Jamal has a utility function 1/2 U W5 , where W is hiswealth in millions of dollars and U is the utility heobtains from that wealth. In the final stage of agame 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 withprobability 0.4.a. Graph Jamal’s utility function. Is he risk averse?Explain.b. Does A or B offer Jamal the higher expectedprize? Explain your reasoning with appropriatecalculations. (Hint: The expected value of arandom variable is the weighted average of thepossible outcomes, where the probabilities arethe weights.)c. Does A or B offer Jamal the higher expectedutility? Again, show your calculations.d. Should Jamal pick A or B? Why?
Jamal has a utility function 1/2 U W5 , 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?
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