Question

Suppose there are two types of people in an insurance market, high and low risks. High risk people are sick 10% of the time and low risk people are sick 5% of the time. The probability any individual is high risk is 40%. Upon getting sick, an individual loses $10,000 in medical expenses. a) What are the actuarially fair premiums for the types? b) If the insurer cannot distinguish between the two types, but the two individuals know their types, then what will be the equilibrium premium? c) Given your answer to part (b), who will exit the market and who will remain in the market? What do we call this? d) What will the premium be if the individuals do not know their type?

Answer 1

Medical expenses = 10000

High-risk people chances of getting sick =10%

Low-risk people chances of getting sick = 5%

Prob individual is high risk is 40%

a) For high risk actuarially fair premium = 0.1 * 10000 = $1000

For low risk actuarially fair premium = 0.05 * 10000 = $500

b) When the insurer cannot know the type of individuals

Equilibrium Premium = 0.4 (1000) + 0.6 (500) = $700

c) At this premium, low risk individual will leave the market given they will find the premium higher than the actuarially fair amount. Only high-risk individuals will remain in the market.

This is called Market failure due to 'Asymmetric Information'

d) If the individual does not know their type, then the premium will be $1000 as it will not be possible to differentiate the two risk types and the low-risk individuals will also be willing to pay the premium for high-risk ones as they are unaware of their type.