Question

2. An individual has a vNM utility function over money of u(x) -Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra S9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9, what minimum probability, p, of losing S7 would ensure that the individual chooses to not play the lottery? (a) p > 0.15 (b) p > 1.08 (c) p > 0.415 (d) p > 0.05 (e) None of the above 2. An individual has a vNM utility function over money of u(x) -Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra S9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9, what minimum probability, p, of losing S7 would ensure that the individual chooses to not play the lottery? (a) p > 0.15 (b) p > 1.08 (c) p > 0.415 (d) p > 0.05 (e) None of the above 1. AAn individual has a vNM utility function over money of u(x) =阪, where x is final wealth. She currently has $8 and can choose among the following three lotteries. Which lottery will she choose? . Lottery 1: Give up her $8 and face the gamble (0.1, 0.5, 0.4) over final wealth levels (S1, $8, $27) . Lottery 2: Keep her $8. .Lottery 3: Give up her $8 and face the gamble (0.2, 0.8,0.0) over final wealth levels (S1, $8, $27) (a) Lottery 1 (b) Lottery 2 (c) Lottery 3 dl) She is indiferent between the three lotteries.

Answer 1

2) Utility when an individual wins extra $9,

The total wealth =$16+$9 =$25

Utility = 25^0.5 = 5

The Total wealth when individual looses $7 = $16-$7 = $9

Utility = 9^0.5 = 3

Utility if the individual does not play the lottery and will keep $16 = 16^0.5 = 4

Expected Utility if an individual chooses to play the lottery =

Let the probability of loosing $7 be p

5*0.15 + 3*p

Now the individual will not choose to play the lottery if the expected utility from playing the lottery is less than the expected utility from not playing the lottery. So the equation will be:

5*0.15 + 3*p = 4

= 0.75+3*p =  4

= 3p=  3.25

= p=  1.08

Now, if probabilty of loss is greater than 1.08 , then the expected utility from the lottery will be less than the expected utility from the not playing the lottery. So p>1.08. So option a is the correct answer.