Wednesday, February 20, 2002

The copyright tax Jim Valenti asked Lawrence Lessig "who does it harm if Mickey Mouse is under copyright for 1,000 yrs?" Lessig struggled to answer, but here's some math that points us in the right direction.

Let's look at music sales. This year, $763M CDs were sold in the US, average price $15. Price elasticity for CDs (in New Zealand--all I could find on google) is -0.5. Assume it's the same in the US. Marginal cost for music (a la Napster) is $0 (note--this is marginal cost, not average variable cost, so chill out about up front costs).

You do the math and come up with the following graph:


What does this mean? If music was available at marginal cost, total good to society would be $25,740M, all of it going to consumers. As things stand, society only gets $22,890, split evenly between producers and consumers. There's a dead weight loss (i.e. money that's burnt to collect this "tax") of $2,857M. This means that market for music is $2,857M smaller than it would be in an efficient market. This is equivalent to a copyright tax rate of about 12% (income tax efficiency is about 20% I think). So, for CDs, you can claim each additional year of copyright costs society $2,857M in dead weight loss.

But this is just for a single year. Copyright currently lasts for authors life plus 70 years (and counting). So, let's treat this as a 140 year annuity of $2,857M at a 5% discount rate. Calculating the present value gives you: 19.978 * $2,857M = $57,078M. This is the present value of the cost to society of a 140 year copyright tax. Coming back to Valenti, if this was increased to 1000 years, it would cost society approximately the same amount, since costs that far in the future are so deeply discounted they fall to zero (i.e. present value multiplier at 1000 years = present value multiplier at infinite years = 20).

So from a financial standpoint, the length of copyright currently might as well be infinite, as it costs society approximately that much. This clearly goes against the "for limited duration" section in the constitution. So when someone asks you "who does extending copyright hurt?" you can answer "everyone, to a tune of about $3B a year just for music." You could also add that the economic length of copyright is currently essentially infinite. Any argument for extending copyright further is about control, not incentive to produce, since it's impossible to increase the incentive to produce any more.
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