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copyright value

Quoted from Slashdot user shimmin (#469139):

Let's give the creator the benefit of the doubt and say that whatever they have created is of enduring value, and the copyright on their creation is worth a perpetuity of some annual income A.

Then, the present value of the copyright is, and will remain, A/i, where i is the interest rate.

Meanwhile, at time t, the present value of the copyright they have already held is A/i * (exp[it] - 1).

So, at some time, it is fair to both the author and public to expire the copyright, because the present value of the copyright (that is being transferred from author to public) is equal to the present value of the copyright that the author has held in the past (that was given to the author by the public). This occurs when t = (ln 2)/i.

Then, the proper term of copyright depends on the interest rate, thusly:

2% 35 years
3% 23 years
4% 17 years
5% 14 years
6% 12 years
7% 10 years
8% 9 years