Risk

Suppose Aladdin has utility function:

U(W) = 8W, W 0 (1)

= W^2 W < 0 (2)

Aladdin has just found the genie's lamp and has wished for a bag of gold since he has nothing at the moment but the clothes on his back. He knows the genie may try to trick him so he has assigned a 25% subjective probability the genie will find a way to take away his clothes which would cost 4 gold to replace. In addition, he has assigned a 50% subjective probability to getting a medium bag of 16 gold, and a 25% probability of getting a large bag of 100 gold.

A. What is the expected value of Aladdin's gamble?

B. What is the variance of the expected value of Aladdin's gamble?

C. What is the expected utility of Aladdin's gamble?

D. What certain amount of money would Aladdin rather have than to face this gamble?

E. Graph Aladdin's utility function on a graph with wealth on the x axis and utility on the y axis. Graph and label the expected value of Aladdin's gamble, the certainty equivalent of this gamble, and the risk premium.