Answer the following questions about someone's career choice. A. If 8, the discount factor, equals 1, what is the net present value for each career choice? Which career will you choose if you are choosing solely based on income? B. Answer part A, but for discount factors of 0.8 and 0.5. What are the net present values of each career, and the choice made for each of these discount factors? C. Now, assume that income is not the only thing that matters to this person. Assume instead that people also gain additional utility, above and beyond income, for doing a job that they like. Naturally, some people like being a doctor, all else equal, and some like being skiers. Assume that the additional utility benefit for being a doctor is distributed Bernoulli with probability P = 0.3 this benefit = 20 and probability Q = 0.7 this benefit equals -15. Assume that the additional utility benefit for being a skier is distributed Bernoulli, with probability P = 0.5 this benefit = 10 and probability Q = 0.5 this benefit = -5. Assume these distributions are independent, meaning that the probability of the additional benefit from being a doctor is unrelated to that of being a skier. Finally, note that these additional benefits accrue to someone each year they are in each career and that they are expressed in income units, so that you can just add them onto the incomes listed in the table above to find total utility for a given career, person, and year. For 8 = 1 and 8 = 0.75, calculate (i) the expected net present value of utility in the population overall and (ii) the probability someone will choose becoming a doctor and the probability someone will choose to become a skier