Question

Suppose you have $100 of endowment, and you are offered a chance to buy a lottery which costs $36. The lottery has 43% of chance to win a prize of $G, or you just lose and get nothing. Suppose your utility function on wealth is u(w)=w^1/2. What is the least prize size G that you will be willing to buy the lottery? (Round to the second digit after decimal point.)

Answer 1

Answer:

96.02

Explanation:

Lottery's Expected utility = $\sqrt{100}$ = 10

Income in good state = 100 - 36 + G = 64 + G

Income in bad state = 100 - 36 = 64

Probability in good state = 43%

Probability in bad state = 100% - 43% = 57%

Expected utility = Probability in good state x $\sqrt{(64 + G )}$ + Probability in bad state x $\sqrt{64\\}$

10 = 43% x $\sqrt{(64 + G )}$ + 57% x 8

10 = 43% x $\sqrt{(64 + G )}$ + 4.56

10 - 4.56 = 43% x $\sqrt{(64 + G )}$

5.44 = = 43% x $\sqrt{(64 + G )}$

5.44 / 43% = $\sqrt{(64 + G )}$

12.65 = $\sqrt{(64 + G )}$

$12.65^{2}$ = $(\sqrt{(64 + G )})^{2}$

160.0225 = 64 + G

G = 160.0225 - 64

G = 96.0225

G = 96.02