Quotas and Transfer Prices - A good or bad idea?

Yesterday I surveyed the class about how many have experienced being closed out of a course they wanted to take.  My impression from that query is that it is fairly common.  I probably should have followed that up with some additional questions:

(1) Has being closed out of the same course persisted for more than one semester?
(2)  Has it happened in a course that was a pre-requisite for other courses you wanted to take?
(3) Has it slowed down your time to graduation?

These questions are meant at getting at the economics issue - is this evidence of severe and persistent excess demand or is it more of the incidental and temporary variety?  After all, the reality of how registration works is that course times, the classroom where the course is taught, and frequently but not always the instructor who will teach the course are set before students register for the class.  Thus there is a similarity, from an economics perspective, between course registration and retail sales.

You will recall that we discussed using an inventory as a buffer to discourage stockouts of merchandise that can occur in the presence of random demand.  We said that the retailer does this to maintain goodwill with customers, who respond by frequenting the store in the future.  That is the nature of the implicit contract in retail.  What does that implicit contract look like for course registration?

If all courses were free electives and if students could assemble their programs of courses as they saw fit (in consultation with their advisers) then the course registration problem would look similar to the retail inventory management problem.  But we know there are a variety of course requirements - Gen Ed, for the major, and then for a minor or a second major if the student happens to be doing one of those.  Those requirements are significant drivers of demand for certain courses.  That demand will be there irrespective of how the department offering the course has honored its side of the implicit contract (or not).  That fact can have a significant impact on the underlying incentives.

Now a tiny bit about what I know regarding transfer prices as they pertain to the student registration problem.  In the 1990s the campus went to a budgeting regime called Responsibility Center Management.  In theory, RCM has each Department receive revenues in accord with the productive activities it engages in and then incur costs for its use of product generated elsewhere in the organization.  The activities and use of other product are metered.  There are transfer prices for each that then determine the department's budget.  For teaching on campus the RCM formula has at least two pieces.  One is per instructional unit.  (IUs are number of students times the number of credit hours per course.)  Another is per number of majors in the department.  There may be a third piece based on minors.  If so, that would reflect a modification in the RCM formulas to encourage more interdisciplinary education.  There was no bit for minors when the RCM formulas were first constructed, about 20 years ago.

Departments in their budget don't pay for classroom space.  Instead, for smaller classrooms, like ours in 123 DKH, the Econ department has priority in scheduling the space.  Only after the Econ department is done can the campus then schedule other classes into that classroom.  In any event, smaller classrooms are not that scarce on campus though there are time of day and day of week issues that make classrooms more scarce.  At 8 AM classrooms are much more available than at 10 AM.  On Friday, classrooms are more available than on Mon - Thurs.

Larger lecture halls, in contrast, are quite scarce and heavily scheduled.  One reason to offer online classes to on campus students is to try to relax the constraint from limited large lecture hall space.

We can now look at the incentives that underlie students being closed out of courses by asking: what would it take for the department to offer another (currently not scheduled) section of the course?  There would be additional costs regarding the personnel to teach that class.  There might also be an opportunity cost for classroom space to consider, particularly if that additional section were itself a large lecture.  For the moment let's consider only the personnel costs.

If demand exceeds the current number of seats in the offering of a class, but one more section would cover all the excess demand, then one can compute the marginal revenue so generated by using the RCM formula and compare that to the marginal cost from the additional personnel needed.  Chronic close outs in the same course would be evidence that the IU piece of the RCM formula is too low.  Indeed, I've heard from an administrator quite recently that is the case.

Now add the classroom issue onto this.  It might be that the additional demand could be handled if the section were held in Foellinger or Lincoln Hall theater, but not in smaller lecture halls.  So then, more than one section would be needed to handle the excess demand.  But that raises marginal cost because now you need personnel to teach multiple sections.  So the limited classroom space for large lecture halls further discourages departments from increasing their capacity in specific courses.

When course requirements are firm, close outs in a class boost future demand for the course, and can exacerbate the issue.  (For Gen Ed requirements, students can often fill those during the summer, quite possibly at the local community college near their home.  That is like buying from the market rather than buying from the upstream division.)

For courses where there is no external substitute, one solution to the excess demand would be to allow other on campus courses to fill the requirement.  There are lots of fights on campus about this, which courses can qualify to satisfy requirement x.  The department that currently offers the course which satisfies the requirement typically does not want competition for IUs from other departments.  They have incentive to block that other course from being considered acceptable.

Another alternative would be to have the IU piece of the RCM formulas vary, so that if there are chronically over subscribed classes, those would get more per IU as incentive to increase supply.  To my knowledge we don't do this sort of thing.  It might seem unfair to do so.  Unfair or not, the current budgeting practice may encourage persistent excess demand for some courses.

Let me close with noting there is some measurement issues with determining how severe the excess demand for classes actually is.  Let me give our class as example to illustrate.  We have two capacity limits.  In the undergraduate section the capacity is 30.  In the graduate section capacity is 6.  There are more seats in the classroom than 36.  These capacities are set by the Econ department.  We have never reached capacity in the graduate section, but we were at capacity in the undergraduate section during much of the first 10-day period when students can add.  Was there excess demand for the course then that never got satisfied?  Or did everyone who wanted to get into the class eventually?

We are no longer at capacity in the undergrad section.  That would seem to show there was no persistent excess demand.  But that is not completely correct.  I can only observe students who want in but can't get in, if those students contact me.  Other students who try to get in but were frustrated in doing so are entirely invisible to me.  Eventually, of course, they have to firm up their schedules and take something else.  That, however, does not mean they prefer their current schedule of courses.