4. University of Notre Dame is a premier institution that draws students from all over the world to its campus. Although it is privately funded, it aspires to world-class quality and reputation, which are enhanced when out-of-state residents enroll. Data suggest that in-state enrollment can be described by the equation: QI = 25,000 - PI, where QI = in-state enrollment and PI = in-state tuition. Out-of-state enrollment is given by: QN = 13,500 - .5PN.

a. If tuition for in-state students is $14,000 and for out-of-state students is $19,000, what is total enrollment and demand elasticity for each type of student?

b. Suppose that the marginal cost to the university of an additional student is $7,000. Is Major University maximizing profit at its current tuition charges? Explain.  

c. Because of major funding cuts, the university is expecting to reduce its total enrollment to 11,000 students next year. The university is free to set any tuition charges it wishes. If the goal is to maximize total tuition revenue, what should in-state tuition, out-of-state tuition, and respective enrollments be?