Suppose an individual is deciding on career paths. She could choose career A, which earns $50,000 per year and has a 10% chance of layoff each year, or career B, which earns 80,000 per year and has a 30% chance of layoff each year. When laid off, she earns 0. Suppose her utility over annual earnings is equal to U(E) = VE (a) What would be her preferred job if she had to choose one or the other? If she could allocate her time to both jobs (e.g., could spend 90% of time in job A and 10% in job B) what would be her ideal allocation of time between jobs? (b) Suppose that Lesley meets Patrick and they decide to marry and share all resources. They both face the same two options for jobs, and their joint utility is the same as above, with E being household income. If they can only choose one job each (AA, AB, or BB), and layoff probabilities are independent, what is the best option for the couple? Explain. (c) Suppose the couple can choose fractions of jobs (i.e. they can choose to allocate their TIME = 1 in fractions, so that one could spend 90% of their job in Career A and the other 10% of their time in Career B.) What would be the optimal allocation of their time? (d) Does this example help explain why young adults are more likely to live with their parents? Explain