¹ See Usher, D., An Imputation to the Measure of Economic Growth for Changes in Life Expectancy (National Bureau of Economic Research, New York, 1971)Google Scholar; Conley, B. C., “The Value of Human Life in the Demand for Safety,” American Economic Review, vol. 66 (March 1976), pp. 45–55Google Scholar; Arthur, W. B., “The Economics of Risks to Life,” American Economic Review, vol. 71 (March 1981), pp. 54–64.Google ScholarPubMed Arthur's criticisms of the compensating variation method of calculating life are unconvincing. In particular, his statement that both earlier human capital models and compensating variation (CV) methods both entail “partial equilibrium approaches that ignore the chain of wider economic transfers set up through society when life is lengthened” is quite misleading. Cost-benefit analysis is, of course, an exercise set up within a partial context as, indeed, is his own model – differentiating such approaches, that is, from a Walrasian general equilibrium model. Moreover, contrary to his allegation, the CV method – stemming as it does from the normative maxim that each person himself places a value on the given change (including a change in the risk of deadh or accident) – is in no way limited in covering the range of consequences, even though there may well be difficulties in the actual estimation of each of a variety of effects or externalities.

² See Cook, P. J. and Graham, D. A., “The Demand for Insurance and Protection: The Case of Irreplaceable Commodities,” Quarterly Journal of Economics, vol. XCI (Feb. 1977), pp. 143–156CrossRefGoogle Scholar; Jones-Lee, M. W., “Maximum Acceptable Physical Risk and a New Measure of Financial Risk Aversion,” Economics Journal, vol. 90 (Sept. 1980), pp. 550–568CrossRefGoogle Scholar; Keeney, R. L., “Evaluating Alternatives Involving Potential Fatalities,” Operations Research, vol. 28 (Jan./Feb. 1980), pp. 206–224.CrossRefGoogle Scholar It must be confessed that economists take sly pleasure when they are attacked for asserting that a finite value can indeed be placed on a human life and, which is probably more provoking to prevailing democratic sentiment, that a rich man's life is worth more then a poor man's life. For we can then explain patiently to the indignant layman that the evaluating economist is not addressing himself to philosophical or transcendental questions. He is aware, for example, that a casual interpretation of the gospels suggests that, if anything, the life of a rich man is worth less than that of a poor man – especially when account is taken of the rich man's tenuous prospects of entering the Kingdom of Heaven.

But once we agree to abide by the money value that people themselves put on the goods and bads they have commerce with here on this earth, the existence of a normal income effect assures, ceteris paribus, that the higher a person's income the higher the value he will place on his life – or, rather, the more he will pay for a given reduction in the risk of death. For accepting some increase in the risk of death, on the other hand, the answers provided by economic theory are less certain, and become ever more uncertain as the increase of that risk becomes larger.

Again, the question of whether the value placed on any given change of risk (from which currently the value of a statistical life is calculated) varies in any systematic way with age cannot be answered by economic theory as theory, only by investigation – unless, of course, we surrender to the recidivist propensities condemned above and calculate the value of a human life by reference, inter alia, to his expected future earnings, and to his utility to the rest of society, if any.

³ Thus Q. would be H^T in Conley's 1976 paper, WE in Arthur's 1980 paper, and RL in JonesLee's 1980 paper.

⁴ To be sure, the paper by Jones-Lee (1980) also introduces the concept of maximum acceptable risk. But he cannot obtain it from his RL figure. He must discover it from direct estimates, or guess at it, or else accept it as a residual from a direct estimate of his Δv/Δp – always assuming he can also place a reliable figure on his RL.

⁵ For a classification of these externalities, the reader is referred to my, “Evaluation of Life and Limb: A Theoretical Approach,” Journal of Political Economy, vol. 79 (July 1971), pp. 687–705.

⁶ For those economists who have never given this matter much thought, either equation can be made plausible by simple example. In equation (2) for instance, suppose that the existing risk of death is 10 percent per annum, and person A is willing to pay as much as $5,000 to reduce this risk to 9 percent. It follows from equation (2) that Δr, being 1/100, and Δv, being $5,000, the value of life V must be equal to $500,000. This value for V may be rationalized as follows:

1,000 persons identical to A would, between them, be willing to pay $5,000 times 1,000 or $5 million per annum to reduce the existing collective risk by one percent per annum. Such a reduction would result, however, in an expected saving per annum of 10 lives. The value of each life saved per annum is, therefore, equal to $5 million divided by 10, or $500,000 as stated. It is common to talk of this value of $500,000 as the value of a statistical life, inasmuch as the particular lives saved cannot be determined in advance.

It may be noted in passing that the simplifying assumption of identical individuals is unnecessary. Each of these 1,000 individuals could have a different CV for the reduction of the same risk to 9 percent. Provided that the aggregate of their CVs is equal to $5 million, the value of a statistical life to this group continues to be equal to $500,000.

⁷ Following the Hicksian definitions, the compensating variation for a given increment of risk is equal to the equivalent variation for the removal of that increment of risk.

