Dorothy is indifferent between a certain payoff of $x and this gamble. What is x?

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Dorothy is indifferent between a certain payoff of $x and this gamble. What is x?

Dorothy has a utility function of the form U = w^0.5 , and faces  a situation in which income is $36 with probability 0.5 and $100 with probability 0.5.

  1. Dorothy is indifferent between a certain payoff of $x and this gamble. What is x?
  2. Suppose Dorothy is offered, for $32, full insurance for the $64 (potential) loss. Will she buy it? Why?

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