If there are 60 identical people and each person has a 10% chance of getting ill
ID: 3219420 • Letter: I
Question
If there are 60 identical people and each person has a 10% chance of getting ill, and the loss of income if you get ill is $1000, how much would an actuarially fair insurance be? If instead there are 20 people who have a 10% chance of getting ill, 20 people with a 30% chance of getting ill and 20 people with a 50% chance of getting ill and if the loss of income if you get ill is $1000, how much would a firm need to charge in insurance to break even? In the case of b., what would you expect to happen to this market? Explain and show any additional calculations. What would your answer for b. be if the people with a 10% chance of getting ill cost $1000, those with a 30% chance of getting ill cost $2000 and those with a 50% chance of getting ill cost $5000.Explanation / Answer
Actuarially fair insurance would be P(ill) * (loss if ill) = 0.1*1000=100
B) actuarially fair premium will be( 20/60*0.1 +20/60*0.3+20/60*0.5)*1000 = 0.3*1000=300
C) We would expect that people with 30% chance would be neutral to taking the insurance or not. People with 10% chance will not take insurance because they will be at loss. People with 50% chance will be at a profit at this premium.
D) acturially fair premium = 20/60 * 0.1*1000 + 20/60*0.3*2000 + 20/60*0.5*5000 = 3200/3 = 1066.66