Now consider a similar career choice with a two period time path of income, given in the following table, between being a primary care doctor and being a surfer. Occupation Primary Care Doctor Income Period 0 1 Income Period 1 P= 0.8: 25 Q = 0.2: 9 P=0.3: 16 Q = 0.7: 9 Surfer 4 There is one key difference between this question and the last one. Now, you are uncertain ahead of time about what the income will be in period 1. You can think of this as reflecting uncertainty about how much you will earn in a given career after choosing to start with it in Period 0 and continuing on into the future in Period 1. P and Q represent the probability of different income outcomes in period 1. For example, there is a 0.8 probability that your income in period 1 is 25 when you choose to become a primary care doctor before period 0. Note that you must choose a career prior to period 0, and stick with it through all periods. A. If 8 = 1 and you are risk neutral, what is your net present value of income for each career? Answer the same question for 8 = 0.8 and 8 = 0.5. B. Solve for the delta that equates the net present value of expected income for these two careers under the assumption of risk neutral utility. C. Now, assume that you are risk averse and that your utility from a certain income amount is the square root of that income amount. E.g. utility from certain income of 25 equals 5. Now, answer part A again but with this new (risk averse) utility function, rather than assuming risk neutrality. D. Answer part B again, but with this risk averse utility function, instead of risk neutrality. E. Take your answer to part D, the discount factor that equates both career paths assuming the utility function in part C. Assume now that you can fully insurance your income stream in period 1 for both careers, with a fair premium. At the discount rate that solves part D, now with full insurance for both career paths which career will you choose? At this discount rate, Occupation Primary Care Doctor Income Period 0 1 Income Period 1 P= 0.8: 25 Q = 0.2: 9 P=0.3: 16 Q = 0.7: 9 Surfer 4 There is one key difference between this question and the last one. Now, you are uncertain ahead of time about what the income will be in period 1. You can think of this as reflecting uncertainty about how much you will earn in a given career after choosing to start with it in Period 0 and continuing on into the future in Period 1. P and Q represent the probability of different income outcomes in period 1. For example, there is a 0.8 probability that your income in period 1 is 25 when you choose to become a primary care doctor before period 0. Note that you must choose a career prior to period 0, and stick with it through all periods. A. If 8 = 1 and you are risk neutral, what is your net present value of income for each career? Answer the same question for 8 = 0.8 and 8 = 0.5. B. Solve for the delta that equates the net present value of expected income for these two careers under the assumption of risk neutral utility. C. Now, assume that you are risk averse and that your utility from a certain income amount is the square root of that income amount. E.g. utility from certain income of 25 equals 5. Now, answer part A again but with this new (risk averse) utility function, rather than assuming risk neutrality. D. Answer part B again, but with this risk averse utility function, instead of risk neutrality. E. Take your answer to part D, the discount factor that equates both career paths assuming the utility function in part C. Assume now that you can fully insurance your income stream in period 1 for both careers, with a fair premium. At the discount rate that solves part D, now with full insurance for both career paths which career will you choose? At this discount rate, how much would you be willing to pay for the full insurance contract for the career you choose