One more cup of coffee

The economics of racing a train

Economists have a way of measuring the value of a human life by how much someone would be willing to pay for safety. If you would pay $50,000 for something that would decrease the odds of you dying by one percent, then that is essentially saying that your life is worth $50,000 / 1% = $5,000,000. Steven Landsburg does a good job of explaining this in a column he wrote for Slate. In it, by the way, he observes that the average life these days is considered worth around four or five million dollars.

An article in this week's Mountain View Voice mentions the intersection of Central Expressway and Rengstorff Avenue as being one of the two intersections in the city with the highest number of accidents. The article notes:

Sitting at this intersection rather frequently, I've observed this many times — someone will try to race their car to sneak under the gates and get across, just before the rushing train gets there.

This made me start to think about the economics behind this. If you can measure the value of a life by how much you would pay to make it safer, surely it is not unreasonable to also measure the value by how much you are willing to trade off by making your life less safe in order to achieve some gain. In this case, the gain is time. Because the people trying to beat the train are almost always going north on Rengstorff, and because those same people are the first to get the green light after the train has cleared, you can, if you beat it, save about two minutes. That's the entire gain.

But now we have to figure out the odds that you won't make it. In other words, how much less safe are you making your life? Well, let's suppose that there's a 1 in 1000 chance that you won't make it — that you get stuck under the gate or on the tracks, or blocked in by the car in front of you — whatever. Further suppose that there is a 1 in 100 chance that if this happens, you'll die. In other words, there is a 99% chance that even if your car gets stuck on the tracks, you'll get out of the car before the train hits it (I sure hope you don't have kids you need to unbuckle as well). Because, well, if the train does hit your car — you are dead. I saw a wreck once where the person didn't make it; the fire department had to use the 'jaws of life' to pry the car off the front of the train. Nasty.

So, what we're left with is a 1 in 100,000 chance that you will die. So, two minutes, divided by this chance, means that your life is worth 200,000 minutes — or 3333 hours. Now let us assume, to pick a random number, that you make $50/hour. (Certainly some people in this area make more, but a lot of people make less.) So, if you race the train to save two minutes, this means that your life is worth:

$166,667.

That's all.

Something to think about the next time the train is coming. Is that really all your life is worth?