This is a more complex question than the early answers imply. A painting sold at a fair auction is worth its purchase price, but that’s the easy case. There are many situations where it’s not so clear cut. Most obviously, what if there isn’t an auction? Is it worth its most recent purchase price, or what people think it would fetch at auction? If experts say similar paintings were sold for X, maybe the value is in that ballpark, but what if there aren’t comparables? The Mona Lisa will never be auctioned off, and is effectively priceless. Does that mean its value is infinity? What amount do you insure a priceless painting for? How is that amount set, and is that the value of the painting? (Or is also partially the value of loss of revenue to the museum?)
All that to say is that the monetary value of art is highly subjective, and because pieces are unique there is higher variance between pieces and across time. The art market works rather well, though, so it doesn’t seem to be a real problem.
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