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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 for each position. 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(w)=w2, where w denotes the actor's wealth. Assume that the actor wants to maximize the expected utility and that he has no wealth other than what he will be paid for in the audition or in the alternative job. Should he go to the audition or should he take the alternative job? Calculate the minimum pay at which he would accept the alternative job? Using that calculaye Richard's "risk premium" for the audition lottery? 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 just the same as Richard and that they are all starving artists, i.e., no initial wealth, just like Richard? Would any of them take an alternative job that pays $140,000 after Richard leaves?

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 for each position. 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(w)=w2, where w denotes the actor's wealth. Assume that the actor wants to maximize the expected utility and that he has no wealth other than what he will be paid for in the audition or in the alternative job. Should he go to the audition or should he take the alternative job? Calculate the minimum pay at which he would accept the alternative job? Using that calculaye Richard's "risk premium" for the audition lottery? 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 just the same as Richard and that they are all starving artists, i.e., no initial wealth, just like Richard? Would any of them take an alternative job that pays $140,000 after Richard leaves?

Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter18: Auctions
Section: Chapter Questions
Problem 18.1IP
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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 for each position. 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(w)=w2, where w denotes the actor's wealth. Assume that the actor wants to maximize the expected utility and that he has no wealth other than what he will be paid for in the audition or in the alternative job. Should he go to the audition or should he take the alternative job? Calculate the minimum pay at which he would accept the alternative job? Using that calculaye Richard's "risk premium" for the audition lottery? 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 just the same as Richard and that they are all starving artists, i.e., no initial wealth, just like Richard? Would any of them take an alternative job that pays $140,000 after Richard leaves?
Transcribed Image Text: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 for each position. 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(w)=w2, where w denotes the actor's wealth. Assume that the actor wants to maximize the expected utility and that he has no wealth other than what he will be paid for in the audition or in the alternative job. Should he go to the audition or should he take the alternative job? Calculate the minimum pay at which he would accept the alternative job? Using that calculaye Richard's "risk premium" for the audition lottery? 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 just the same as Richard and that they are all starving artists, i.e., no initial wealth, just like Richard? Would any of them take an alternative job that pays $140,000 after Richard leaves?
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