Economics - General

Comparing Cost-Benefit Analysis and Social Welfare Functions

When evaluating whether a policy or medical treatment approved, policymakers often rely on cost-benefit analysis (CBA).  However, how does one measure costs and benefits?  Costs are often measured in monetary terms and benefits are often measured as decreases in mortality or morbidity.

One way to ensure to tradeoff cost and benefits is to monetize health benefits using the value of a statistical life (VSL) framework.  VSL measures the marginal rate of substitution between fatality risk in a specified time period, and wealth. In other words, it is the change in an individual’s wealth required to compensate him for a small change in his risk of dying during the period, divided by the risk change.  Policymakers use VSL as an input to value health benefits in cost-benefit analysis.

Another approach to evaluate policies or medical treatmetns is to use a social welfare function.  In the social welfare function (SWF), treatment costs and health benefits are arguments in a utility function.  For instance, a utilitarian SWF simply sums individual utilities.  The goal of policymakers is to maximize utility of the entire population.  Another approach is to use a concave SWF where the utility of the worst-off members of society receives more weight than the best-off.

How does the use of VSL and SWF compare?  And article by Adler, Hammitt and Treich (2014) provides a comparison.

Effect of wealth on VSL: VSL increases with wealth.  Wealthier individuals have more money and thus generally are willing to pay more to extend their life.  Thus, simple SWF are sensitive to wealth. In practice, however, policymakers generally ignore differences in VSL due to wealth in policy analysis.

Risk equity: Some people have proposed that the utilities of people with higher risk of dying should count more in the SWF.  In fact, some have proposed a “risk equity” model policies should equalize individuals risk of dying. Standard utilitarian SWF is insensitive to baseline risk, but more complex forms of SWF (i.e., those that weight utilities differently) can be sensitive.  Technically, “transformed utilitarian and prioritarian SWFs are positively sensitive to baseline risk if the transformation function is convex but negatively sensitive if this function is concave.”

Catastrophe aversion. Some policies may not change the number of deaths but may change how they occur.  “[I]ncidents in which many people die (e.g., an airliner crash or a nuclear disaster) are regarded as worse than an equal number of fatalities in unrelated events (e.g., traffic crashes or heart attacks) and catastrophic potential appears to be a major determinant of risk perception.”  Thus, one may wish for SWF to place more value on catastrophe aversion.  “However, empirical evidence suggests that the public does not support using a larger VSL for catastrophic risks.” (Rheinberger 2010)  CBA and standard SWF however, do not incorporate catastrophe aversion into their valuations.  Only “ex post transformed utilitarian and prioritarian SWFs will do so with a concave transformation function.”


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