The art world's eyes were watering last week when a work by Paul Gauguin sold for a record $300m, or £197m, the highest sum ever paid for a painting.

It was not just experts and collectors who felt emotional, though. The gallery in Basel, where Gauguin's portrait of two Tahitian women, titled When Will You Marry, or Nafea Faa Ipoipo, had been hanging, would also have shed a tear. Not only was it losing this gem, but the Swiss owner of the collection it was part of had fallen out with it and removed all the works on loan to the gallery in search of a better home.

Though it has not yet been confirmed, it is widely assumed that the painting was bought by Qatar Museums. Certainly, the kingdom of Qatar has made headlines in recent years for the fortune it is prepared to spend on Western art, such as the then-record £158m reportedly paid for Cezanne's The Card Players in 2011, and £93.5m for a Francis Bacon. Before his death last year, Sheikh Saud bin Mohammad al-Thani, former minister of culture, is thought to have spent around £1bn on art works for his nation. Clearly, his legacy lives on.

Astronomical figures such as these are reminiscent of the tulip mania of the 1600s, catapulting art into the realm of modern football, where the prices paid for players are equally mind-boggling. But at least with sport one can accept the argument that players deserve a fair cut of the revenue raised by television rights, sponsorship and gate. One wonders, though, how any gallery or museum can justify this kind of expenditure. The buyers' calculation of intrinsic worth can have nothing to do with the simple arithmetic of the number of visitors famous works will attract, and how much they can be charged to get through the turnstile.

For many of us, thinking of a painting in terms of pounds and dollars is cheapening, turning art into a base commodity rather than a brilliant exercise in self-expression. It feels vulgar and wrong to look at a canvas and imagine what was paid for it, as if this subtly makes it more impressive. Art lovers take as much pleasure in a good painting that costs a few hundred pounds as in one priced in millions. A work by Peter Doig, which might set you back £7m, is no more beautiful or interesting to my eye - talented though he is - than a Raeburn or Bellany worth a fraction of that. Nor does the £74m paid a couple of years ago for Edvard Munch's The Scream make it any more or less fascinating than when it sat drying on the easel, long before it was heralded as an emblem of the nihilistic age.

For Qatari buyers, however, the stakes are even higher than the sums they are prepared to pay. The actual painting is in some ways irrelevant, other than the kudos it will bring. In this respect, £197m is nothing when set against the importance of establishing Qatar's cultural credentials and attracting international prestige and visitors. For the richest country on earth, such an outcome is presumably priceless. Yet the effect of record-breaking prices on the art world is not just unsettling but unstabilising, inflating the market in artworks beyond their natural price.

Of course, it is hard to define what a reasonable price for art might be. As The Two Roberts exhibition at the Scottish National Gallery of Modern Art in Edinburgh shows, fashion rather than intrinsic quality greatly influences what people will pay, and when. One day MacBryde and Colquhoun were favourites of the galleries; a few years later, their canvasses were stacked, unwanted, against the studio wall, while they struggled to pay their rent.

Which brings us back to Gauguin. Like so many of his kind, he died in poverty, his work not appreciated as it deserved until long after he had gone. Rembrandt, arguably the greatest painter ever born, died without a penny, as did Vermeer and El Greco. Worst of all was Van Gogh who in his lifetime sold only one of his paintings (for about £70), and died not just a pauper but insane.

The gulf between artists' lives and the egregious price tags on their masterpieces is sobering. The image of the starving artist in the garret is not the figment of a romantic imagination, but a grim, unglamorous truth. Even today, none but the most popular artists does more than scrape by. Meanwhile, in auction houses and galleries and in the vaults of private collectors, canvas has become a new currency, one tainted even more than most, it seems, by greed, delusion and power.