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

We present a simple theoretical framework for analysing values of environmental improvements in continuous time, for individuals that can be either healthy or ill, with constant transition between the states and constant mortality rates in each state, and when direct welfare, mortality and morbidity are all affected by environmental quality. We first show that the values of being in each of the two live states can be represented by two Bellman dynamic programming equations, and derive values of statistical life in good health (VSL(H)) and in illness (VSL(I)), and “values of statistical health” (VSH(H) and VSH(I)). We then find the individual’s valuation of (small) instantaneous environmental changes, and of permanent environmental changes (“environmental investments”), and show how these valuations are related to VSL(H) and VSL(I) respectively. VSL(I) is often greater than VSL(H), and the values of environmental improvements are often higher in the ill state than in the healthy state, in particular when a typical illness is short-lasting and when the marginal value of consumption is substantially lower in the ill state than in the healthy state.