Problem, 18 points. 6. Suppose you are considering buying a newer vehicle to replace an unreliable car that no longer fits your lifestyle. You can buy a pre-owned (used) vehicle, or you can buy a brand spanking new one. However, you are uncertain of your job prospects for the coming year. How may be (1) unemployed, (2) a half-time employee, or (3) a full-time employee. You assess the probability of being unemployed as .10, the probability of being half-time as .40, and the probability of being full-time as .50. The following table lists the payoffs (in thousands of dollars) of each option for each state of the world compared to a baseline case of doing nothing. What are the expected net benefits in each case? (Show your work). What kind of car, if any, should you buy? (Assume discounting is already captured in the payoffs). Unemployed time Buy used Buy new -3 -10 +3 +2 full-time +3 +4 Finally, suppose you can find out your employment status for next year for a small fee. Might it make sense to do so? Hint: as part of your answer, show what your purchasing decision would be if you knew for certain that you would be 1) unemployed, (2) a half-time employee, or (3) a full-time employee.