I read a lovely paper on patents today, by Michele Boldrin and David K. Levine. The following excerpt specifically engaged me:

We do believe, along with many of our colleagues, that a patent system designed by impartial and disinterested economists and administered by wise and incorruptible civil servants could serve to encourage innovation. In such a system, very few patents would ever be awarded: only those for which convincing evidence existed that the fixed costs of innovation were truly very high, the costs of imitation were truly very low, and demand for the product was really highly inelastic.

They go on to recommend their 2008 paper for a more detailed explanation, but I’m just writing a blog entry here, so I’m going to speculate for now without doing more research: could patent length be calculated from these three factors so as to be optimal to innovation? It’s a question of how to relate the following variables:

  • CI: the cost of innovation, which should be high for patents to be long
  • CC: the cost of copying (or imitation), which should be low for patents to be long
  • ED: the elasticity of demand for the product, which should be low for patents to be long
  • PL: the patent length, calculated as a function of the previous values

Naively, we could use:

PL = CI / (CC * ED)

However, the units don’t make sense. I imagine that ED would be a unit-less ratio, and that CC and CI would be measured in a currency. Perhaps subtract one cost from the other and multiply by some factor that converts from money to time. This would make clear the need for a factor like:

  • RF: the recuperation factor, the amount of monopoly time it would require to recuperate some amount of cost

A less naive formula would then be:

PL = RF * (CI – CC) * ED

Okay, I’ll let the econ guys work out the details, but it’s fun to think about. If your invention only deserves six months of monopoly time, are you really going to file a patent?

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