posted by Felix .
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?