# The Demand Curve for Life

At the 2009 International Transport Economics Conference Bruno De Borger, Erik Verhoef, and I were having dinner, Erik raised an interesting question about the use of statistical value of life in evaluation studies. Suppose there is a road improvement which will save 1 life per year, reducing the number of fatalities from 2 to 1 per year (out of 1000 people using the road). Assume all travelers are identical. What value of life should be used in the analysis?
Normally, we would do the equivalent of trying to compute for each traveler what is the willingness to pay for a 50% reduction in the chance of death by driving (from 2 in 1000 to 1 in 1000), and multiply that by the 1000 people whose chance of dying is reduced.
An alternative approach is to figure out the willingness to pay for the driver whose life is saved. So how much would you pay to avoid dying (with certainty) (i.e. what is your Willingness to Pay)? The answer to the first question is usually taken to be all of your resources (you would pay you everything so I won’t kill you).
Alternatively how much can I pay you to allow you to let me kill you (Willingness to Accept)? The answer to this second question is: I would have to pay you an infinite amount of money in order for you to let me kill you.
Both of those sums of money (everything or infinity) likely exceed the willingness to pay to reduce the likelihood of dying with some probability, multiplied by the number of people experiencing it.
In economic terms, we are comparing the area under the demand curve (the consumer’s surplus) for life (which has a value asymptotically approaching infinity as the amount of life approaches 0 (death approaches certainty) for a single individual, with the marginal change in the likelihood of survival multiplied by all individuals (i.e. the the quadrilateral between the y-axis of price and the same demand curve, between Pb and Pa) which describes the change in price for a change in survival).
On the one hand, using the marginal change for everyone rather than total change for the one person whose life is saved, we will give a lower value to safety improvements. On the other hand, the value of life to the individual himself is much higher than the value of life of that individual to society at large.

## 2 thoughts on “The Demand Curve for Life”

1. Jason Scheppers says:

All of this is quite morbid, but I would think that it is not possible pay some one to kill them immediately. They are not capable of receiving payment since the form of the payment could not be imparted to them where they could spend the payment. While I don’t like this practice at all, I would suspect that many people take payment for doing things that lead to an earlier death. My example would be coal miners, they have to know the risks, but they take the jobs. The key to why this is economically possible is that the payment is made much earlier than the reduction in life.
As for society, we should be very carefully. The cost to society of the death of 1 individual is the benefits provided by that individual minus costs that we incur to render services to him.
The success of our society will much more likely hinge on educating our next generations and having entrepreneuership as compared to extending life expectancy.
The auto manufacturers are leading the way in reducing transportation fatalities. The question is whether the legal system will effectively allow more autonomous safety features to vehicles that make them safer, and when will the Peltzman effect kick-in and cause riskier behavior.

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2. Phil Goetz says:

Since we are debating what to do with tax dollars being spent on other people, we should use the valuation people place on other peoples’ lives.

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