Question

Sara has a utility function u=500-100/c, where c is her consumption in thousands of dollars. If Sarah becomes a clerk, she will make $30,000 per year for certain. If she becomes a pediatrician, she will make $60,000 if there is a baby boom and $20,000 if there is a baby bust. The probability of a baby boom is 75% and of a baby bust, 25%. A consulting firm has prepared demographic projections that indicate which event will occur. What is the most that she should be willing to pay for this information?

Answer 1

Her utility in case of a certain income is U = 500 - 100/30 = 496.67. Find her utility in case of baby boom

U(BB) = 500 - 100/60 = 498.33 and in case of baby bust U(BU) = 500 - 100/20 = 495

Find the expected utility EU = 0.75*498.33 + 0.25*495 = 497.5.

We see that at this utility her consumption should be

497.5 = 500 - 100/c

100/c = 2.5

c = 40000

Hence her income is increased by 40000 if she has a knowledge of the event. The most she can pay is therefore the difference of certain income and this income = 40000 - 30000 = 10000.