Kenneth Arrow (1966, 1971; Arrow and Lind 1970) pioneered much of what we know about individual risk aversion and the social rate of discount. He couched most of his analysis in the context of partial equilibrium models or the Arrow–Debreu complete market structure. Since that time, much work has been done to develop useful models of incomplete market structure. I have in mind especially the Diamond–Dreze model for studying the stock market (Diamond 1967; Dreze 1974) and the capital asset pricing (CAP) model introduced by Lintner (1965) and Sharpe (1964). The purpose of this chapter is to reexamine some of Arrow's early contributions in the context of these structures. First, we develop measures of the social risk premium in the context of the Diamond–Dreze model. These measures turn out to involve the degree of individual risk aversion [as captured in the measures developed by Arrow (1965) and Pratt (1964)], as we should expect. But, in addition, they incorporate project betas, which reflect the degree of correlation between project risk and the underlying uncertainty. These project betas play much the same role as asset betas in the CAP model.

Having developed the appropriate corrections for risk, we ask whether the public sector should behave any differently from the private sector in risk discounting. Aside from differences in betas, we find no compelling reasons for unequal treatment when comparing small projects.