Wednesday, February 03, 2010

CBA and Bulletproof Clothing

Here is a CNN story on a Colombian tailor who makes his clothing bulletproof, even at point blank range. It opens up an interesting cost-benefit question for a social welfare analyst:

Let's assume that point-blank assassins aim at their targets in a manner that maximizes the probability of death:
p(Death) = p(Hit)*p(Death|Hit).

Where p(Hit) is a function of size of the area on the target (torso is a higher probability shot than the head, for instance), but p(Death|Hit) shrinks with the size of the area on the target (torso shots are less likely to kill than head shots).

Suppose, pre-bulletproof clothing, the dominant strategy for point-blank assassins is a single shot to the torso. It is observed by the population at risk that there is a stochastic random distribution around the area of the heart and torso. This creates the sufficient demand for bulletproof clothing.

If enough of the target population adopt bulletproof clothing, it seems to me the dominant equilibrium strategy shifts to head-shots, which remain unprotected but are harder to hit. On the net, I think we could expect the number of successful assassinations to decrease, but will it be enough collectively to justify the new more expensive tailoring? Could this be an individually rational but collectively irrational product? Things can get really interesting if you assume different levels of risk aversion among assassins.

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