⁸ Consistency requires that the area between the vertical axis and the line that is vertical through remain blank. For should we begin instead on the vertical axis at a point v₀ – indicating the individual's income along with the certainty of death – then whatever the terms presented to die individual for reducing the risk of death, he will either remain where he is at v₀ or else he will choose a point (along the terms-of-trade line from v₀) which is right of die vertical line through . He cannot, that is, choose a point to die left of since such a point would then be on an indifference curve diat is to the left of , and any set of indifference curves to die left of not only violates die assumption about die critical nature of but must also cut the asymptotic indifference curves to the right off in Figure 3, thereby violating the consistency axiom.

⁹ See Broome, J., “Trying to Value a Life,” Journal of Political Economy, vol. 49 (February, 1978), pp. 91–100Google Scholar; and subsequent comments in the same journal, vol. 12 (October 1979), pp. 259–262.

¹⁰ Needleman, L., “The Valuation of Changes in the Risk of Death by Those at Risk,” Manchester School, vol. XLVIII (September 1980), pp. 229–256.CrossRefGoogle Scholar

¹¹ Thaler, R. and Rosen, S., “The Value of Saving a Life: Evidence from the Labour Market,” Discussion Paper 74–2, Economics Department, University of Rochester, (1974).Google Scholar

¹² Blomquist, G., “Value of Life Saving: Implications of Consumption Activity,” Journal of Political Economy, vol. 87 (June 1979), pp. 540–558.CrossRefGoogle Scholar

¹³ Mulligan, P., “Willingness to Pay for Decreased Risk from Nuclear Plant Accidents,” Working Paper No. 3, Energy Extension Program, Penn-State Univ., Nov. 1977;Google ScholarFrankel, M., “Hazard, Opportunity, and the Valuation of Life,” Preliminary Report, Economics Department, University of Illinois (November 1979).Google Scholar

¹⁴ My 1971 paper suggested, in passing, that this fact of life can explain why the individual bodi gambles and insures without invoking the utility hypothesis advanced by Friedman and Savage (1946).

One testable (and distinguishable) implication of my suggested hypothesis is that people would prefer to enter ten lotteries, each having a one in 10,000 chance of winning a prize X, to the opportunity of entering a single lottery having a one in 1,000 chance of winning the same prize X. Another would be that people who would pay no more than $100 to fully insure their homes against a one in 1,000 risk of destruction by fire, would be willing to pay more than $10 to fully insure their homes against a one in 10,000 risk of the same fire hazard.

¹⁵ Where there is a small likelihood of removing the subject's irrationality – manifest over the required magnitudes of Δr - from some existing level of risk, the economist may wish to experiment with larger magnitudes of Δr in the attempt to discover some range of consistent Δvs. If, over such a range, the Δvs vary (approximately) in direct proportion to the Δrs, the persistent economist might take the liberty of extending this proportionality to the smaller changes in Δrs that are actually involved in the project under scrutiny. The Δ vs so calculated would have to be regarded, however, as an upper limit.

¹⁶ It is, perhaps, unnecessary to repeat that this simplifying condition is not essential. It is sufficient if the aggregate of the Δvs for the one million people affected by the risk reduction Δr₁, comes to $1 billion, and by the risk reduction Δr₂ comes to $0.8 billion.

¹⁷ Notwithstanding the standard format of economic evaluation, method I – in which the benefits are calculated in terms of the value of (statistical) lives saved – is not a genuine cost-benefit analysis. It is equivalent, rather, to a cost-effectiveness analysis. It is a ranking of the alternative projects by reference to the least cost of saving a statistical life – plus a proviso, however, that for a project to enter the lists, the cost per life saved must not exceed its value.

¹⁸ Passages such as the one below in Arthur, “Risks to Life,” p. 64, are revealing:

A change in the pattern of the mortality schedule, it was shown, should be assessed by the difference it makes to expected length of life, production, reproduction, and consumption support; loss of life should be assessed by the expected opportunity costs of lost years, production and reproduction, less support costs.

Clearly, there is no social sanction – more precisely, no sanction from the basic axiom of economic evaluation – in the word “should” as used above. The “should” can be intended only to refer to conclusions that are to be inferred from the model as elaborated by the author.

¹⁹ A given Δr is itself open to a number of alternative interpretations. For example, an increased annual risk of one in 1,000 of a specific sort of death could mean (a), an expected increase of n/1000 deaths annually for a community of n individuals affected by the project in question, there being no way of discovering in advance the exact number of deaths that will occur in any future year. This has been the interpretation of Δr as used in the text. Alternatively, however, the same Δr could refer to (b), a situation in which each year exactly n/1000 deaths will occur. Again, this same Δr could be used to express (c), the expected destruction each year of a community of, say, 10,000 people within a region containing 1,000 such communities. (In this connection, see Keeney, “Equity and Public Risk,” Operations Research, (May/June 1980); and Jones-Lee, M. W., Hummerton, M., and Abbot, V., “Equity and Public Risk: Some Empirical Results,” Opinion Research, vol. 30 (January/February 1982), pp. 203–207).Google Scholar People will not, in general, be indifferent as between these three alternative interpretations of the same Δr.