Jamal has a utility function U 5W1/2 , 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 Jamal a choice between

(A) $4 million for sure and (B) a gamble that pays

$1 million with probability 0.6 and $9 million with probability 0.4.

a. Graph Jamal’s utility function. Is he risk averse?

Explain.

b. Does A or B offer Jamal the higher expected prize? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.)

c. Does A or B offer Jamal the higher expected utility? Again, show your calculations.

d. Should Jamal pick A or B? Why?