Shen has a utility function U=W12U=W12, where WWis his wealth in millions of dollars and UUis the utility he obtains from that wealth. In the final stage of a game show, the host offers Shen a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million with probability 0.6.

Use the blue curve (circle points) to graph Shen's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million.

Utility Function024681012141618205.04.54.03.53.02.52.01.51.00.50Utility (Thousands)Wealth (Millions of dollars)11, 3

True or False: Shen is risk averse.

True

False

Choice offers Shen a higher expected prize. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.)

Choice offers Shen a higher expected utility.

Shen should pick choice .