According to insurance theory, agents who have insurance coverage have less incentives to make preventive actions. In the case of complete coverage, this behavior, called ex ante moral hazard, is so strong that policy holders make no preventive action. Shavell [1979] shows that the optimal insurance contract must contain a deductible in order to give incentives to policy holders. In this article, we argue that this result cannot be obviously extended to the health insurance sector taking into account that policy holders internalize the benefit of their preventive actions through their health state improvement. Using a bi-dimensional utiliTY function, we show that a deductible is not necessarily optimal : it may induce a decrease of the wealth that increases the cost of preventive actions.
