Question

Joe's wealth is $100 and he maximizes his expected utility. Joe’s utility as a function of his wealth is U(W) = W1/2. Joe might oversleep his economics exam. He figures there is only a 1 in 10 5 chance that he will, but if he does, it will cost him $100 in fees to the University to take an exam later. Joe's neighbor, Mary, never oversleeps. She offers to wake Joe one hour before the test, but he must pay her for this service. What is the most that Joe would be willing to pay for this wake-up service? a. $10 b. $9 c. $19 d. $100 e. $12.7

Answer 1

Probability of over sleeping P_os = 1/10

Probability of not over sleeping P_nos = 9/10

Cost of over sleeping= $100

Also the initial wealth is $100

So,

The expected utility = P_os *(100 - 100)^1/2 + P_nos *(100 - 0)^1/2

= 1/10*(0)^1/2 + 9/10*(100)^1/2

= 9

Therefore, Joe's  willingness to pay at most is equal to expected utility

E(100 - y) = 9

(100 -y)^1/2 = 9

100 - y = 81

y = 19

So ans is c) $19.