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There are many things that are valuable to people, but which they would rather not pay for. They include public goods and externalities, like infrastructure and education and a reasonable amount of military. It makes a lot of sense that people would rather enjoy art for free if they had the option, and since the majority of art experience can be easily duplicated and transmitted, why pay for it yourself? There is also another benefit of art stimulating further intellectual and creative development of a society, perhaps yielding second order benefits that are hard to quantify. Thus overall, it can make a lot of sense for government to pay for art as a society.