Class, 9/22

In class today we talked about the value of a human life. One student proposed that we could multiply the amount that a person would earn per year by the number of years worked. We decided that a kind of "average" amount would be appropriate, chose $50,000/year and 40 years to get a value of $2 million. There was some discussion about the costs of an individual to society, but I pointed out that people do pay taxes so maybe that's not something that enters into the equation. I also stated that although the exact number varies from government agency to agency, one such number I had recently read had the transportation department valuing a human life at around $5 million. In our philosophy of Fermi Problems, $2 million and $5 million are not that far removed, so our estimate wasn't bad.

We then asked whether air bags would be something that the government should require, given the cost of an air bag and the number of people that would be saved per year if air bags were required. This required estimating several numbers. One is the number of highway fatalities per year. Several numbers were raised, of the order of several hundred thousand per year. I knew that the actual number is smaller, about 50,000 per year. OK, that's only a factor of 10 (significant, but not horrible). Armed with this number and the population of the U.S., which everyone thought was about 300 million, we figured that the incidence of highway deaths is about 1 per 10,000 per year. We also estimated that maybe 1/3 (and the person who made this estimate thought it was high, which it is) of the deaths could be saved if air bags were installed in every car. The actual number of saved lives is estimated at about 10,000 per year.

So now we set up a very simple decision tree. On one branch, if air bags are installed, that saves 10,000 lives per year, each worth an estimated 5 million dollars, for a total savings of 50 billion dollars per year. On the other hand, one student said that to replace the air bags in a car costs about $700, but that's more than it costs to install them initially, which may be about $300. We also estimated that maybe 20 million cars go on the road each year. That adds up to an additional $6 billion per year. So, by investing $6 billion in air bags each year, we'll save lives estimated in value at $50 billion. This cost-benefit analysis says that the government should mandate air bags, as the net savings to society is only one-tenth of the cost of mandating them.