Two weeks ago I sat the second of two semester exams in my introductory microeconomics course. (That the economics department here would not exempt me from EC 101 is another story.) This morning, the grades for that second semester exam went online. As much as I discount grades for their imperfect ability to gauge performance, I did happen to take a look, expecting that the grade would be at or around what I had predicted.

To my great horror, I received but 76 of the 90 possible points on the exam. (That's about 84%, or a B.) In and of itself, that number is not terribly terrifying; worrying, yes, but nothing life threatening. No, I find this number particularly irksome because I have a strong feeling that at least 14 of the 14 points my professor deprived me have everything to do with the bizarre pseudo-math my intro economics class employs. In other words, Bates College's woefully inadequate math requirements for economics courses have the perverse side effect of deflating my grade.

I can understand that not everyone has the opportunity to take calculus in high school. But I can't understand why it's so unreasonable to require anyone taking any kind of economics course to be, at the minimum, concurrently enrolled in a calculus course. In my annoyance with the current economics curriculum, I popped over to MIT OpenCourseWare and took a look at their introductory microeconomics course. I doubt a student could receive anything better than a C on the first problem set without at least a basic understanding of single variable differential calculus.

Some people I have raised this point with argue that, if I'm as smart as I claim to be, using simplified formulas to do numerical analysis in economics should be easy, and thus have a positive effect on my grade. After all, isn't simple addition, multiplication and division easier than differentiating functions?

I can't argue with the fact that it's easier to compute the marginal cost using a formula that takes the sum of two values and divides it by another. While I would scarcely call taking the derivative of a function and plugging in a value difficult, it is at least relatively easier than the previous method.

On the other hand, not using calculus requires me to fundamentally change the way I think about problems. Take the method I must use to calculate marginal cost. Rather than receive a nice differentiable total cost function, I am generally provided a total cost table with a few quantities and their corresponding levels of total cost to the firm. Something that looks like this:

Now, given this table, to find the "correct" marginal cost at 2 units of output, I would take the difference in total cost between 1 unit and 2 units of output and divide that by the difference in production:

(404-401) / (2-1) = 3

To find the marginal cost using the magic of mathematics, I would take my improvised total cost function, differentiate and find the value of the differentiated function at 2 units:

TC(Q) = Q²+400
TC'(Q) = MC(Q) = 2Q
MC(2) = 4

(I realize that this total cost function does not satisfy some important first- and second-order conditions that a total cost function should. I just don't feel like spending the time to cook up a perfect function for the sake of illustrating this point.)

Note that the two methods produce different answers! This is due to the fact that the first "correct" method is essentially just an extremely crude approximation of the second value discovered with basic tools of mathematical analysis. And it's not the only approximation I could use either. The derivative at 2 could also be approximated using (0, 400) and (2, 404), or any number of other points around the one I want the derivative at. Which begs the question: why bother teaching people a method that's only trivially easier, but which introduces such huge differences in understanding and such a huge error in calculation?

Perhaps fittingly, economists generally define irrational behavior as behavior in which an actor makes a systematic error in his or her thinking.

In my desperation, I have considered using B-splines to construct differentiable functions through the points provided in one table or another to free myself from the confines of basic arithmetic. (Apparently even linear functions are too complicated for my microeconomics class!) The only problem with that, of course, is that any answers I find using that method will probably not be equal to the numbers someone would find using the prescribed methods.

I can only hope that intermediate microeconomics, which I've signed up to take next semester, employs some real numerical analysis. That, and I really hope that my potentially bad grade in microeconomics doesn't send to bad a signal to future employers and graduate programs.