A professor of economics gives multiple choice exams each semester. He curves the exams by giving the maximum possible points to the high score on the exam. For example, if a 50 question exam is worth 100 points and the top score in the class is 40, then each question is worth 100/40 = 2.5 points if answered correctly and 0 otherwise. Grades are then awarded as follows: 65% or better = “excellent”, 48% or better = “good”, 34% or better = “satisfactory”, and below 34% = “fail”.
A. Could the students form a cartel (sustainable or not) to ensure that each student received an “excellent” for the exam?
B. Would a student who was concerned with relative class standing have an incentive to cheat?
C. Is it likely that such a cartel would be successful in a large class?
D. If the students form a successful cartel, what grade would each student receive on the exam?
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A. It is not possible for the students to form a sustainable cartel to ensure that each student received an "excellent" on the exam. This is because the professor curves the exam based on the top score in the class. Therefore, even if the students agreed to all answer incorrectly, the highest score on the exam would still determine the maximum possible points and ultimately the curve.
B. A student who is concerned with their relative class standing may have an incentive to cheat in order to improve their grade. Since the exam is curved based on the highest score in the class, a student may feel the need to outperform their peers in order to achieve a higher grade. Cheating could potentially give them an advantage over others, increasing their chances of receiving a higher grade.
C. It is unlikely that a cartel would be successful in a large class due to various factors such as anonymity among students and the difficulty of coordinating and enforcing a cheating agreement. In a large class, it becomes harder for students to effectively communicate and maintain a secretive agreement without being detected by the professor or other students.
D. If the students were able to successfully form a cartel and answer the questions incorrectly, the top score would be artificially lowered. As a result, all students would receive a higher number of points when the exam is curved. However, the specific grade each student would receive depends on the relative performance of the students within the class. If the top score in the class is still considered "excellent" (above 65%), then each student in the cartel would receive an "excellent" grade. However, if the exam results in a lower highest score, the grading scale for "excellent", "good", "satisfactory", and "fail" would adjust accordingly.