9. Doogie lives for four periods. He has just completed the first period of his life (by getting his high school diploma). Doogie is trying to decide on his future career path. He's very good at opening things up and fixing them, so he has narrowed his options to two possible paths. He will either become an auto mechanic or a brain surgeon. If Doogie becomes an auto mechanic, he will earn $25,000 as an apprentice in period 2, $50,000 as a solo mechanic in period 3, and $75,000 as a master mechanic (with apprentice) in period 4. . If Doogie becomes a brain surgeon, he will pay $50,000 to attend college in period 2, another $75,000 to attend medical school in period 3, and will earn $300,000 in period 4. Doogie must make all tuition payments at the beginning of each period, he is paid at the end of every period, and he can borrow and lend at a rate of 8% per period. a. What is the present discounted value (PDV) of Doogie's possible career paths? If Doogie wants to maximize the PDV of his lifetime earnings, which career should he choose? b. Would Doogie's choice change if he was making his decision at birth? Would the PDV of his earnings streams be different at birth? Would Doogie's evaluation of this investment change if he started life with a trust fund of $1 million? Explain. (Assume that Doogie's high school education in period 1 is necessary for both career paths and is costless.) c. How would your answer change if Doogie could work for an additional 10 periods after period 47 How would your answer change if the discount rate decreased? (Answer intuitively in terms of whether the surgery track becomes relatively more or less attractive). d. The actual lifetime earnings of brain surgeons are much higher than those of auto mechanics, yet we observe that the number of auto mechanics is much greater than the number of brain surgeons. How can the human capital model explain these patterns