A Theory of Optimal Copyright

There have been plenty of arguments over copyright and what an appropriate term for it should be, but, to my knowledge, precious few mathematical theories, especially those that take into account the impact of digital technologies.

Enter Rufus Pollock, with his splendid paper Forever Minus a Day: Some Theory and Empirics of Optimal Copyright. And if you get the feeling from the title that this may not be exactly beach literature, you are probably right:

Take any exogenous variable X which affects the welfare function (whether directly and/or via its effect on production N). Assuming that the initial optimal level of protection is finite, if d2W/dXdS is positive then an increase (decrease) in the variable X implies an increase (decrease) in the optimal level of protection.

Go that? Well, get this, at least:

Using a simple model we characterise optimal term as a function of a few key parameters. We estimate this function using a combination of new and existing data on recordings and books and find an optimal term of around fourteen years. This is substantially shorter than any current copyright term and implies that existing copyright terms are non-optimal.

Non-optimal: there you have it in a nutshell. (Via Boing Boing.)