Contracting with Present-Biased Consumers in Insurance Markets

Present bias challenges consumers with self-control problems when they implement precautionary efforts in insurance markets. To explore how rational insurance companies respond to this bias, this paper analyzes a contract design problem in a monopolistic insurance market with ex ante moral hazard. We consider two types of consumers with this bias: the “naifs”, who do not foresee the present bias and make decisions in a myopic way, and the “sophisticates”, who foresee the bias and incorporate it in the decision process. Relative to the benchmark case where consumers are time-consistent, we show that (i) present bias reduces the monopoly profit, regardless of the consumer type; (ii) present bias can either reduce or increase the coverage of the profit-maximizing insurance contract depending on the extent of the bias; and (iii) when present bias is severe, the insurance company can profitably exploit naifs but not sophisticates. These results still hold when consumers are heterogeneous and their types are unknown to the insurance company.