18.5 Suppose that left-handed people are more prone to injury than right-handed people. Lefties have an 80 percent chance of suffering an injury leading to a $1,000 loss (in terms of medical expenses and the monetary equivalent of pain and suffering) but righties have only a 20 percent chance of suffering such an injury. The population contains equal numbers of lefties and righties. Individuals all have logarithmic utility-of-wealth functions and initial wealth of $10,000. Insurance is provided by a monopoly company.

a. Compute the first best for the monopoly insurer (i.c., supposing it can observe the individual's dominant hand).

b. Take as given that, in the second best, the monopolist prefers not to serve righties at all and targets only lefties. Knowing this, compute the second-best menu of policies for the monopoly insurer.

c. Use a spreadsheet program (such as the one on the website associated with Example 18.5) or other mathematical software to solve numerically the constrained optimization problem for the second best. Make sure to add constraints bounding the insurance payments for righties: 0x 1,000. Establish that the constraint 0x is binding and so righties are not served in the second best.