Life-cycle preferences over consumption and health: when is cost-effectiveness analysis equivalent to cost–benefit analysis?

In this paper we derive a set of conditions that is both necessary and sufficient for the consistency of QALY based decision making with life-cycle preferences over consumption and health status. Cost benefit analysis is always consistent with life-cycle preferences over consumption and health status. This follows because cost benefit analysis imposes no assumptions on the lifetime utility function over consumption and health status. Consequently, to show under which conditions cost effectiveness analysis is consistent with life cycle preferences over consumption and health also answers the question under which conditions cost effectiveness analysis is consistent with cost benefit analysis. This paper focuses on the question when the outcome side of cost effectiveness analysis, i.e., QALY maximisation, is consistent with life cycle preferences. The paper is structured as follows. In Section 2, we derive the central result of this paper, that QALY maximisation is consistent with life cycle preferences only if the utility function over consumption and health status can be decomposed multiplicatively and the utility of consumption is constant. Section 3 provides an axiomatic analysis of the conditions under which the utility function over consumption and health status is multiplicative. Section 4 further examines the implications of the multiplicative model for the valuation of longevity and the willingness to pay for a QALY gained. We derive expressions for the willingness to pay for a QALY gained in several decision contexts and identify the principal factors that determine it.