Question

Iron Man, Captain America and Thor have the following utilities for wealth:

Iron Man : U(W) = W

Captain America : U(W) = 10√ W

Thor : U(W) = W2/100

Suppose all are faced with the following gamble: with probability 50/50 their wealth is either $100 or $0.

1. Calculate the expected value of the gamble for each individual.

2.  Calculate the expected utility of the gamble for each individual.

Answer 1

Let A be the event when wealth is $100. Let B be the event when wealth is $0 . P(A)= 0.5 , P(B)= 0.5

1. Expected value= P(A) ( $100) + P(B) ( $0)

= 0.5 ($100) + 0.5($0)

= 50

Since all of them face the same gamble, expected value will be same for all.

2. Expected utility of Iron man = P(A) [U(100)] + P(B) [U(0)]

= 0.5 [ 100] + 0.5[0]

= 50

Expected utility of Captain America= P(A) [U(100)] + P(B) [U(0)]

= 0.5[ 10*(100)^1/2] + 0.5[ 10*(0)^1/2]

= 0.5 [10*10]

= 50

Expected utility of Thor= P(A) [U(100)] + P(B) [U(0)]

= 0.5[ 100²/100] + 0.5[ 0²/100]

= 0.5[ 100]

= 50