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

Question

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.

Q. 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 the service?

Explanation / Answer

If teaching is chosen
U(x) = certainty * (1 - 1/x) = 100% * (1 - 1/5) = 0.80

If acting is chosen
If successful U(x) = (1 - 1/x) = (1 - 1/400) = 0.9975
If unsuccessful U(x) = (1 - 1/x) = (1 - 1/2) = 0.50

Probability of success = 1%
Probability of failure = 99%
Expected U(x) in acting = 1%*0.9975 + 99%*0.50 = 0.009975 + 0.495 = 0.504975

If Sarah pays for the service, she will choose acting if she will be successful else teaching

so the expected U(x)
= probability of successful actor*U(x) of successful actor + probability of failure in acting*U(x) of teacher - cost of consulting the career expert
= (1%*0.9975) + (99%*0.80) - 0.01
= 0.009975 + 0.792 - 0.01
= 0.791975

So sarah should NOT pay the career expert as she can make better U(x) if she sticks with teaching (0.80) against consulting the expert (0.791975)

Please rate my answer!
Thanks in advance :)

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