The Economics of Suicide

To my knowledge, nobody has ever committed economist-assisted suicide.

Nonetheless, the value of continued life is one that implicitly comes up in many Macro models. In Overlapping Generations models, for instance, agents live (a maximum of) two periods, with a chance d of dying after the first period. Implicitly, the utility of dying is zero. Likewise, in almost any Macro model, the beta with which agents discount the future can be considered to include the probability of dying. This is valuable: it allows us to use infinite-horizon models, where agents consider themselves likely to live one more year - no matter how old they are.

As long as death is considered strictly exogenous (i.e. the agent can't affect his chances), this isn't a big problem. But what about when he makes choices that do affect those chances? This issue came up in a discussion of army recruiting. According to my math, the chances of dying in Iraq if one joins the U.S. military are something on the order of 1/500; not huge, but not infintesimal. Compare this to the 2.8% of U.S. Army personnel who perished in World War II (the same figures for Japan, Germany, and the USSR are upwards of 24%) (Wikipedia). Probability of death similarly factors into models of cigarette smoking and other risky behavior.

All of this points to rational actors placing a finite utility on death. Happily, this coincides with the needs of most models. Some popular utility functions are strictly negative (which appeals to the pessimist in me), asymptoting to zero at the highest levels of consumption, and diverging to negative infinity for zero consumption. Economists modeling risky behavior - or suicide - should take heed and avoid such utility functions: otherwise, agents will optimally commit suicide!