Two essays on the economic value of prevention.

Summary The first essay studies the properties of the willingness-to-pay (WTP) measure proposed by Jones-Lee to evaluate the gain associated with a reduction in risk, but by modifying its model. Instead of assuming that the utility function depends on the state (and that it is more increasing and more concave in the absence of a loss), we consider that this function is identical but that a loss simply results in a decrease in wealth. In this case, we show that the cap is no longer in general a concave function of the probability reduction. In the exponential case, for example, it is even convex. We then study the link between the cap and the risk premium. We show that the cap can be considered as a generalization of the risk premium (which corresponds to the cap associated with a complete elimination of the loss) but that some of its properties do not generalize. For example, it is not true in general that the cap increases with the individual's risk aversion. We then study the possibility of aggregating the individual caps using Arrow-Debreu contingent prices. The collective cap is obtained by measuring the market value of the contingent asset corresponding to the risk reduction. In particular, it is linear with respect to the probabilities, which is not generally the case for individual caps. In the second essay, we study an adaptation of a famous model of Ehrlich and Becker to the study of preventive activities in the health field. Three instruments are used to limit this risk: primary prevention (which limits the probability of the disease), secondary prevention (which limits the severity of the occurrence) and curative medicine.