Survival versus Consumption

Abstract

We develop an indirect method to estimate utility and willingness to pay (WTP) for reductions in the risk of death at various ages. Using a life-cycle model of consumption, we assume that an individual sets his consumption level each year so as to maximize his expected lifetime utility. Alternative assumptions about opportunities for borrowing and annuities characterize two polar types of societies. In our Robinson Crusoe case, an individual must be entirely self-sufficient, and annuities are not available. In our perfect markets case, an individual can borrow against future earnings and purchase actuarially fair annuities; we show that under these assumptions WTP is the sum of livelihood (discounted expected future earnings) and consumer surplus. To illustrate our methods, we derive WTP for an average financially independent American man under plausible assumptions. The model is calibrated to 1978 earnings (e.g., $18,000 per year for men aged 45–54 with at least some income). In the Robinson Crusoe case, WTP increases from $500,000 at age 20 to a peak of $1,250,000 at age 40, and declines to $630,000 at age 60. In the perfect markets case, age variations are less pronounced; WTP is $1,050,000 at age 20, peaks at $1,070,000 at age 25, and declines to $600,000 at age 60. These results suggest that individuals value risks to their lives at several times the pro-rata share of their future earnings.