The person buying it and the person selling it. If someone is willing to buy a painting at a specific price, and someone else is willing to sell that painting at that price, that is what the painting is worth.
Dont try to look for a deeper sense of worth in art, there isnt one, it is all “how much will someone give me for this”
Things are only worth what someone is willing to pay. If the only buyer for a painting is offering $100, its worth $100.
Art is extremely subjective, and really the only thing to go off of, is what similar art, by that artist has sold for previously. And if none, then as similar as they can find to it, that has sold.
Theres tons of art experts, and appraisers, and collectors, etc. And for as many as you’ll find, you’ll get that many different answers for worth. Its all just guesses, until you find people actually willing to pay for it.
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.
Appraisers basically. And how do appraisers determine the price? On some level it’s based on some fundamental data like what price has the piece commanded thus far if it’s been sold a few times already and we know the numbers. What prices do the artist’s other paintings sell for? How rare is the painting? And then it goes to auction and the final price is significantly higher than the floor price, and that sets the floor price pretty much for the next time it is sold.
The reality though is that it’s arbitrary and often the prices are inflated on purpose.
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