Using Calculus to Determine “Optimal Copyright”

Although we associate calculus with the hard sciences, in fact it’s an important tool for economic and business analysis.
For instance, I just found a reference to a paper “Forever Minus a Day?: Some Theory and Empirics of Optimal Copyright” (PDF) which uses some parameters and calculus theory to propose that copyright should only be about 15 years in order to maximize overall creative output.
That is (if I understand this correctly) too little copyright inhibits creativity because artisans could not earn a fair profit, but too much copyright can also inhibit creativity because it cuts off access to preexisting materials which could be recombined in a new work (e.g. Andy Warhol might not have legal access to a famous Marilyn photo to redo). The analysis also factors in production and distribution costs as well as increases in cultural resources from new works.
I think is an interesting take on a complex policy issue. You might not agree with the assumptions (I suspect some producers would rather increase their own profits than add to the cultural stockpile), but it’s worthwhile for someone to write down their assumptions on optimal policy, then maybe use a more “objective” way to find answer.
I don’t expect copyright terms to be reduced anytime soon, but an analysis like this might be persuasive in keeping them from getting any longer.
After all, even when “Steamboat Willie” (1st Mickey Mouse cartoon) enters the public domain, Disney will have plenty of tricks to keep later versions locked down a little longer (maybe even a lot longer). See the Superboy vs Superman Copyright saga for a sample of what I mean.

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