Multiplicative Utilities for Health and Consumption

Many challenging medical/financial decisions require a decision maker to express preferences for lifetime streams of health and consumption. To express such preferences, we develop two multiplicative utility forms from basic conditions. These forms have many advantages over the leading additive form and extend the way in which life years are adjusted in the popular quality-adjusted life-year model. Unlike additive forms, a decision maker with one of our multiplicative forms can express correlation aversion in consumption streams. In the special case of constant health and consumption streams, our forms reduce to a double exponential utility in life duration. When the decision maker is correlation averse in consumption streams, this form can express risk aversion, decreasing absolute risk aversion and increasing relative risk aversion in life duration. This reduced form under correlation aversion also has standard gamble probabilities (proportional time trade-offs) that increase (decrease) in life duration. In addition, it has standard gamble probabilities that exceed proportional time trade-offs. The properties of this reduced form under correlation seekingness are also examined and discussed in the context of the empirical evidence on attitudes toward risks in life duration, standard gamble probabilities, and proportional time trade-offs.