1) A director has invited ten actors for an audition. They know that, after the audition,...

 

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1) A director has invited ten actors for an audition. They know that, after the audition, one of them will obtain the leading role, which pays $4,000,000. Two of them will obtain secondary roles, which pay $250,000 each. The others will get no job, and will be given $4,900 for their trouble. The ten actors have comparable talents, and face equal chances of being selected. 1a) What is the expected value of the director's invitation for each actor? 1b) Suppose that one of the actors (call him Richard) is offered an alternative job by a different director. The alternative job pays $140,000. If he accepts the alternative job, he will have to miss the audition. His utility function is U(x)=√x, where x denotes the actor's income. Assume that the actor wants to maximize the expected utility of his income. Should he go to the audition or should he take the alternative job? What is the minimum pay at which he would accept the alternative job? What is Richard's "risk premium"? 1c) Suppose that Richard accepts the alternative job. What is the expected value of the audition for each of the remaining nine actors? What is the expected utility of income for each of the remaining nine actors, assuming that their utility function is U(x)=√x? Would any of them take an alternative job that pays $140,000? 1) A director has invited ten actors for an audition. They know that, after the audition, one of them will obtain the leading role, which pays $4,000,000. Two of them will obtain secondary roles, which pay $250,000 each. The others will get no job, and will be given $4,900 for their trouble. The ten actors have comparable talents, and face equal chances of being selected. 1a) What is the expected value of the director's invitation for each actor? 1b) Suppose that one of the actors (call him Richard) is offered an alternative job by a different director. The alternative job pays $140,000. If he accepts the alternative job, he will have to miss the audition. His utility function is U(x)=√x, where x denotes the actor's income. Assume that the actor wants to maximize the expected utility of his income. Should he go to the audition or should he take the alternative job? What is the minimum pay at which he would accept the alternative job? What is Richard's "risk premium"? 1c) Suppose that Richard accepts the alternative job. What is the expected value of the audition for each of the remaining nine actors? What is the expected utility of income for each of the remaining nine actors, assuming that their utility function is U(x)=√x? Would any of them take an alternative job that pays $140,000?