A university president once proposed a scholarship program that would reduce tuition for students graduating at the top of their high school class. The higher the rank of the student, the steeper the scholarship discount. For example, students in the top 10 percent of their high school class would get a scholarship to cover 50 percent of their tuition; students in the 20th percentile would get a 33 percent scholarship discount, and students below the 30th percentile would pay full tuition.

a. Forget the zero elasticity estimate listed on Wikipedia.

b. Using what you know about how price elasticity changes as one moves along the demand curve, discuss how such a program would affect the academic quality of the incoming class (the number of students in the top 10, 20, and 30+ percent of their class).

c. Under what conditions would such a program increase the revenue of the university?