Answer Happy

3. 25 points Assume that you have been admitted to two different university educations (A and B). Education A is very advanced and demands a high effort from your side in order to get through it. However, if you do graduate you will get (with certainty) a very good job (interesting, stimulating and with a high salary); if you do not graduate from education A, you will have to settle with an uninteresting job with a low salary. Education B is relatively simple and everyone graduates who gets admitted and they get “satsifactory” jobs (pretty fun and with a medium salary). Assume that your life-time income with the best job (if you graduate from education A) is YA = $2,000,000, the life-time income from the bad job you have to settle for if you fail to graduate from education A is YA = $500,000, and the life-time income you get from the pretty good job you get if you choose education B is YB = $1,200,000. Assume that you estimate your chances to graduate from education A to 50% and that your utility function for life-time income is: U(Y) = In Y. (a) Which education gives the highest expected life-time income? (b) Which education will you choose if you strive to maximize your ex- pected utility? Explain. (c) What level of life-time income that you get from education B, would make you indifferent between A and B? What is the minimum wage- premium that you demand in order to choose education A in front of B? (d) Assume that there are many students in your situation, i.e., they want to start education A, but worry that they may fail. Assume

that the probability that a randomly selected person will graduate from education A is 50%, irrespective of how many students that are admitted, and that all students have the same probability of graduating. Assume that 1000 students start education A and that they agree to pool (i.e. add) their incomes thereafter into a “life- time income pool”, how big will this “pool” be? how large is each pool-member's part of the aggregate income? (e) How much is each student prepared to pay in order to be a member of the “income pool”? Explain how pooling of risks benefit pool- members and why it “works”. no aggregate risk at all. 7