Suppose that left-handed people are more prone to accidents than right-handed. Lefties have a certain chance of suffering an injury equivalent to a $500 loss; righties only have a 50 percent chance. The population contains 10 lefties and 10 righties. All individuals have logarithmic utility-of-wealth functions and $1,000 of initial wealth.

a. Solve for the full-information outcome (i.e., supposing it can observe the individuals dominant hand) for a monopoly insurer. How much per-consumer profit does it earn from each contract?

b. Solve for the profit-maximizing outcome for a monopoly insurer when consumers have private information about their types. How much per-consumer profit does it earn from each contract? Does it make sense to serve both types?

c. Solve for the full-information outcome for perfectly competitive insurers.

d. Show if consumers have private information about their types, any separating contract for righties that involves a nontrivial level of partial insurance will always attract lefties away from their separating contract if contracts involve fair insurance as required by perfect competition. Conclude that the competitive equilibrium must involve righties receiving no insurance. Further, conclude that the adverse selection problem is so severe here that any competitive equilibrium is equivalent to the complete disappearance of insurance in this market.