Equilibrium in Competitive Insurance Markets with Moral Hazard

This paper examines the existence and nature of competitive equilibrium with moral hazard. The more insurance an individual has, the less care will he take. Consequently, insurance firms attempt to restrict their clients' aggregate insurance purchases. If individuals' aggregate insurance purchases are observable, each firm will ration the amount of insurance its clients can purchase and insist that they purchase no insurance from other firms. This paper focuses on the alternative situation where firms cannot observe their clients' aggregate insurance purchases. We show that firms will still attempt to restrict their clients' aggregate purchases, but now they must do so indirectly. One possibility is that all firms sell only policies with a sufficiently large amount of coverage that individuals choose to purchase insurance from only one firm. Another possibility is that each firm offers a latent policy in addition to its regular policy. Latent policies are not purchased in equilibrium, but serve to restrict entry. If an entering firm offers a supplementary policy, an individual will purchase not only this policy plus his previous policy but also the latent policy. The latent policy is designed so that the individual reduces effort by enough to render any entering policy unprofitable.