Insurance Market:

Anyone can purchase insurance for 1 point. If you are sickly and become ill and you have insurance, you will be compensated 3 points. If you are healthy, there is no benefit from insurance - insurance only pays out if you become ill and healthy people cannot become ill. You must pay the 1 point to purchase insurance even if you do not become ill.

Decision 1: You do not know your type. You can either be sickly or healthy with a 50% chance of each. Each person chooses to either purchase insurance or not.

Decision 1 Answer

I choose to buy insurance.

Decision 2: Here we will simulate the market if you did know your type - sickly or healthy. You must make a choice for each type that you might be. You are either sickly or healthy but you must make a choice in each case and only the choice which is your true type (which is randomly assigned) is enforced.

Decision 2 Answer

If sickly, buy insurance

If healthy, do not buy insurance

QUESTION:

The questions do not need to be answered mathematically or with a calculation. If you feel the need to use mathematics to make a calculation, then you are free to do so but the questions are merely asking you for a number and how you arrived at that number. If you do not do any calculations to arrive at the number, just say how you arrived at the number. (There are no incorrect answers.)

Question 1: If you purchased insurance in decision 1, what would be the maximum number of points you would have paid to purchase insurance? Explain how you arrive at this number.

Question 2: For this question I want you to think of yourself as the insurance company which is selling insurance. If you knew the data from decision 1, what would be the minimum price you would sell insurance at? Explain how you arrive at this number.

Question 3: Again, for this question I want you to think of yourself as the insurance company which is selling insurance. Given the information from decision 2 and assuming that people know if they are sick or healthy, what would be the minimum price you would sell insurance at in this market? Explain how you arrive at this number.