Consider the same setup as in Problem 18.5, but assume that insurance is offered by competitive insurers. a. Ignore the issue of whether consumers’ insurance decisions are rational for now and

Consider the same setup as in Problem 18.5, but assume that insurance is offered by competitive insurers.
a. Ignore the issue of whether consumers’ insurance decisions are rational for now and simply assume that the equal numbers of lefties and righties both purchase full insurance whatever the price. If insurance companies cannot distinguish between consumer types and thus offer a single full-insurance contract, what would the actuarially fair premium for this contract be?
b. Which types will buy insurance at the premium calculated in (a)?
c. Given your results from part (b), will the insurance premiums be correctly computed?
Reference: Problem 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.e., 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:
. Establish that the constraint
is binding and so righties are not served in the second best.

Leave a Reply

Your email address will not be published.