Valuation of environmental improvements in continuous time with mortality and morbidity effects

We present a model for valuing environmental improvements in continuous time, for individuals that can be either healthy (H) or ill (I), with constant transition between the states and constant mortality rates in each state, when environmental quality affects welfare, mortality and morbidity. The values in states H and I, VSL(H) and VSL(I), are derived from two Bellman dynamic programming equations. The individual's valuation of (small) instantaneous environmental changes, and of permanent environmental changes (“environmental investments”), are shown to depend on both VSL(H) and VSL(I), for each of the states H and I. We show that VSL(I) may exceed VSL(H), and the value of environmental improvements in the ill state may exceed those in the healthy state, in particular for short-lasting illness and when the marginal value of consumption is lower in state I than in state H.