How much would you pay to live longer? Most people would say an infinite amount. In practice, however, this is not the case. For instance, you can drive slower to reduce your risk of a car crash. In this case, you trade off your time with your probability of death. Or, to continue the care safety theme, one could buy the most expensive car seat with the highest safety track record. However, not everyone buys the most expensive car seat.
Economist measure preferences using a utility function and one can readily adapt a utility function to measure the value of a statistical life. Let one’s expected utility be:
- EU=(1-p)ua(w)+p ud(w)
where p is the probability of death in the current period, ua(w) and ud(w)are the utlity of weath conditional on suriving and not suriving. If we differentiate with respect to both w and p, we get:
How do we interpret this result? A paper by Hamitt et al. (2012) provides the answer:
…in the standard model expectancy conditional on surviving the current period increase the utility of survival ua(w) and may increase the marginal utility of wealth conditional on survival ua‘(w). Reductions in life expectancy and health clearly limit the opportunities for gaining utility from wealth…and there is some empirical evidence that impaired health reduces the marginal utility of wealth…Depending on the magnitudes of the effects on the total and the marginal utilities of wealth given survival, better health and increased longevity may increase, decrease, or not affect VSL.
Clearly, the value of wealth at dealth depends on the value individuals place on bequests. In individuals do not value bequests, then:
I am pretty sure u_d(w)=0