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

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

Step-by-step explanation:

First, Calculate the expected utility

Expected utility =
`√(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
`√(( 64 + G ))` + Chance to lose x
`√(64)`

10 = 25% x
`√(( 64 + G ))` + ( 100% - 25% ) x
`√(64)`

10 = 25% x
`√(( 64 + G ))` + 75% x 8

10 = 25% x
`√(( 64 + G ))` + 6

10 - 6 = 25% x
`√(( 64 + G ))`

4 = 25% x
`√(( 64 + G ))`

4 / 25% =
`√(( 64 + G ))`

16 =
`√(( 64 + G ))`

`16^(2)` =
`(√(( 64 + G )))^(2)`

256 = 64 + G

G = 256 - 64

G = 192