What is art worth?
Is the value based on aesthetic worth?
Does the artist decide?
Is the value the result of a consensus of opinion?
Is it a result of hype?
Does the market decide?
Does the market decide fairly?
Just who or what decides what art is worth?
Perception and value come into play to some degree.
How you perceive a work may be a big influence on how much you value it.
Where that art work is placed also influences how you view it:
A pot in a kitchen cabinet or on a table looks different from one sitting on a shelf in a show booth with lots of other pots like it. And different yet again when it is located in a gallery with other art "Stars" vying for your attention.
A piece on the table and one sitting alone in a lighted cabinet with glass doors could cost exactly the same; actually be duplicates, but one will be judged as worth more because of it's location and presentation. An isolated object, separated from the rest, is enhanced by it's location. A picture of a work, properly lighted and rendered in a good color printing always looks far more 'important' than the actual piece itself.
Put it in a modern museum with only a few other objects and it really looks important and the monetary value skyrockets. After all, someone decided that this was a worthy piece.
Museums pieces are vetted by art experts and it is known that they pay astronomical sums for art. Or it was a donation from either a wealthy person or even the artist. In any case, the work is judged to be an outstanding example of it's kind.
I'm always a bit saddened and sorry to hear someone say, "I don't know anything about art." or "I'm no expert when it comes to art." because they are afraid they might make a bad choice or throw their money away on something that another might sneer at. This is too bad because the market really is not fair. Bad work gets into museums; excellent work can be produced by a master who never gets recognized.
In the end, it is the person who chooses, buys, and owns the art that is the ultimate judge of how valuable it is. It is the person who elects to posses, prize, view or live with that art who is the ultimate judge of it's value.