Question

Suppose you have $100 of endowment, and you are offered a chance to buy a lottery which costs $36. The lottery has 25% of chance to win a prize of $G, or you just lose and get nothing. Suppose your utility function on wealth is . What is the least prize size G that you will be willing to buy the lottery

Answer 1

Answer:

The least prize size G that I will be willing to buy the lottery is 192

Explanation:

First, Calculate the expected utility

Expected utility = $\sqrt{100}$ = 10

There are two cases

Case 1

I win = 100 - 36 + G = 64 + G

Case 2

I lose = 100 - 36 = 64

Hence the expected utility can be calculated as follow

Expected utility = Chance to win x $\sqrt{( 64 + G )}$ + Chance to lose x $\sqrt{64}$

10 = 25% x $\sqrt{( 64 + G )}$ + ( 100% - 25% ) x $\sqrt{64}$

10 = 25% x $\sqrt{( 64 + G )}$ + 75% x 8

10 = 25% x $\sqrt{( 64 + G )}$ + 6

10 - 6 = 25% x $\sqrt{( 64 + G )}$

4 = 25% x $\sqrt{( 64 + G )}$

4 / 25% = $\sqrt{( 64 + G )}$

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

$16^{2}$ = $(\sqrt{( 64 + G )})^{2}$

256 = 64 + G

G = 256 - 64

G = 192