Rachel is willing to pay some percentage of this excess $500 to Emma if the profit turns out to be $1500. That is, a bonus to Emma is in the form of $500*x, where x is a fraction between 0 and 1. To induce Emma to work hard, x must be greater than or equal to some percentage. Answer this number as % and up to 2 decimal places. (That is, your answer should be between 0 and 100.)
Emma (the agent) works for Rachel (the principal). Emma's utility function is given by U=C0.5 if she doesn't work hard, and U=C0.5-3.0 if she works hard. If Emma works hard, the expected profit for Rachel increases from $1000 to $1500. Rachel cannot directly tell whether Emma works hard or not.
Rachel wants Emma to work hard. Rachel is willing to pay Emma a flat salary of $144 plus a bonus. Since the expected profit increases from $1000 to $1500, Rachel is willing to pay some percentage of this excess $500 to Emma if the profit turns out to be $1500. That is, a bonus to Emma is in the form of $500*x, where x is a fraction between 0 and 1. To induce Emma to work hard, x must be greater than or equal to some percentage. Answer this number as % and up to 2 decimal places. (That is, your answer should be between 0 and 100.)
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