Question

1. Alexandrea has utility ?= 500 −(100/I) where I is income in thousands of dollars. Alexandrea can become a clerk and make $30 thousand dollars a year with certainty or she can become a pediatrician and make $60 thousand a year if there is a baby boom and $20 thousand a year if there is a baby bust. There is a 75 percent chance of a boom and a 25 percent chance of a bust. Fortunately, a consulting firm has done a lot of research on demographics and knows what will happen (i.e., they can provide certainty but there is a 75 percent chance they will say “Boom” and a 25 percent chance they say “Bust”). What is the most Alexandrea would be willing to pay to find out the answer?

Answer 1

Solution:

If Alexandrea becomes a clerk, her yearly earnings would be $30,000 (with certainty)

If she becomes a pediatrician, her earnings would not be certain, and differ on probabilities. So, we calculate the expected earnings. Expected earning = sum(probability of state*earning from state)

Expected earning (as a pediatrician) = 0.75*60000 + 0.25*20000

Expected earning = 45000 + 5000 = $50,000

Alexandrea already has a sure option of earning with her, so that is at the least she would be willing to end up with.

Then, it must be: expected income from pediatrician - amount willing to pay >= income from clerk

50000 - x >= 30000

x <= 50000 - 30000 = 20000

So, most Alexandrea would be willing to pay is $20,000.

(We do not compare the utility levels as the amount Alexandrea would be willing to pay is a one time payment (to know the required), so to deduct it from yearly earnings doesn't make much sense).