Benefit-Cost in a Benevolent Society

Alice and Bob live together. Though they are fond of each other, they maintain separate budgets. They have been offered a chance to rent a larger apartment. It has two extra rooms; a study for Alice and a lounge for Bob. Alice would be willing to pay $100 a month for the study and Bob would be willing to pay $100 a month for the lounge. Alice would never use the lounge and Bob would never use the study, but each likes the other to be happy. For this reason, Alice is willing to pay $50 a month for Bob to have the lounge and Bob is willing to pay $50 a month for Alice to have the study. The additional rent for the larger apartment is $250 per month. Should they accept the offer on the grounds that total benefits from the larger apartment are $300, or reject it on the grounds that total benefits are only $200? To pose the question more generally, how should benefit-cost analysis account for the value that benevolent individuals place on other people’s pleasure from public goods? When adding up benefits to be compared with costs, should we sum the private valuations, the altruistic valuations, or something else? W. Kip Viscusi et al. (1998) proposed that the benefits from improvements in public health “consist of two components, the private valuation consumers attach to their own health, plus the altruistic valuation that other members of society place on their health.” They conducted a survey, ingeniously designed to isolate these two components. They asked their subjects to state their willingness to pay for a hypothetical product that would reduce their own personal risks of contracting a carefully described illness. In a separate question, they asked subjects for their willingness to pay for an advertising campaign that would result in an equivalent reduction in risk for all members of a larger population. The authors point out that even a slight concern for the well-being of each member of a large population could amount to a substantial total willingness to pay for benefits to others. In a sample of citizens of Greensboro, North Carolina, Viscusi et al. found that, on average, subjects were willing to pay about five times as much to reduce a specific hazard for all North Carolinians as to reduce this hazard for themselves alone. For a similar benefit to all U.S. citizens, subjects would be willing to pay about six times as much as for themselves only. Even if these hypothetical claims of altruism are overstated, the magnitude of the altruistic component of public benefits appears to be significant. Thus, the question of how to treat altruistic valuations in benefit-cost analysis is a matter of the first order of importance. Before attempting a general answer, let us try to resolve the dilemma of Alice and Bob. Suppose they decide to take the new apartment and split the rent equally. If they do this, then considering only her self-interest, Alice will be worse off. She is giving up $125 in return for a study that she values at only $100. Perhaps she will be compensated by an improvement in Bob’s well-being? But Bob is now paying $125 for a lounge that he values at $100. It does not seem reasonable that two people who care about each other could both benefit from an outcome that makes each of them privately worse off. The fable of Alice and Bob suggests a general principle. If we are to count the sympathetic gains each obtains from the other’s enjoyment of the shared public good, then we should not forget also to count sympathetic losses each bears from the share of its cost paid by the other. To deepen our understanding of this principle, we need an explicit model of interpersonal benevolence. We begin with a simple utility model that is consistent with the story of Alice and Bob. Alice and Bob have private utility functions