Sunday, August 19, 2007

Canceling the Marginal Section

Enrollments are down at the Maricopa Community Colleges and as a result, a number of sections have been cancelled. So how does a college determine how many sections to cancel?

The way economists answer that question is to do some marginal cost analysis. Since decisions are made at the margin, it is the best way to predict behavior.

To make a rational choice you compare marginal cost to marginal benefit. If the marginal benefit is greater than the marginal cost, you are better engaging in the activity so you do it. If the marginal cost is greater than the marginal benefit, you would be worse off, so you don't. So let's look at the marginal cost and marginal benefit of offering one more (or one less) section.

The marginal section is taught by adjunct faculty. At Mesa Community College there are about 900 adjuncts and just over 300 residential faculty. About 60% of sections are taught by adjuncts. The salary for an adjunct is $766 per load hour. A load hour and a credit hour are the same for most classes, labs being the exception. For a 3 credit hour course like ECN 212, Principles of Microeconomics, the adjunct salary is $2,298. In addition, there are some incremental overhead costs - payroll taxes, classroom HVAC, copies, secretarial support, IT support... Those things add up so lets call the incremental cost of a section $3,000 to $3,500.

The marginal benefit to the college of an additional section is the additional revenue it generates. That comes from three sources, tuition, district funding, and state funding. Tuition is $65 per credit hour, or $195 for a 3 hour class. Using tuition only, a class needs 12 students to cover adjunct faculty salary (12 x $195 = $2,340). It needs 15 students to cover salary plus $700 in incremental overhead (15 x $195 = $2,925).

Now you’ll argue that I’ve left out the incremental funding from the district, which is true. But is there really any incremental funding available? Most of the district’s revenue comes from property taxes. Those are independent of enrollment. It is what it is. If one college gets more by having more sections with smaller class sizes, then another college gets less. They will react by doing exactly what the other college did. Since the total size of the pie doesn’t get bigger (just because enrollment did) district funding per student has to fall. Hence, in the long run, there is no incremental funding per student available from the district. (This is called a zero sum game.)

Now you can make exactly the same argument about the state subsidy. You just have to do it at the district level rather than the college level. (This is left as an exercise for the reader.)

So how does a college determine which sections to cancel? Based on the marginal cost analysis, the college is making a rational choice when it cancels sections with less than 15 students.

(Please note that I am not privy to any business deliberations made by any of the colleges. I do not know their specific costs beyond the publicly available information. I do not know if the colleges are actually using marginal analysis to make their decisions. However, as an economist, I do know that marginal analysis accurately predicts behavior.)

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