Question

9. Problems and Applications 29 Dmitri has a utility function U =wi, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Dmitri a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $9 million with probability 0.6. Use the blue curve (circle points) to graph Dmitri's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million. Utility Function Utility (Thousands) 0 Httttttttt 0 2 4 6 8 10 12 14 16 18 Wealth (Millions of dollars) 20

Answer 1

True.

Expected value is as follows:

(a)4million ; (b) 0.4*1+0.6*9=5.8million

Thus choice b offers a higher expected prize

Expected utility in option(a)= 1*(4)^1/2=2million

Expected utility in option(b)= 0.4*(1)^1/2 + 0.6*(9)^1/2=2.2million

So, choice B offers a higher expected utility

So, Dmitri should pick choice B.