Question

3. Harry has utility function for income U(I) = I^2. Harry has certain income I = $50. Harry

is offered a chance to play a game in which he loses $50 with probability p and wins $50 with

probability (1 − p). What is the largest value of p for which Harry will play the game?

(a) 0.25

(b) 0.40

(c) 0.50

(d) 0.75

Answer 1

In case of certain income,

Harry's utility=U(50)=50^2=2500 utils

In case, Harry decides to play the game,

Income in case he looses the game=50-50=0

Utility in case he looses the game=U(0)=0^2=0

Probability that he looses the game=p

Income in case he wins the game=50+50=100

Utility in case he wins the game=U(100)=100^2=10000

Probability that he wins the game=p

Expected utility=p*U(0)+(1-p)*U(100)=p*0+(1-p)*10000=10000-10000p

At the largest value of p, Harry will be indifferent to not playing and playing i.e.

10000-10000p=2500

10000p=7500

p=0.75

Correct option is

d) 0.75