Sarah has the utility function U(x) = 1 - 1/x, where x is the present value of her lifetime income. ...

Sarah has the utility function U(x) = 1 - 1/x, where x is the present value of her lifetime income. Sarah is trying to select a career. If she goes into teaching, she will make x=5 with certainty. If she pursues acting, she will make x=400 if successful or x=2 if unsuccessful (and therefore ends up waiting tables). The chance of succeeding in acting is 1% if she pursues acting.
a.   Determine which career Sarah will choose. Is she choosing the career with the higher expected value? Explain.
b.   An acting career expert charges 0.01 to determine if a person will succeed at acting. By going to an expert, Sarah can choose the best career according to her skills. Assuming that the expert is able to correctly determine if Sarah will be a successful actor, will she pay for this service?