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mylen [45]
2 years ago
11

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
Business
1 answer:
Sphinxa [80]2 years ago
3 0

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

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