Abstract

The social value of risk reduction (SVRR) is the marginal social value of reducing an individual’s fatality risk, as measured by some social welfare function (SWF). This is the linchpin concept for applying social welfare functions to the domain of fatality risk regulation. This Article investigates SVRR, using a lifetime utility model in which individuals are differentiated by age, lifetime income profile, and lifetime risk profile. We consider both the utilitarian SWF and a “prioritarian” SWF, which applies a strictly increasing and concave transformation to individual utility. We show that the prioritarian SVRR provides a rigorous basis in economic theory for the “fair innings” concept, proposed in the public health literature: as between an older individual and a similarly situated younger individual (one with the same income and risk profile), a risk reduction for the younger individual is accorded greater social weight even if the gains to expected lifetime utility are equal. We also systematically compare the SWF framework to benefit-cost analysis (BCA), which is currently the dominant policy-analysis method in governmental practice and applied economics. The value of statistical life (VSL) is BCA’s measure of the social value of reducing an individual’s risk. The comparative statics of prioritarian and utilitarian SVRRs with respect to age, income, and baseline survival probability are significantly different from VSL. Finally, we illustrate how the SVRRs and VSL assign priority in risk reduction, via an empirical simulation based upon the U.S. population survival curve and income distribution. This empirical exercise shows that prioritarian SVRRs with a moderate degree of concavity in the transformation function conform to lay moral judgments regarding lifesaving policies: the young should take priority but income should make no difference.

Highlights

  • The methodology of benefit-cost analysis (BCA) does not support the idea that gains to the young are socially more valuable than equal gains for the old.6. In this Article, we examine the fair innings concept as part of a broader analysis of the use of social welfare functions (SWFs) to value risk reduction, and a comparison of the SWF framework to BCA

  • We show that the ex ante prioritarian Social Value of Risk Reduction (SVRRi) and ex post prioritarian SVRRi both display Priority for the Young and the logically stronger property of “Ratio Priority for the Young.”

  • We analyze what our model implies with respect to age effects on social value of risk reduction (SVRR) as well as value of statistical life (VSL) by considering two individuals i and j, with identical risk profiles and income profiles, but the first older than the second (Ai > Aj). Both SVRRi and Value of Statistical Life (VSLi) are determined by individual i’s status quo income profile and risk profile. (See Propositions 1a, 1b, 1c, 2b.) in analyzing the properties of SVRRi and VSLi as well as Section 4, we will not need to refer to incomes or probabilities, or to utilities as a function of incomes and probabilities, other than status quo values

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Summary

Introduction

Is it socially more important to save the lives of younger individuals, than to save the lives of the old? It seems hard to dispute that younger individuals should take priority with respect to lifesaving measures to the extent that age inversely correlates with life expectancy remaining, at least if the younger and older individuals are situated with respect to the other determinants of wellbeing (health, income, etc.). If Anne is situated to Bob, except for being younger, and a given reduction in Anne’s current mortality risk produces a larger increase in her life expectancy than the same reduction in Bob’s, the risk reduction for Anne seems socially more valuable. The SWF framework provides a systematic methodology for answering such questions It gives guidance in determining how the social value of reducing an individual’s fatality risk (in these cases, her risk of dying from Covid-19) should vary, or not, depending upon her age, income, and other characteristics. Understanding these relative social valuations, for three major SWFs—utilitarian, ex ante prioritarian, and ex post prioritarian—is precisely the topic of this Article

Model of the population
Age effects and “priority for the young”
Age effects and the utilitarian SVRR
Age effects and the ex ante prioritarian SVRR
Age effects and the ex post prioritarian SVRR
Age effects and VSL
Age effects: a summary
Sensitivity to income
Income and baseline risk: summary
Conclusion
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