UK about what is going on here, because in London you would hardly know that Edinburgh is happening at all. The coverage is fitful in the press and largely non-existent on broadcast, at least by comparison with the coverage of the Glastonbury music festival.

Yet, for public service broadcasters like the BBC trying to justify the licence fee, Edinburgh should be a great opportunity to show that it can promote high cultural standards even as it remains popular. I can't understand why it doesn't devote a channel to the Edinburgh Festival in August. It's not as if there is anything much else going on. The wealth of material here, from Macbeth on stilts (don't laugh, it was really rather good) to Ricky Gervais (boo) on the Edinburgh Castle is crying out for the kind of broadcasting effort the BBC routinely puts into the Proms.

I'm sure Edinburgh will survive, for these are problems of success rather than failure. But that success needs recognition and the involvement of the great cultural institutions. The new nationalist government in Edinburgh has seen the light and is promising to invest in Edinburgh's festivals in order to use them as an international showcase for a new Scotland. The previous Labour regime was too poisoned by its own philistinism to realise the enormous potential of this unique event. But it shouldn't be left to the SNP to take culture seriously - this is, or should be, a British achievement. It's time to nationalise the Edinburgh festival.