Jamal has a utility function U=(w^1/2) , 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, or (B) a gamble that pays $1 million with a probability of 60% or $9 million with a probability of 40%.
A. Graph Jamal's function. Is he risk averse? Explain.
B. Does A or B offer Jamal a 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 a higher expected utility? Again, show your calculations.
D. Should Jamal pick A or B? Why?