Consider a situation where there are two types of people: A and B. These people
ID: 2534941 • Letter: C
Question
Consider a situation where there are two types of people: A and B. These people have different likelihoods of becoming sick. The tables below describe each person type's likelihood of being healthy or sick, and the cost for each potential outcome. Also, each person type is risk averse and has some valuation of their potential healthcare costs. Person A's health lottery Cost Probability 0.95 0.05 Healthy 100 Sick Type A's valuation of their health 'lottery' -10 Person B health 'lottery' Cost Probability 0.75 0.25 Healthy 100 Sick Type B person's valuation of their health lottery: -30 Suppose there are both type A and B people in the market but the insurance company is unable to price discriminate. Further, suppose there is a 0.50 probability that any customer is a type A person and 0.50 probability that a customer is type B. What would we expect the insurance company to charge for health insurance given these probabilities? [Enter this value as a positive number.]Explanation / Answer
Valuation of Person A health lottery
Valuation = -10 x (0.95 x 0 + 0.05 x -100) = 50
Valuation of Person B health lottery
Valuation = -30 x (0.75 x 0 + 0.25 x -100) = 750
Charge by insurance company = (Person A valuation x probabiltiy of type A) + (Person B valuation x probabiltiy of type B)
= (50 x 0.50) + (750 x .50) = 400