Question

Insurance Market: Anyone can purchase insurance for 1 point. If you are sick and become ill you and you have insurance, you will be compensated 3 points. If you are healthy there is no benefit from insurance. 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 sick or healthy with a 50% chance of each. Each person chooses to either purchase insurance or not.

Decision 2. Here we will simulate the market if you did know if you are sick. To do this, you must make a choice for each type that you might be. You are either sick or healthy but you must make a choice in each case and only the choice which is your true type (which is randomly assigned as outlined below) is enforced. write your decision for the experiment with one decision for each type that you might be.

In summary, your discussion should look similar to the one below.

Decision 1: XXX

Decision 2: if sick YYY

                    If healthy ZZZ

Now, Where XXX, YYY, and ZZZ are your decisions to either buy or not buy insurance

Answer 1

1 point for purchase

3 points compensation when one is ill

No points when one is not ill

Decision 1:

X - Opting for one's type - Type C or Type D... any other type

X - Sick or healthy - Any of the two options for type C or type D

X - Purchase insurance or not - For a type, sick or healthy; purchase or not

XXX - Multiplication principle, or, the product counting principle (combinatorics) can be used

Type A person who is sick and has already purchased insurance gets 3 points; This will be 2 points more than the cost of buying insurance

Decision 2:

if sick YYY

if healthy ZZZ

if sick --- Type C, Type D ..... Type N (Randomly assigned) ----- Can be detected or not by the insurance firm --- Insurance available? Premium available? ------- Purchase or not

Probability for the decision --1/N *1/2*1/2*1/2*1/2

N types that can be assigned randomly; 50 percent probability of it being detected or not getting detected; there are two choices hence a 50 percent probability (if the disease is tested for and can be detected, then the person gets it as a sick individual; otherwise the person will have to disclose, otherwise, getting the insurance money may be difficult later.)

The choices to be made after this are is insurance available, is premium higher, to purchase or not