Going back to the feudal period, art and commerce were very separated. Art was considered culture and was not allowed unless it reflected the glory of god and the king. The economics of art was based on patronage. It was a status symbol and those who could afford it would sponsor artists to create works in their name.
The capitalist relationship to art is commodification. Art becomes just another product.
These things are not absolute statements, capitalism is not pure capitalism, there's plenty of other economics going on, but capitalism is now the most present or defining mode of production. So, in today's world we still see plenty of artistic patronage, and many anti-capitalist artists. Many artists seem to think patronage is the only way to successfully be artists, but they are wrong. We need to reject all the old forms of artistic economics and aggressively pursue new forms.
Artists seeking patronage are one and a half revolutions behind and they are only able to survive (and barely survive at that) because so many of the bourgeoisie are back there with them. But, the bourgeoisie is becoming always less interested in playing aristocracy, so we need to move ahead or we'll fall behind.
What's happening to art now?
I can't predict the full parameters of the new economy of art, but i do know it's going to be based on experiences. The art object's value declines constantly and we're at the point where many art objects can be mass produced and reproduced at little or no cost. Different mediums encounter this problem in different ways. More on that later.The fastest growing sector of the economy is the entertainment industry, but new technologies undermine capitalism's approach to art. This will cause a shift from an emphasis on art-commodities to art-experiences.