# 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.

# Discount rates on human lives

From Tyler Cowan: Don’t apply positive discount rates to human lives:

“Ben Trachtenberg writes:

This Article presents two new arguments against “discounting” future human lives during cost-benefit analysis, arguing that even absent ethical objections to the disparate treatment of present and future humanity, the economic calculations of cost-benefit analysis itself – if properly calculated – counsel against discounting lives at anything close to current rates. In other words, even if society sets aside all concerns with the discounting of future generations in principle, current discounting of future human lives cannot be justified even on the discounters’ own terms. First, because cost-benefit analysis has thus far ignored evidence of rising health care expenditures, it underestimates the “willingness to pay” for health and safety that future citizens will likely exhibit, thereby undervaluing their lives. Second, cost-benefit analysis ignores the trend of improved material conditions in developed countries. As time advances, residents of rich countries tend to live better and spend more, meaning that a strict economic monetization of future persons values the lives of our expected descendents above those of present citizens. These two factors justify “inflation” of future lives that would offset, perhaps completely, the discount rate used for human life. Until regulators correct their method of discounting the benefits of saving human lives in the future, the United States will continue to suffer the fatal costs of underregulation, and agencies will remain in violation of legal requirements to maximize net benefits.”

I think in practice we have to discount future lives, if the discount rate were zero, then we should do nothing for the present as the infinite future would dominate any calculation. I am dubious health inflation will continue unabated. The discussion on the article is interesting and worth reading.