Consider the market for health insurance. Suppose that the market is comprised of 4
groups of people of differing risk categories. There are a large and equal number of
people in each group, but insurers cannot tell which group a person belongs to (i.e. this is
a situation of asymmetric information). Each group faces a risk of requiring medical
treatment of value $10,000.
Suppose that the willingness to pay of people in each group is as follows:
Risk 20 40 60 80
WTP 2,500 5,200 6,800 8,500
Actuarially
fair premium
Risk Premium
a) Complete the table of actuarially fair insurance premiums that could be charged to
each group separately by an insurance company large enough to diversify the
risks. How do these compare to the willingness to pay?
b) Suppose now that the risk category is private information. What is the average
riskiness of a person seeking insurance? What premium would an insurance
company have to charge to break even?
c) Will all the agents participate at this price? If not what would be the composition
of risks facing the insurer? Would the premium found above be sufficient to
cover the risks taken by the insurer?
d) Continue with this logic. What will be the price of insurance in the equilibrium
and which groups will participate?
e) Is this an efficient outcome?
