Prof. Gilderoy Lockhart gives quizzes in his Defence Against the Dark Arts class. His students can...

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Prof. Gilderoy Lockhart gives quizzes in his "Defence Against the Dark Arts" class. His students can choose either low effort (e,= 0) or high effort (eH= 1) when they study. When low effort is exerted, the probability of passing the quiz is 1/4 and the probability of failing it is 3/4. When high effort is exerted, the probability of passing the quiz is 3/4 and the probability of failing it is 1/4. Prof. Lockhart assigns scores Sp and Sp for "pass" and "fail", respectively. Students' utility functions are given by u(S, e) = √S- - - e. = a. In Week 1, Prof. Lockhart announces that Sp Sp = 100, a measure that proves to wildly enhance his popularity. Show that students will choose low effort. b. In Week 2, his vanity wounded after noticing that no one studied, Prof. Lockhart announces that those who pass the quiz will get 100, while those who fail will get the score Sp. In order for students to choose high effort, Sp must be set at less than or equal to what value? Prof. Gilderoy Lockhart gives quizzes in his "Defence Against the Dark Arts" class. His students can choose either low effort (e,= 0) or high effort (eH= 1) when they study. When low effort is exerted, the probability of passing the quiz is 1/4 and the probability of failing it is 3/4. When high effort is exerted, the probability of passing the quiz is 3/4 and the probability of failing it is 1/4. Prof. Lockhart assigns scores Sp and Sp for "pass" and "fail", respectively. Students' utility functions are given by u(S, e) = √S- - - e. = a. In Week 1, Prof. Lockhart announces that Sp Sp = 100, a measure that proves to wildly enhance his popularity. Show that students will choose low effort. b. In Week 2, his vanity wounded after noticing that no one studied, Prof. Lockhart announces that those who pass the quiz will get 100, while those who fail will get the score Sp. In order for students to choose high effort, Sp must be set at less than or equal to what value?

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To determine whether students will choose low effort or high effort in Week 1 we need to compare the ... View the full answer