Answer Happy

1, Sam just graduated from high school and is considering whether to start working immediately or to attend a 4-year university. He currently has a job offer that promises a life-time income of 2 million dollars. After graduating from the university, Sam can find a job with 4-million-dollar life- time income with probability 1/2 and a job with 2-million-dollar life-time income with probability 1/2. The total cost of attending the 4-year university is 0.2 million dollars. Sam cannot afford this cost on his own and must obtain a government loan with an interest rate of 20%. (a) Should Sam attend the university or not? Prove your answer. (b) All else the same, now suppose the university program is very challeng- ing and Sam may have to drop out after the first semester with probability 1/2. If he drops out, he can only find a job with a life-time income of 1.5 mil- lion dollars. Attending the university for the first semester costs 0.01 million dollars. Again, the government loan rate is 20%. In this situation, should Sam attend the university? Prove your answer.