1. Assume that Betsy’s utility function is given by equation U=Y0.3 where Y is measured in thousands of dollars. Betsy’s current job pays her $20,000 (Y=20) per year and she can earn this amount next year with certainty. Betsy is offered a different job but in this new job,
Betsy has a 50% chance of earning $36,000 (Y=36) and a 50% chance of earning only $15,000 (Y=15).
a) Should Betsy take the new job?
b) Does your answer change if Betsy’s utility function is U=Y0.9? Why?
c) Does your answer change if Betsy’s utility function is U = Y1.25? Why?
2. Many states have scratch offs with several different monetary payoffs. For ex, the “$500 a week for life” in New York offers the payout and odds structure noted below.
(a) What is the anticipated value of playing, supposing you live 60 more years and there are 52 weeks in every year.
(b) The cost of playing is $1. If your utility is U= V + Y, where V = entertainment value in dollars, how much V do you need to receive with certainty in order to play?
(c) Consider a dissimilar structure where you pay $1 and the payout is $250 with odds of winning equal to 1 and 323. Also, U = V + Y.85. What is the minimum entertainment value in this case?
Payout Odds
$1 1 and 10
$2 1 and 15.15
$4 1 and 62.5
$5 1 and 125
$10 1 and 100
$20 1 and 166.67
$40 1 and 2,100
$100 1 and 50,400
$250 1 and 126,000
$500/wk 1 and 7,938,000