Consider the market for health insurance. Suppose there are three people. Healthy Hal, Average Al, and Portly Pete. All three of these people will buy health insurance if it costs less than or equal to his actuarily fair insurance rate. Hal's true cost to insure is $5,000, Al's true cost to insure is $10,000, and Pete's true cost is $15,000.
a) Suppose the insurance company must offer a single policy to all customers, and it tries to be fair by averaging the costs of its three customers. What premium will it charge? Who will choose to buy insurance at that price?
b) Observing who has actually purchased a policy, the insurance company decides to adjust its premium to be the average cost of the observed customers in part (a). What premium will it charge?
Which customers will buy insurance at this price?
c) Once again, the insurance company observes who actually purchased insurance, and decides to adjust its premium to the average cost of its observed customers in part (b). What premium will charge? Which customers will buy insurance at this price? Is this market efficient? If not, suggest
some mechanism that might improve its efficiency.

For part (a), 1/3(5000+10000+15000)=10000? Al and Pete will buy
For part (b), 1/2(10000+15000)=125000; Pete will buy. The market is not efficient.
For part (c), 15000; Pete will buy
Am I right for the answers? And what will be the mechanisms to improve the market?