Problem 5 An expected utility maximizer with strictly concave utility function U
ID: 1120761 • Letter: P
Question
Problem 5 An expected utility maximizer with strictly concave utility function U and initial wealth W faces an exogenous probability p of having an accident that would cost him Sd to deal with. An insurance company lets him buy insurance on the following terms: he pays a premium rr up front, and in the event of an accident the company returns to him Sr. Assume r is greater than p (both are less than (a) Explain why this means insurance is actuarially unfair. b) Will the individual still always buy a strictly positive amount of insurance? Justify your (c) (unrelated to (a) and (b) above) Discuss how a seller of insurance has to worry about adverse selection. Beyond the insurance industry, where else are individuals confronted by adverse selection?Explanation / Answer
a) Yes, it is acctuarially unfair as the probability of person to meet with an accident is 'p' but the premium charged by the insurer is 'r' which is greater than 'p' premium on insurance is something which charged looking at all the exogeneous variables and premium is set accordingly. So the preium charged should be equal to the probability of meeting with an accident.
b) Yes, the person will buy the strictly positive amount of insurance because he has the probaility of meeting with the accident 'p'. So to cover that you need a positive amount of insurance .
c) Seller of insurance can face adverse selection when there is information asymmetry. Suppose the insuree doesnt disclose the full information about him like prevaling ailment, genetic issues etc Then the insurance company will charge him less premium as well as could have to pay charges if insuree is ill or if he dies etc.
Other than insurance industry, Bank industry also faces adverse selection issue. While providing loan, bankers go for due deligence but the borrower can hide of manipulate the data. Thereby creating adverse selection.