You are assuming that copyright does significantly increase the number of new works created, and that the labor employed to create these extra works would not be more valuably spent on other pursuits--a common problem with subsidies. You are also ignoring the cost of copyright to society, including the cost of enforcement, the undermining of respect for the law, the impact to the government's claims of legitimacy, the loss of potential derivative works, and the loss of works whose copyright holders wish to suppress or simply fail to consider valuable enough to preserve. The cost in liberty alone is enough to render the whole enterprise a net loss.
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