Moral hazard in loss reduction and state-dependent utility

We consider a state-dependent utility model with a binary loss distribution, wherein moral hazard occurs in loss reduction. The findings are as follows: First, partial insurance is optimal under state-dependent utility. Second, the optimal insurance coverage and effort level are affected by the relative sizes of the marginal utilities in the loss and no-loss states. (i) If the marginal utilities are equal between the two states, the optimal coverage and effort are identical to those in the state-independent case. (ii) If the marginal utility in the loss state is greater (less) than that in the no-loss state, the optimal coverage and effort cannot simultaneously be less (greater) than those in the state-independent case. Both coverage and effort can be greater (less) than those in the state-independent case when state dependency is sufficiently large. The compensating variation decreases (increases) as state dependency increases if state dependency is sufficiently large. Although the effect of state dependency on the sensitivity of effort with respect to coverage is unclear, sensitivity decreases (increases) when the loss distribution function is convex in effort.