The Cost of Crime - How to value a life
Posted by John Irons at April 13, 2000 02:27 PM
How to value a life.
Why 6.1 million? I can hear many of you yelling at the screen "But a
human life is priceless!".
Well, first let me shatter that illusion, a life does not have infinite
value. If a single life were infinitely valuable, then we should devote
all of our resources to saving a single life. Did you buy a cup of coffee
today? If so, that 50 cents could have been put towards buying a new bath
mat, or any other safety device that could protect your or someone else's
life. Even by driving to work in the morning you are risking your life
and other's. If the value of life were indeed infinite we would never be
prepared to increase risk in any way, and we would never devote any resources
to any non lifesaving activity.
Since we do engage in risky behavior and spend money on coffee, movies,
computers, and other luxuries, we must be placing an implicit, and finite,
value on life.
Since I have now (hopefully) convinced you that the value of life is
finite, we should be able to, in principle at least, be able to measure
its value. Here's an example to show you how it might be done.
Suppose that you are considering buying a new car. This car has an option
for a super sophisticated new air bag system which will save your life
in 1/4 of the cases of an otherwise fatal crash. Say that the odds of getting
into such a crash are 1/100. So, the odds of having your life saved if
you buy the device is 1/400.
The device costs a hefty 10,000, so you decide to take the risk and
decide not to buy the air bag. By making this decision, you are saying
that the the expected benefit of the device is not worth the cost.
expected value of life; no purchase > expected value of life; with
purchase
The expected value of a life under uncertainty is given by the mathematical
expectation operator: the value of an uncertain outcome is p * X + (1-p)
* Y where p is the probability of receiving a payoff of X and (1-p) is
the probability of receiving payoff Y. (I will also assume what is called
"risk neutrality," but the calculation can be done without this assumption).
Since, with probability of 1/400, you're dead and get nothing, this gives
us:
(399/400) * value of life + 1/400 (0) > (value of life - $10,000)
Using some simple algebra...
(1/400) value of life < $10,000
value of life < $4 million!
Of course, more careful estimates look closer at the probabilities and
describe better the behavior of people, but this is the general idea -
by looking at the risk taking behavior, we can form some idea about how
people place a value on their own life.
The $6.1 million number comes from an average of several previous studies
on the topic. For more details see W.
K. Viscusi, "The Value of Risks to Life and Health" in the Journal
of Economic Literature 31(4) 1993 for a complete review. Also see Risk,
Regulation and Responsibility on the web.
Disagree? Too high? Too Low? Think a life is worth more than 6.1
million?
Post
your thoughts in the Forum.
Posted by John Irons at April 13, 2000 02:27 PM
