Question

George Steinbrenner, the owner of the New York Yankees, has a utility function of wins, w, in a season given by U(w) = (1/2)w². Mr. Steinbrenner has been offered a trade. He believes if he completes the trade, his probability of winning 125 games is 10%. There is also an 90% chance the team won't gel and the Yankees will win only 90 games.

1. What will be Mr. Steinbrenner's expected utility if his belief is correct and he takes the offer?  (please just input the number without the comma, please keep 2 decimal places)

2. As the head coach, you dislike the trade. You are going to promise Mr. Steinbrenner that the Yankees will win at least X games. What is the smallest number of X that can stop the trade? X=  (Please input an integer)

Answer 1

1) EU = .1*U(125) + .9*U(90)

Probability of good state = .1

Bad state probability =.9

EU = .1*(.5*125²) + .9*(.5*90²)

= 4426.25

2) Minimum number of games , that can stop the trade,

Is Certainty equivalent (CE)

So , U(CE) = EU = 4426.25

So, .5*(CE)² = 4426.25

CE = 94.08

so smalllest number of games X = 94